MASTER 

NEGA  TIVE 

NO.  92-81076 


MICROFILMED  1993 
COLUMBIA  UNIVERSITY  LIBRARIES/NEW  YORK 


as  part  of  the 
"Foundations  of  Western  Civilization  Preservation  Project" 


Funded  by  the 
NATIONAL  ENDOWMENT  FOR  THE  HUMANITIES 


Reproductions  may  not  be  made  without  permission  from 

Columbia  University  Library 


COPYRIGHT  STATEMENT 


The  copyright  law  of  the  United  States  -  Titie  17,  United 
States  Code  -  concerns  the  making  of  photocopies  or 
other  reproductions  of  copyrighted  material. 


Under  certain  conditions  specified  in  the  law,  libraries  and 
archives  are  authorized  to  furnish  a  photocopy  or  other 
reproduction.  One  of  these  specified  conditions  is  that  the 
photocopy  or  other  reproduction  is  not  to  be  "used  for  any 
purpose  other  than  private  study,  scholarship,  or 
research."  If  a  user  makes  a  request  for,  or  later  uses,  a 
photocopy  or  reproduction  for  purposes  in  excess  of  "fair 
use,"  that  user  may  be  liable  for  copyright  infringement. 

This  institution  reserves  the  right  to  refuse  to  accept  a 
copy  order  if,  in  its  judgement,  fulfillment  of  the  order 
would  involve  violation  of  the  copyright  law. 


AUTHOR: 


BAIN,  ALEXANDER 


TITLE: 


LOGIC,  DEDUCTIVE  AND 
INDUCTIVE. 

PLACE: 

NEW  YORK 

DA  TE : 

1889 


Restrictions  on  Use: 


COLUMBIA  UNIVERSITY  LIBRARIES 
PRESERVATION  DEPARTMENT 


Master  Negative  # 


BIBLIOGRAPHIC  MICROFORM  TARGET 


Original  Material  as  Filmed  -  Existing  Bibliographic  Record 


I 


Bl 


t§X\J\J 


T 


Bain,  Alexander,  1818-1903. 
Logic,  deductive  and  induotire,  by  Alexander    , 

tin:   m  p""  '^  t       '''  ''-''   Weton,^1889J 


Diitilui  Llbitny  iif  rhiluiieiJhj.  107^        i   i 

'  ( ) ! 


Oopy  *B  Bwuard  OullUfeu  LiUrary.  «^- yrrlr.   flinu^i' 
in  hoQk.oema.096»Y  ■'      • 


23160 


u 


j 


TECHNICAL  MICROFORM  DATA 


FILM     SIZE;      Sf^^ REDUCTION    RATIO: 

IMAGE  PLACEMENT:   lA    ^    IB    IIB 

DATE     FILMED: ^->-f? INITIALS____jl£/f;^__ 

HLMEDBY:    RESEARCH  PUBLICATIONS.  INC  WOODBRIDGE.  CT 


c 


Association  for  information  and  image  iManagement 

1100  Wayne  Avenue.  Suite  1100 
Silver  Spring,  Maryland  20910 

301/587-8202 


\ 


Centimeter 


TTT 


2         3        4 

liiiiliiiili 


iiiiiniiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiMiii 


Inches 


T  M       I 


5         6         7        8 

liiiiliiiiliiiiliiiiliiiiliiiiliii 


1 


M   I   I   I   M 


1.0 


I.I 


1.25 


9        10       11        12       13       14       15    mm 

iiliiiiliiiiliiiiliiiiliiiiliiiiliinliiiniiiiiiiiiiiiiiiiiii 


|4  5 

150 

l63 

171 


12.8 


3.2 


u 


III  4  0 


1.4 


TXTTyrr 
4 

2.5 


2.2 


2.0 


1.8 


1.6 


I  I  I 


T 


m 


MfiNUFflCTURED   TO   fillM   STPNDRRDS 
BY  APPLIED   IMRGE,    INC.     : 


T||4^ 


5     J- 


«■% 


■V*f.'- 


■  *' t-' 


i-^-l' 


^S^?^ 


iM^r'  ^■ 


1 

> 

*■!:■ 

1^ 

L*"T 

*a, 

> 

■|r* 

-  1: 


I"^!- 


*=■;,. 


#:il^. 


-;■?'. 


Ml 


*•"  «, 


>-,v-:iir"...^:..«,,,:j*»:.,-i';- 


^ 


1^*; 


!i»»i» . 


>- 


%■ 


th 


• 


y 


V' 


i 


LOGIC: 


t 


DEDUCTIVE  AND  INDUCTIVE. 


{    ! 


BT 


ALEXANDER  BAIN,  LL.  D., 


ysw  AST)  BBriSBD  EDITION. 


NEW  YORK: 
D.  APPLETON   AND   COMPANY, 

I.  3.  AND  s   BOND  STREET. 
1889. 


% 


PREFACE. 


1 


The  present  work  aims  at  embracing  a  full  course  of  Logic, 
both  Formal  and  Inductive. 

In  an  introductory  chapter,  are  set  forth  such  doctrines 
of  psychology  as  have  a  bearing  on  Logic,  the  nature  of 
knowledge  in  general,  and  the  classification  of  the  sciences ; 
the  intention  being  to  avoid  doctrinal  digressions  in  the 
course  of  the  work.  Although  preparatory  to  the  under- 
standing of  what  follows,  this  chapter  may  be  passed  over 
lightly  on  a  first  perusal  of  the  work. 

The  part  on  Deduction  contains  the  usual  doctrines  of 
the  Syllogism,  with  the  additions  of  Hamilton,  and  a  full 
abstract  of  the  novel  and  elaborate  schemes  of  De  Morgan 
and  Boole. 

The  Inductive  portion  comprises  the  methods  of  induc- 
tive research,  and  all  those  collateral  topics  brought  for- 
ward by  Mr.  Mill,  as  part  of  the  problem  of  Induction ; 
various  modifications  being  made  in  the  manner  of  state- 
ment, the  order  of  topics,  and  the  proportion  of  the  hand- 
ling. The  greatest  innovation  is  the  rendering  of  Cause 
by  the  new  doctrine  called  the  Conservation,  Persistence, 
or  Correlation  of  Force. 

Mr.  Mill's  view  of  the  relation  of  Deduction  and  Induc- 
tion is  fully  adopted,  as  being  the  solution  of  the  otherwise 
inextricable  puzzle  of  the  syllogism,  and  the  means  of 
giving  unity  and  comprehensiveness  to  Logic. 


■".^ 


96830 


^^ 


IV 


PREFACE. 


A  separate  division  is  appropriated  to  the  Logic  of  the 
Sciences,  with  the  view  of  still  further  exemplifying  the 
logical  methods,  and  of  throwing  light  upon  various  points 
in  the  sciences  themselves.  The  review  comprises  all  the 
theoretical  or  fundamental  sciences— Mathematics,  Physics, 
Chemistry,  Biology,  and  Psychology ;  the  sciences  of  Classi- 
fication, or  Natural  History  ;  and  two  leading  Practical 
sciences — Politics  and  Medicine. 

The  department  of  Definition  is,  for  the  first  time, 
brought  under  a  methodical  scheme,  and  rendered  of  co- 
ordinate value  with  Deduction  and  Induction,  as  a  branch 
of  logical  method.  The  modes  of  defining,  as  a  generalizing 
process,  are  given  under  two  canons,  a  positive  and  a 
negative ;  and  attention  is  called  to  the  chief  obstacles- 
uncertainty  in  the  denotation  of  words,  and  the  gradual 
transition  of  qualities  into  their  opposites. 

In  discussing  Fallacies,  I  have  canvassed  the  grounds 
for  the  usual  practice  of  detaching  the  violations  of  logical 
rules  from  the  exposition  of  the  rules  themselves ;  and 
have  endeavoured  to  show  that  the  only  portions  of  the 
subject  proper  to  reserve  for  separate  handling,  are  the 
Fallacious  tendencies  of  the  Mind,  and  Fallacies  of  Con- 
fusion, As  these  are  subjects  of  great  moment,  and  admit 
of  wide  illustration,  both  are  considered  with  some  minute- 
ness. 

None  of  the  controversies  in  the  subject  are  overlooked  ; 
but  it  has  hern  deemed  advisable  to  separate  them  from 
the  main  body  of  the  work.  In  an  Appendix,  are  em- 
braced the  various  Classifications  of  the  Sciences,  the  Pro- 
vince of  Logic,  the  Classification  of  Nameable  Things,  the 
Universal  Postulate,  the  meanings  of  Analysis  and  Syn- 
thesis, the  Theories  of  Induction,  the  Art  of  Discovery, 
and  the  maxims  of  Historical  Evidenca 
To  adapt  the  work  to  an  elementary  course  of  Logic, 


f 


>i 


\    i 


I 


if 


f 


t 


PBEFACE.  y 

the  parts  to  be  omitted  are  the  Additions  to  the  Syllogism 
the  Logic  of  the  Sciences,  and  the  chapters  in  the  Appen- 
dix. The  junior  student,  or  the  candidate  for  a  pa^s 
exammation,  without  attempting  to  master  or  commit  these 
reserved  portions,  might  yet  find  their  perusal  of  service 
in  understanding  the  rest. 

There  is  a  general  conviction  that  the  utility  of  the 
purely  Formal  Logic  is  but  small ;  and  that  the  rules  of 
Induction  should  be  exemplified  even  in  the  most  limited 
course  of  logical  discipline.  I  would  suggest  that  an  in- 
creased attention  should  be  bestowed  on  Definition  and 
Classification,  with  reference  both  to  scientific  study  and 
to  matters  not  ordinarily  called  scientific. 

As  I  may  be  open  to  the  charge  of  presumption  in 
appearing  as  a  rival  to  Mr.  Mill,  I  will  venture  the  remark, 
that  an  attempt  to  carry  out  still  more  thoroughly  the 
enlarged  scheme  of  logical  method,  seems  the  one  thing 
hitherto  wanting  to  the  success  of  his  great  work. 

AainDEEN,  March,  187(i 


7 


OOKTENTS 


lUTRODUCTION    . 


PAas 


BOOK  I, 

NAMES,    NOTIONS,    AND   PROPOSITIONS. 


VBkT. 

I.  Names  or  Terms 
II.  Classes,  Notions,  or  Concepts 
III.  Propositions 


4i 
61 
73 


BOOK  11. 

DEDUCTION. 

I.  The  Syllogism  .... 

II.  Recent  Additions  to  the  Syllogism 

III.  Functions  and  Value  of  the  Syllogism 

IV.  Trains  of  Reasoning  and  Deductive  Sciences 
V.  Demonstration — Axioms— Necessary  Truth 


183 
178 
207 
214 
219 


BOOK  III 

INDUCTION. 

I.  Meaning  and  Scope  of  Induction  .... 

II.  The  Ground  of  Induction— Uniformity  of  Nature— Laws  of  Na- 
ture        .....•• 
m.  Induction  of  Coexistence  .  .  .  «  • 

IV.  Law  of  Causation    ....•• 
V.  Eliminarion  of  Cause  and  Effect— Observation  and  Evperiment 
VI.  The  Experimental  Methods       ..... 
VII.  Examples  of  the  Methods    ..... 
V^III.  Frustration  of  the  Methods        ..... 
IX.  Chance,  and  its  Elimination  .... 

X.  Induction  aided  by  Deduction   .  .  .  .  • 

XI.  Secondary  Laws — ^Empirical  and  Derivative 
XII.  Explanation  of  Nature  ....•• 

XIII.  Hypotheses  .  .  .  .  . 

XIV.  Approximate  Generalizations  and  Probable  Evidence   . 

XV.  Analogy        .....•• 
KVI.  Credibility  and  Incredibility      ..... 


231 

238 
241 
246 
271 
279 
297 
806 
814 
825 
882 
846 
868 
865 
870 
378 


s 


•  •• 

vm 


CONTENTS. 


jBOOK  IV. 


DEPINITIOK. 


■AP. 


I.  Canons  of  Definition 
II.  General  Names 
III    Classification 


PASS 

884 
401 
414 


) 

BOOK  V, 

LOGIC   OF   THE    SCIENCES. 

'■ 

1.  Logic  of  Mathematics    .... 

.     429 

II.  Logic  of  Physics      ..... 

451 

III.  Logic  of  Chemistry        .... 

.     472 

IV.  Logic  of  Biology      ..... 

488 

V.  Logic  of  Psychology      .... 

.     605 

VI.  Sciences  of  Classification      .... 

622 

VII.  Logic  of  Practice           .... 

.     645 

■*£. 

nil.  Logic  of  Politics       ..... 

547 

IX,  Logic  of  Medicine          .... 

.676 

BOOK  VI. 

FALLACIES. 

I.  Mill's  Classification  of  Fallacies 

n.  The  Position  of  Fallacies 

IIL  Fallacious  Tendencies  of  the  Mind 

IV.  Fallacies  of  Confusion   . 

V.  Logical  Fallacies 


599 
603 
606 
616 
625 


PAST  I, 


DEDUCTION 


APPUNmA'. 

A. — Classifications  of  the  Sciences 
B. — The  Province  of  Logic 
C. — ^Enumeration  of  Things    . 
D. — ^The  Universal  Postulate 
E. — Aristotelian  and  Scholastic  Fallacies 
F. — ^Analysis  and  Synthesis 
G. — Growth  of  the  Logic  of  Induction 
H. — ^Art  of  Discovery         .  .  , 

L — Historical  Evidence 
K. — Explanation  of  Some  Logical  Terras  . 


627 
689 
652 
664 
678 
681 
687 
697 
707 
716 


\ 


wl 


^tmmimm 


INTRODUCTION. 


1.  Logic  may  be  briefly  described  as  a  body  of  doctrines 
and  rules  having  reference  to  Truth. 

The  functions  of  Logic  will  be  afterwards  given  with  par- 
ticularity and  precision.  For  the  present  we  remark  that  it 
concerns  the  Truth  of  things,  no  matter  what  the  subject  be. 
While  in  one  aspect  it  is  theoretical,  in  the  prevailing  aim  it  is 
practical. 

In  this  introductory  chapter  we  are  to  consider  the  following 
topics, 

(1)  The  Psychological  data  or  groundwork  of  Logia 

(2)  The  First  Principles  of  Logic. 

(3)  The  Classification  of  the  Sciences. 

(4)  The  diflTerent  views  of  the  Province  of  Logic, 

(5)  The  Divisions  of  Logic. 

PSYCHOLOGICAL   DATA    OF  LOGIC. 

2,  Logic,  under  every  view,  involves  frequent  references 
to  the  laws  and  workings  of  the  mind ;  and  the  more  so 
the  more  we  extend  its  province. 

In  the  common  Logic  of  the  Schools,  the  Svllflpiiilfr*ol?" 
Deductive  Logic,  explanations  are  usually  ^^gp^  the  intel- 
lectual processes  named  Perception  or  SiMP^Jpprehension, 
Abstraction  or  the  formation  of  concepts  oflnotions.  Judgment 
or  the  laying  down  of  propositions,  and  Reasoning  or  the 
drawing  of  inferences  or  conclusions  from  premises. 

In  the  Inductive  Logic,  an  enquiry  is  instituted  into  oup 


I 


2  PSYCHOLOGICAL  DATA    OF  LOGIC. 

idea  of  Cause ;  in  connection  with  which,  notice  is  taken  of 
the  controversj  respecting  the  Origin  of  our  Knowledge  in 
the  Mind,  namely,  as  to  whether  it  be  wholly  derived  from 
experience,  or  whether  any  portion  of  it  fas  Cause,  the  Axioms 
of  Mathematics,  &c.)  be  intuitive,  instinctive,  or  innate. 

It  is  considered  a  part  of  Logic  to  set  forth  the  theory  and 
the  limits  of  the  Explanation  of  phenomena ;  for  which  pur- 
pose a  reference  must  be  made  to  the  structure  of  the  mental 
powers.  This  was  the  avowed  aim  of  Locke,  in  bis  Essay  on 
the  Understanding,  one  of  the  greatest  contributions  to  the 
science  of  mind. 

Under  such  circumstances,  the  most  satisfactory  course  ap- 
pears to  be  to  bring  forward  and  expound,  once  for  all,  at  the 
commencement,  whatever  portions  of  Psychology  are  in  any 
way  implicated  with  the  rules  and  methods  of  Logic  But  the 
exposition  must  necessarily  be  brief. 

Discrimination  or  Relativity. 

3.  In  order  to  make  M^feely  there  must  be  ^  change  of 
impression  ;  whence  all  feeling  is  t\vo-sided.  /This  is  the 
law  of  Discrimination  or  Eelativity.  ) 

Observation  shows  that  unbroken  continuance  of  the  same 
impression  is  attended  with  unconsciousness  ;  and  that  the 
greater  the  change  or  transition,  the  greater  th  j  consciousness. 
An  unvarying  touch,  or  a  monotonous  sound  ceases  to  be  felt ; 
in  an  even  temperature,  we  'lose  all  consciousness  of  heat  or 
cold.  Still  more  convincing  are  the  instances  showing  that 
changes  affect  us  in  proportion  to  their  greatness  and  sudden- 
ness. Abrupt  transitions  are  stimulating  and  exciting  ;  the 
first  exposure  to  sun-light  after  being  in  the  dark,  the  first 
mouthful  of  water  when  we  are  thirsty,  the  moment  of  transi- 
tion from  poverty  to  wealth — are  accompanied  with  the  highest 
degree  of  feeling  ;  after  which  there  is  a  gradual  subsidence  of 
the  excitement. 

Hence  the  fact  of  our  being  under  some  agency  of  sense  or 
feeling  does  not  of  itself  attest  our  mode  of  feeling;  there 
must  farther  be  given  the  condition  immediately,  and  for 
some  time  previous.  That  a  man  is  the  possessor  of  a  thou- 
sand pounds  to-day  is  not  a  sufficient  criterion  of  his  feel- 
ings as  regards  worldly  abundance.  If  a  year  ago,  the  same 
man  possessed  nothing,  he  feels  in  a  way  totally  different  from 
him  that  ha<s  fallen  to  that  amount  from  a  fortune  of  ten  thoa- 
Rand  pounds. 


DISCBIMINATION   OB  RELATIVITY.  3 

4.  As  regards  Knowledge,  there  must  likewise  be  a  tran- 
sition, or  change ;  and  the  act  of  knowing  includes  always 
two  things. 

When  we  consider  our  mental  states  as  Knowled<Te,  the 
same  law  holds.  We  know  heat  by  a  transition  from°  cold  • 
bght,  by  passmg  out  of  the  dark;  up,  by  contrast  to  down! 
Ihere  is  no  such  thing  as  an  absolute  knowledo-e  of  any  one 
property ;  we  could  not  know  *  motion,'  if  we  were  debarred 
trom  knowmg  *  rest.'  No  one  could  nnderstand  the  meaning 
ot  a  straight  hue,  without  being  shown  a  line  not  straight  I 
bent  or  crooked  line.  °     * 

We  may  attend  more  to  one  member  of  the  couple  than  to 
the  other.     In  this  way  only  can  we  think  of  an  individual 
property      We  may  be  thinking  more  of  the  heat  than  of  the 
cold,  of  the  straight  than  of  the  crooked ;  the  one  may  be  the 
explicit,  the  other  the  implicit  subject  of  our  thoughts.     As  our 
transitions  may  be  in  two  directions— from  heat  to  cold,  and 
trom  cold  to  heat— we  have  a  difference  of  feeling  in  the  two 
cases.     We  are  more  conscious  of  heat,  when  passing  to  a 
higher  temperature,  and  of  cold  when  passing  to  a  lower/    The 
state  we  have  passed  to  is  our  explicit  consciousness,  the  state 
we  have  passed /rowi  is  our  implicit  consciousness. 
^  '  The  principle  of  Eelativity  has  wide  and  important  bearings 
m  Logic.     It  will  appear  in  Naming ;  in  Definition  ;  in  Pro- 
positions or  Affirmation.     It  will  be  appealed  to  in  rectifying 
a  large  class  of  Fallacies— the  fallacies  of  the  suppressed  rel^ 
tive,  or  of  the  Absolute. 

Agreement  or  Si^mlarity. 

6.  When  an  impression  is  repeated,  after  an  interval  we 
are  affected  with  a  new  and  peculiar  consciousness, '  the 
shock  or  consciousness  of  Agreement  in  difference. 

We  see  a  candle  flame  ;  it  is  withdrawn ;  after  a  time,  it  is 
brought  back.  We  have  now,  in  addition  to  the  luminous 
ettect  of  the  presentation,  a  shock  or  feehng  of  agreement 
Identity,  repetition ;  a  state  no  less  concerned  in  our  intellec- 
tual operations  than  the  shock  of  difference  or  discrimination. 
We  are  constantly  experiencing  the  repetition  of  former  im- 
pressions, in  circumstances  more  or  less  altered,  and  we  are 
affected  with  a  greater  shock  according  to  the  greatness  of 
the  alteration.  The  degree  or  intensity  of  the  consciousness 
ot  Agreement  may  vary  through  a  wide  range,  from  the  sHght 


i^ 


k 


Ill 


4  PSYCHOLOGICAL  DATA  OF  LOGia 

recognition  of  a  new  day  to  the  flasli  of  a  great  discovery  of 
identification,  like  Newton's  assimilating  the  fall  of  a  stone  to 
the  deflection  of  the  moon  towards  the  earth. 

Knowledge  as  conjoining  Difference  and  Agreement, 

6.  Our  knowledge  of  a  fact  is  the  Discrimination  of  it 
from  differing  facts,  and  the  Agreement  or  identilication  of 
it  with  agreeing  facts. 

The  only  other  element  in  knowledge  is  the  Eetentive 
power  of  the  mind,  or  memory,  which  is  implied  in  these 
two  powers. 

Our  knowledge  of  heat  is  (1)  a  series  of  shocks  of  Difference 
or  discrimination  between  heat  and  cold,  and  (2)  the  Agree- 
ments or  repetitions  of  the  same  shocks  under  change  of 
circumstances. 

Besides  the  transition  heat-cold,  which  is  the  primary  cog- 
nition of  heat,  we  make  other  transitions  into  other  sensations. 
We  have  occasion  to  pass  from  a  sensation  of  warmth  to  a 
sensation  of  light,  and  the  difference  of  the  two  brings  out  a 
new  discriminative  consciousness,  and  gives  a  new  meaning  to 
warmth,  and  also  to  light ;  heat  is  no  longer  simply  the  con- 
trast of  cold,  it  is  also  the  contrast  of  the  feeling  of  luminosity. 
So,  every  new  sensation  that  we  pass  to  from  heat,  with  con- 
sciousness of  difference,  gives  a  new  negative  meaning  to  heat ; 
it  is  not  taste,  nor  smell,  nor  hardness,  nor  sound. 

Again,  our  mental  impression,  knowledge,  or  idea  of  a 
shilling,  is  the  sum  of  all  its  differences  from  the  things  that 
we  have  contrasted  it  with,  and  of  all  its  agreements  with  the 
things  that  we  have  compared  it  to.  We  call  it  round  ;  sig- 
nifying that  it  differs  from  things  called  square,  oblong,  oval, 
&c.  ;  that  it  agrees  with  other  things  called  round — that  we 
have  been  frequently  struck  with  the  identity  of  this  figure  in 
many  different  combinations. 

So  with  the  weight  of  the  shilling.  We  know  weight  by 
difference,  and  by  agreement ;  we  recognise  a  shilling  as  heavier 
than  some  things,  lighter  than  others ;  which  is  difference ;  and 
as  identical  with  a  third  class,  which  is  agreement. 

The  knowledge,  idea,  or  recollection  of  any  concrete 
object,  is  thus  the  aggregate  of  those  mental  exercises  of 
Discrimination  and  Agreement,  fixed  and  retained  in  th* 
mind  by  the  power  called  retentiveness,  or  memory ;  by  which 
power  of  retention  we  are  able  to  discriminate  and  compare 


VAKIETIES   OP  KNOWLEDGE.  5 

present  impressions  with  past,  and  to  accumulate  a  vast  stock 
of  m'bntal  effects  or  deposits,  called  ideas,  knowledge,  thought. 

Knowledge  is  of  two  kinds,  called  Object  and  Subject. 

7.  The  knowledge  of  a  shilling,  of  a  house,  of  a  mountain,  of 
a  star,  is  said  to  be  objective ;  it  relates  to  the  object,  or  the 
outer,  world.  The  knowledge  of  a  pleasure  or  a  pain,  or  of 
the  succession  of  ideas  in  the  mind,  relates  to  the  subject,  or 
the  internal,  world.  We  have  a  great  accumulation  of  both 
kmds  of  knowledge  ;  some  minds  abounding  more  in  one,  some 
more  in  the  other. 

Knoioledge  as  (1)  Individual  and  Concrete,  or  (2)  General 

and  Abstract 

'  \^^^-  ^J^^^^^^^Q  of  a  table  in  a  room,  at  a  particular  time,  is 
m  the  highest  degree  individual  or  concrete.  The  knowledge 
relatmg  to  any  table,  at  any  time,  is  said  to  be  general  and 
abstract.  By  the  mental  power  of  Agreement  or  Similarity, 
we  bring  to  mmd  different  individual  tables,  attending  to  their 
points  of  community,  in  spite  of  many  diversities.  We  affirm 
properties  common  to  them  all.  This  is  the  generaUsiuff 
power  of  the  mind.  It  is  one  of  the  most  signal  functions  of 
our  mtelhgence,  and  is  purely  an  outgoing  of  the  fundamental 
power  named  Agreement,  or  Similarity. 

Dispute  as  to  the  Character  of  General  Knowledge,  called 

also  Abstract  Ideas, 

9  In  General  Knowledge,  strictly  so  called,  there  is 
nothing  but  the  fact  of  agreement  among  a  number  of 
separate  particulars ;  which  agreement  is  signified  by  the 
use  of  a  common  name. 

A  general  name,  as  'circle,'  *  round,'  'animal,*  'wise,'  is 
applied  to  things  agreeing  in  a  certain  respect,  while  differino- 
in  other  respects,  to  signify  their  agreement.  ° 

It  has  been  supposed  that  the  points  of  community  of 
agreemg  things  exist  apart  from  the  things.  This  view  is 
called  Realism. 

It  was  believed  by  a  certain  school  of  philosophers,  deriving 
from  Plato,  that  there  exists,  in  the  universe  of  being,  a  Circle 
ID  general  or  circular  Form  without  substance,  size,  or  colour; 
Uiat  m  hke  manner,  there  are  archetypal  Forms  of  Man,  of 


ii^trnmoi. 


6  PSYCHOLOGICAL  DATA   OF  LOGIC. 

i^^h  ^^  P'?^^'.*^^-    A^^""  a  severe  controversy,  which  ra^d 
m  the  scholastic  period,  this  view  was  abandoned. 

Kealism  is  still  exemplified,  however,  in  the  doctrine  of  an 
Independent  External  World,  and  also  in  the  doctrine  of  the 
separate  existence  of  Mind  or  Soul.  In  strictness,  the  External 
World  is  known  only  as  perceived  by  our  senses:  Mind  is 
known  only  as  conjoined  with  body. 

Another  mode  of  regarding  the  fact  of  community  ia 
diversity,  is  to  suppose  that  the  miud  can  represent  to  it- 
selt  m  a  notion,  the  points  of  agreement  by  themselves 
and  can  leave  entirely  out  of  sight  the  points  of  differ- 
ence.    This  IS  Conceptualism, 

r.nfi^°Ki"^  *^^^^''  ."^.P"^^  ^^^^^^  '*^  existence,  we  are  sup- 
posed  able  to  think  of  the  round  figure  to  the  exclusion  of  t^ 
other  properties  of  the  individual  circles-material,  colour,  size 
Ihis  too  IS  incorrect.  It  exaggerates  the  mind's  power  of 
giving  a  preference  of  attention  to  some  of  the  attributes  of  a 
concrete  object,  as  a  wheel,  or  a  shilling.  We  may  think 
S  ""!?  }^  ^^"^dj^ess,  and  little  of  the  size ;  but  we^annot 
colour  roundness,    without  thinking  of  some  size  or 

w-^^  ""^^^  "^f^  of  thinking  an  abstraction,  or  of  concen. 
Vh^  )Fi?       T""^'  ''P''''  ''''^  property,  is  to  think  alternately  of 
the  different  objects  possessing  the  property.     We  can  best 
think  of  roundness  by  having  in  view  various  round  thincrs 
differing  m  material,  size,  colour,  &c.     The  effect  of  the  mind's 
passing  and  repassing  between  the  individuals,  is  that  the 
trrf«r-%     fi'  'l^\^^^^^  prominence,  and  the  other  proper- 
ties  fall  mto  the  background,  without,  however,  being^extin- 
guislied.     The  great  fact  constantly  underlying  Abstraction 
18  the  mustering  of  individuals  agreeing  in  the  mifsHrdiffer: 
cnce. 

mn^^.T  '°  *''•  ^^}'*-^^  ''"'"S  ^'°g'«  individuals  to  typify  a 
mnltitnde ;  as  in  the  diagrams  of  Euclid.  We  do  Lot  in 
geometrical  reasoning,  think  of  a  great  number  of  circular 
things ;  we  can  study  the  circle  upon  one  figure,  provided  wl 
^e  care  to  affirm  nothing  as  to  size,  co^W.^or  materi^t 
wh^h  facts  are  inseparable  even  from  the  barest  diagram 

When  the  logician  speaks  of  a  Notion,  Concept,  or  Abstract 
Ide^  he  must  not  be  understood  as  implying  anything  be- 
yond the  agreement  of  a  certain  number  of  things  in  a  fiy^ 
manner.  °  K^vea 


IflE   INDIVIDUAL  AND   THE  GENERAL.  y 

Our  idea  of  an  Individual  a  conflvxc  of  Generalities. 

10.  What  we  term  the  Perception  of  an  individual,  as  a 
given  tree,  is  not  simply  a  sense  impression  of  the  moment, 
It  is  an  aggregation  of  many  generalized  impressions. 

When  we  look  at  a  tree,  we  are  affected  by  a  great  number 
ot  ditierent  influences— colours,  shape,  size,  &c.  Now,  every 
distinguishable  impression  recalls  the  previous  stamps  of  the 
same,  by  Agreement  or  Similarity ;  and  the  idea  of  the  tree  is 
not  an  original  sense  presentation,  but  a  compound  of  this 
with  old  presentations.  Every  feature  of  the  tree  suggests  a 
classification  upon  that  point ;  the  green  and  brown  colours 
are  telt  only  as  the  collective  impressions  of  those  shades  of 
colour. 

In  our  minds,  therefore,  the  Concrete  and  the  Abstract  are 
inextricably  blended.  Of  a  pure  concrete,  not  also  resolved 
into  classifications  or  abstractions,  we  have  no  experience. 
Uur  knowledge  proceeds  in  both  ways  at  once ;  individuals 
giving  generals  and  generals  re-acting  upon  individuals.  If 
there  was  one  concrete  thing  in  the  world,  having  no  property 
m  common  with  any  other  known  concrete  thing,  we  mio-ht, 
by  gazing  upon  that,  and  comparing  it  with  itself,  possess  an 
Idea  of  a  concrete  individuality,  where  no  generality  was  im- 
plicated  ;  but  such  a  concrete  would  be  very  different  from  any 
concrete  known  to  us.  We  are  not  in  the  position  to  imagine 
such  an  idea.  ^ 

11.  The  speciality  of  a  concrete  Indivicjual  is  that  it  is  a 
definite  aggregate  not  confounded  with  other  individuals. 

The  number  of  general  properties  pointing  to  the  individual 
must  be  such  as  to  give  it  a  definite  or  special  character, 
instead  of  leavmg  it  indefinite  or  common.  The  tree  that  I 
now  look  at,  is  individualized  by  a  concurrence  of  properties 
never  realized  before  ;  or  if  not  by  such  concurrence  itself,  by 
Its  surroundings,  and  all  the  circumstances  of  time  and  place, 
accompanying  its  perception.  A  shilling  is  individualized 
by  ita  adjuncts  of  place  and  time. 

12.  The  distinction  between  Presentation  and  Represeni- 
atton,  is  the  distinction  between  a  definite  conflux  of 
generalities,  and  an  indefinite  conflux. 

A  shilling  in  the  hand  is  a  Presentation.  A  shilling  as  a 
general  com  of  the  realm  is  Representative ;  it  is  common  to 


I 


8 


PSYCHOLOGICAL  DATA  OF  LOGIC. 


matiy  places  and  times  and  circumstances,  and  not  bound 
down  to  one  definite  situation  and  one  definite  moment. 

13.  The  names  of  Individuals  usually  correspond  to  their 
character  as  a  conflux  of  generals. 

In  a  few  instances,  we  have  names  that  bear  no  reference  to 
generalities,  as  when  a  certain  individual  man  is  named — Caesar. 
These  are  proper,  or  meaningless  names  ;  the  bare  symbols 
for  separating  the  thing  from  other  things.  But  in  the  vast 
majority  of  instances,  the  name  follows  the  manner  of  conceiv- 
ing the  thing — that  is,  by  specifying  the  concurring  generalities. 
A  large  gothic  building;  a  stout  man  of  forty;  a  cubical 
crystal,  with  a  certain  hardness  and  specific  gravity,  found  in 
a  certain  formation ; — are  examples  of  designations  in  strict 
accordance  with  the  ideas  of  the  things. 

Philology  confirms  this.  The  primitive  names  of  such  con- 
crete objects  as  sun,  moon,  father,  mother,  have  all  a  gene- 
ralized meaning  ;  *  moon  *  is  the  measurer,  *  father '  is  the 
feeder,  and  so  on.  There  seems  to  be  no  possibility  of  con- 
ceiving individuals  without  classifying  and  generalizing  at  the 
same  time  ;  and  the  one  name  means  both  an  individual  and 
a  general. 

The  intellectual  function  of  Agreement,  or  Similarity,  as  the 

basis  of  Reasoning. 

14.  Reasoning,  in  every  form,  supposes  the  operation  of 
Similarity— the  assimilating  of  one  tbing  to  some  other 
thing. 

The  most  general  type  of  Reasoning  is  to  infer  from  one 
particular  fact  to  another  particular  fact  of  the  same  kind  • 
the  likeness  being  both  the  means  of  suggestion,  and  the  jus-' 
tification  of  the  transfer  of  properties.  We  throw  a  stone  into 
a  pool;  it  makes  a  splashing  noise,  sinks  to  the  bottom,  and 
diffuses  a  series  of  waves  from  the  point  where  it  fell.  Wo 
infer  or  reason,  or  presume,  that  another  stone  thrown  into 
the  same  pool  will  be  followed  by  the  same  series  of  effects  • 
and  we  may  extend  the  inference  to  another  pool,  or  to  any 
mass  of  liquid.  This  is  to  infer,  to  reason,  to  transcend  our 
actual  experience,  to  make  an  affirmation  respecting  the  un- 
known. Now,  the  mind  is  prompted  by  the  likeness  of  the 
sases  to  take  this  step  in  advance,  to  anticipate  what  is  to 
happen.     One  would  not  infer  that  a  handful  of  dried  leave* 


KINDS  OF  KEASONING.  9 

^rould  produce  all  the  consequences  of  throwing  the  stone  • 
we  never  expect  either  through  our  instinctive  belief,  or 
through  our  experience  of  the  world,  that  the  same  effects 
will  arise  under  different  circumstances. 

This  mode  of  Reasoning  is  in  constant  use,  and  extends  to  the 
animal  intelligence.  An  animal  accustomed  to  find  a  shelter 
under  a  bush,  reasons  from  one  bush  to  another  bush,  being 
moved  solely  by  the  resemblance  of  the  second  to  the  first.  A 
dog  is  deterred  by  the  menacing  movement  of  a  strange  per- 
son wielding  a  strange  stick:  the  partial  resemblance  to 
former  experiences  is  enough  to  rouse  its  fears. 

A  second  mode  of  Reasoning  is  when  by  the  help  of  general 
language,  we  infer  from  one  or  a  few  cases,  to  all  cases  of  the 
kind  ;  as  when  we  conclude,  after  a  certain  number  of  trials, 
that  all  stones  sink  in  water,  that  all  matter  of  vegetable  origin 
is  combustible,  that  all  animals   are   generated   from   other 

animals.     This  is  Induction,  in  the  more  technical  sense the 

inferring  not  from  particulars  to  other  particulars,  but  from 
particulars  to  universals.  The  mental  process  is  still  Simi- 
larity, or  the  process  whereby  one  thing  suggests  other 
resembling  things.  It  is  by  similarity  that  we  assemble  in 
the  mind  all  kindred  facts  that  have  ever  come  under  our 
knowledge ;  we  then  are  able  to  compare  the  points  of  agree- 
ment, with  a  view  to  an  accurate  general  statement,  in  other 
words,  an  Inductive  proposition. 

The  third  kind  of  Reasoning,  called  Deductive,  is  also  based 
on  the  tracing  of  resemblance.  When  we  infer  that,  because 
all  stones  sink  in  water,  a  certain  body  will  sink  (which  is 
Deduction),  it  is  because  that  body  resembles  the  rest,  or  has 
the  points  of  community  indicated  by  the  general  word 
*  stone.*  When  we  have  mastered  a  general  principle,  it  is 
by  similarity  that  we  discover  cases  to  apply  it  to,  and  so  ex- 
tend our  knowledge  deductively. 

Origin  of  our  Knowledge  in  Experience, 

15.  Our  knowledge  of  the  world,  both  of  matter  and  of 
mind,  is  the  result  of  our  conscious  Experience. 

As  regards  the  Material,  outer,  or  object  world,  we  gain 
oar  knowledge  through  the  ordinary  Senses,  coupled  with 
our  Movements,  under  the  three  laws  of  our  Intelligence— 
VM.,  Difference,  Agreement,  and  Refcentiveness.  We  see,  hear, 
touch,  tast«,  smell ;  we  have  our  active  energies  aroused  by 
ihmge  resisting,  by  movements,  and  by  things  extended ;  we 


■mli 


10 


PSYCHOLOGICAL  DATA  OF  LOGIC. 


?    f 


discriminate  and  identify  impressions  ;  we  acqnire  permanent 
recollections,  and  associate  things  presented  in  combination  • 
and,  by  all  these  processes  (exemplified  at  full  length  in  Mental 
bcience,    or    Psychology)    we  lay  np  our  stock  of  imafferv 
ideas,  or  thoughts,  of  the  world  of  sensible  experience. 

As  regards  the  Mind,  or  the  knowledge  of  our   inner  life 
the  senses  do  not  avail  ns.     We  are  directly  and  immediately 
conscious  of  our  feelings,  thoughts,  and  volitions,  and  acquire 
a  store  of  permanent  recollections  of  these  also.     We  remem- 
ber our  different  pleasures  and  pains,  and  the  order  of  their 
occurrence  ;    we  learn  not  merely  things,   but  our  ideas  of 
Uiings,  and  the  laws  of  the  rise  and  succession  of  these  ideas 
Thus,  it  is  a  fact  of  our  mental  or  subjective  life,   that  we 
easily  recall  to  mind  whatever  strongly  engaged  our  attention 
in  the  reality. 

•    \^'  ?  ^^^  ^.^^"  ^\\Q\i^^  that  some  parts  of  our  knowledcre 
instead  of  being  the  result  of  experience,  like  the  greater 
portion,  are  intuitive  or  inherent  to  the  mind,  apart  from 
the  operation  of  the  senses  upon  actual  things,  or  the  par- 
ticular phenomena  of  the  subjective  consciousness. 

At  different  stages  in  the  progress  of  Philosophy,  there  have 
been  given  different  lists  of  intuitive,  or  h  priori  elements  of 
knowledge.  At  the  present  day  the  controversy  turns  chiefly 
on  these  four  notions— Time,  Space,  Substance,  Cause. 

It  18  maintained  that  there  is  in  these  notions  something 
that  experience  could  not  give ;  so  that  some  different  oriffiS 
must  be  sought  for  them.  ^ 

I,  B^'i^!  ?r^''L  ^'^®'  *^®  supporters  of  the  Experience  theory 
hold  that  the  Moving  energies,  with  the  Senses  and  Self-Con- 
sciousness,  aided  by  the  intellectual  functions,  can  account  for 
all  these  notions. 

For  example,  Time  is  an  abstraction :  and,  like  all  other 
abstractions,  IS,  properly  speaking,  a  certain  mode  of  likeness 
among  individual  things  or  feelings  of  the  mind.  All  our 
experiences,  whether  object  or  subject,  are  regarded  by  us  as 
more  or  less  enduring  ;  the  attribute  of  Time  is  the  assimilation 
or  classification  of  enduring  states,  as  enduring.  Apart  from 
these  actual  experiences  of  differences  and  agreements  of 
enduring  things,  there  can  be  no  such  thing  as  Time,  unless 
on  the  exploded  doctrine  of  Realism,  nor  any  self-subsistinfj 
notion  Qi  lime,  unless  on  the  erroneous  theory  of  Conceptual- 
ism.  In  the  absence  of  objects  and  states  continuing  or 
anduring,  an  intuition  of  Time  is  a  self-contradiction  ;  in  the 


ALLEGED  INTUITIVE  KNOWLEDGE. 


11 


presence  of  such  experiences  of  enduring  things,  discriminated 
and  compared  on  the  point  of  endurance,  we  cannot  but  have 
an  idea  of  Time. 

Next  as  to  Space,  or  Extension,  the  fact  common  to  all 
Matter  and  not  pertaining  to  mind.  Extension  belongs  both 
to  solid  matter,  and  to  the  intervals  between  the  masses  of 
solid  matter,  which  intervals  are  measured  by  the  same 
sensibilities  namely,  the  muscular  feelings  of  motion,  sup- 
ported by  the  passive  sensations. 

The  a  i?nm  philosophers  allege  that  Space  comes  from  no 
experience,  but  is  already  inherent  in  the  mind  before  any- 
thing  IS  perceived ;  being  the  condition  of  our  perceiving 
tnings  external.  ° 

In  opposition  to  this  view,  it  is  contended  that  Space  in 
the  abstract  is  merely  the  community  or  similarity  of  extended 
bodies,  and  of  the  intervals  between  them,  commonly  called 
empty  space.  We  compare  all  those  things  on  this  particular 
point  of  agreement;  we  occasionally  think  of  them  under  this 
comparison  ;  and  in  so  doing  we  are  thinking  of  Space.  This 
IS  the  only  view  compatible  with  Nominalism.  An  innate 
lorra  ot  bpace  is  a  species  of  Conceptualism. 

The  pure  intuition  of  Space  is  said  to  be  the  source  of  our 
knowledge  and  belief  of  the  Axioms  of  Geometry,  this  being 
held  to  have  a  character  that  no  experience  can  explain.  In 
the  case  of  these  Axioms,  the  a  priori  revelation  takes  the 
lorm  of  Principles,  and  not  of  mere  Notions  ;  but  the  fact  is 
the  same,  although  differently  viewed.  *  That  two  straight 
lines  cannot  enclose  a  space  ;'  'that  things  equal  to  the  same 
thing  are  equal  to  one  another:'  are  held  by  those  that 
contend  for  an  intuition  of  space,  to  be  intuitive. 

ihe  Idea  of  Cause  is  included  among  the  alleged  intuitions. 
It  may  be  expressed  either  as  a  mere  Notion  or  as  a 
Pnnciple  namely,  * thateveirefiectmusth^^  An 

equivalent  proposition  is,^ti^r^ij;i;riri^ifo;;2^r  that 
what  has  been   will  be.'      The  contention  is,  that  while,  by 

fn^'lF^^T^N  ^^  f  A^^^  ^^'''''^^  ^^^^^  *^^*  particular  effects 
follow  the  law  of  Cause,  or  of  Uniformity,  we  could  not  from 
expenence  know  that  every  effect  has  and  must  have  a  cause, 
that  what  has  been  will  always  be.  ' 

The  idea  of  Substance  means  that,  underiying  all  the 
phenomenon  or  appearances  of  Matter  and  of  Mind,  there  is 
an  unknown  or  unknowable  substmtum,  called  Substance, 
Noumerion,  Permanent  Existence.  This  idea  we  cannot  pos- 
sibiy  obtam  from  expenence ;  the  very  statement  of  it,  shows 


12 


PSYCHOLOGICAL  DATA  OF  LOGIC. 


t^f 


w^ 


fchat  it  passes  bejond  experience ;  yet  some  philosophers  con- 
tend  that  we  are  obhged  to  assume  and  believe  in  itf 

As  apphed  to  Mind,  Substance  is  another  name  for  Personal 
Identity,  or  the  supposed  continuity  of  each  one's  mental 
existence--the  canvass  that  receives  and  holds  together  all  the 
feelmgs,  thoughtB,  volitions,  that  make  up  the  stream  of  our 
conscious  life. 

According  to  the  counter  doctrine  on  this  head,  the  notion 
ot  bubstance  is  fictitious,  incompetent,  and  unnecessary.     The 
real  meaning  of  Substance,  as  applied  to  matter,  is  the  point 
of  community  of  all  material  bo^ws,  the  most  highly  general- 
ized  fact  respecting  them  ;  otherwise  expressed  by  Resistance, 
Inertia,  Momentum,  the  Mechanical  property  of  matter      The 
meaning  of  Substance  as  applied  to  Mind  is  the  most  hi^hlv 
generalized  property  or  properties  of  mind~the  facts  wherein 
all  minds  agree  ou  comparison,  and  which  caused  them  to 
receive  the  common  designation  Mind,  as  opposed  to  not-mind. 
or  matter       Ihese     generalized  points   of   community  are 
i^eelmg,  Yohtion,  and  Intellect,  the  three  facts   attaching  in 
various  degrees  to  whatever  is  accounted  Mind. 

The  nature  of  Belief  as  applied  to  the  controversy  respect- 

9,ng  tlie  origin  of  Knowledge, 

17.  There  is  a  natural  tendency  to  believe  much  more 
than  we  have  any  experience  of. 

The  primitive  disposition  of  the  mind  as  regards  belief  is 
to  suppose  that  whatever  is  wiU  continue,  that  what  exists 
bere  and  now,  exists  everywhere  and  at  all  times.  This  in- 
born credulity  is  checked  and  abridged  by  our  experience ; 
we  soon  discover  that  we  have  been  assuming  too  much  ;  and 
by  degrees  we  abate  our  confidence  and  adapt  our  views  to 
the  reality  of  things. 

The  following  are  common  examples  of  the  tendency.  Be- 
fore experience,  we  believe  that  as  we  feel  now,  we  shall 
always  leel ;  that  other  people  feel  as  we  do  ;  that  what  hap- 
pens to  us  happens  to  all ;  that  whatever  any  one  tells  us  is 
true.  By  the  natural  impetuosity  of  the  mind,  we  form  these 
assurances  ;  experience  did  not  create  them,  but  rather  mode- 
rates and  checks  them. 

That  we  should  treat  any  partial  experience  as  universal, 
being  thus  a  consequence  of  blind  instinctive  forwardness  is 
no  proof  of  what  really  happens  in  nature.  As  we  are  so  liable 
to  extend  our  assertions  beyond  the  facts,  we  should  be  par- 


r 


BELIEF  PASSES  BEYOND  EXPERIENCE.  13 

I 
tionlarly  on  oar  gaard  against  nniversal  declarations      This  is 

TMLfzT'j:r  °'''"'"^"  "^*-«' '"''» ^  ^-ii^g -- 

To  make  tiie  application  to  the  particular  case  of  cansation 
We  are  very  ready  to  faU  into  statements  as  to  the  un^eSa^^ 
of  cause  and  effect;  but  so  we  do  with  m^y  oZr' h W 
where  we  find  ourselves  utterly  wrong.  The  rLl  ev'den3 
the  Law  of  Causation  must  be  something  different  from  our 
being  disposed  to  believe  it.  Moreui,  irom  our 

Noihinff  can  he  ajlrmed  as  true,  except  on  the  warrant  of 

experience. 

18  As  the  natural  disposition  to  believe  carries  us  into 
falsehood,  we  must,  notwithstanding  our  instincts  cHnc  to 
experience  as  the  only  standard  of  truth.  ° 

BeHrf  EvI^h'^  ''°"°'?  ^'°'"  *•"«  -^^'"^  a°d  sources  of 
fit  i    Even  the  supporters  of  innate  principles,  at  the  pre- 

w^h1h^'„^?°".i-'''  *•>«««  PriD-'iples  cannot  arise  Except  aW 
with  the  actual  things ;  a  qualification  that  subjects  the  innate 
wa,  WK  ''^P'^tely  to  the  measure  of  experiince!  Tif  S 
was  nothing  innate  about  them.  Our  intuition  of  Cause  i^ 
o^^e^arnnl      "Y''  "^elf  only  when  we  have  observed  a  number 

rISed  Vfth'oT  ^""^  ''^"'''  "  '^'  *'^-«f°-.  involved  and 
impiicatea  with  our  experience  to  such  a  dcijreo  as   to  be 

deprived  of  an  mdependent  standing.  There  if  no  means  of 
discovermg  what  the  intuitions  wofld  dictate  of  thrmseW 
fnt  f  r?""''' "V"^'"^'  "^^^^^ty.  therefore,  they  must  te 

Our  Knmvledge  is  Limited  ly  our  Sensibilities. 

.J^\  M^^  ^^^  *^'^  '"  ^°°^  ^^^t  things  affect  our  various 
sensibilities  or  what  may  be  compounded  of  thesi  and 
our  knowledge  extends  no  farther.  ' 

We  have  a  certain  number  of  sensibilities,  namelv  in  th« 
Senses  (Passive),   and  in  the  Muscles  (Acti;e)  ;    2d  when 
any  of  these  IS  affected  we  have  knowledge  or  experience 
we  know  sight,  sounds,  touches,  tastes,  smells,  andvS 
organic    affections;    we    know    resista;ce    and    mov^S 

We    have   many   experiences   from  the    discrimination  and 


12 


PSYCHOLOGICAL  DATA  OF  LOGIC. 


that  it  passes  beyond  experience ;  yet  some  pbilosophers  ooii- 
tend  that  we  are  obliged  to  assume  and  believe  in  it. 

As  applied  to  Mind,  Substance  is  another  name  for  Personal 
Identity,  or  the  supposed  continuity  of  each  one  s  mentel 
existenoe— the  canvass  that  receives  and  holds  together  all  the 
feelings,  thoughts,  volitions,  that  make  up  the  stream  of  our 

conscious  life.  ^  , .    ,      -i  xi.         *• 

According  to  the  counter  doctrine  on  this  head,  the  notion 
of  Substance  is  fictitious,  incompetent,  and  unnecessary.  The 
real  meaning  of  Substance,  as  applied  to  matter,  is  the  pomt 
of  community  of  all  material  bodies,  the  most  highly  genei-ai- 
ized  fact  respecting  them  ;  otherwise  expressed  by  Resistance, 
Inertia,  Momentum,  the  Mechanical  property  of  matter,  ihe 
meaning  of  Substance  as  applied  to  Mind  is  the  most  highly 
generalized  property  or  properties  of  mind— the  facts  wherein 
all  minds  agree  ou  comparison,  and  which  caused  them  t» 
receive  the  common  designation  Mind,  as  opposed  to  not-mind, 
or  matter.  These  generalized  points  of  community  are 
Feeling,  Volition,  and  Intellect,  the  three  facts  attachmg  m 
various  degrees  to  whatever  is  accounted  Mind. 

The  nature  of  Belief  as  applied  to  the  controversy  respect- 
ing tlie  origin  of  Knowledge. 

17.  There  is  a  natural  tendency  to  believe  much  more 
than  we  have  any  experience  of. 

The  primitive  disposition  of  the  mind  as  regards  belief  is 
to  suppose  that  whatever  is  will  continue,  that  what  exists 
here  and  now,  exists  everywhere  and  at  all  times,  ihis  in- 
born credulity  is  checked  and  abridged  by  our  experience ; 
we  soon  discover  that  we  have  been  assuming  too  much  ;  and 
by  degrees  we  abate  our  confidence  and  adapt  our  views  to 

the  reality  of  things.  e.^.     .     :i  -r 

The  following  are  common  examples  of  the  tendency.  I5e- 
fore  experience,  we  believe  that  as  we  feel  now,  we  shaU 
always  feel ;  that  other  people  feel  as  we  do  ;  that  what  hap- 
pens to  us  happens  to  all ;  that  whatever  any  one  tells  us  is 
true.  By  the  natural  impetuosity  of  the  mind,  we  form  these 
assurances  ;  experience  did  not  create  them,  but  rather  mode- 
rates and  checks  them.  . 

That  we  should  treat  any  partial  experience  as  universal, 
being  thus  a  consequence  of  blind  instinctive  forwardness  is 
no  proof  of  what  really  happens  in  nature.  As  we  are  so  liable 
to  extend  our  assertions  beyond  the  facts,  we  should  be  par- 


V 


BELIEF  PASSES  BEYOND  EXPERIENCK.  13 

ticularly  on  our  guard  against  universal  declarations.  This  is 
one  of  the  weaknesses  of  human  nature,  and  a  leading  source 
01  fallacy  and  error. 

To  make  the  appUcation  to  the  particular  case  of  causation. 
We  are  very  ready  to  faU  into  statements  as  to  the  universality 
of  cause  and  efiect ;  but  so  we  do  with  miany  other  thingau 
where  we  find  ourselves  utterly  wrong.  The  real  eviden^of 
the  liaw  of  Causation  must  be  something  different  from  our 
bemg  disposed  to  believe  it. 

Nothing  can  he  affirmed  as  true,  except  an  the  warrant  of 

experience, 

18  As  the  natural  disposition  to  beUeve  carries  ns  into 
talsehood,  we  must,  notwithstanding  our  instincts,  clin^  to 
experience  as  the  only  standard  of  truth*  "^ 

This  inevitably  follows  from  the  nature  and  sources  of 
Uehef.  Even  the  supporters  of  innate  principles,  at  the  pre- 
sent  day,  admit  that  these  principles  cannot  arise  except  alon? 
with  the  actual  thmgs  ;  a  qualification  that  subjects  the  innate 
notions  as  completely  to  the  measure  of  experience,  as  if  there 
was  nothing  innate  about  them.  Our  intuition  of  Cause  is 
supposed  to  show  itself  only  when  we  have  observed  a  number 
of  examples  of  cause  and  effect;  it  is,  therefore,  involved  and 
implicated  with  our  experience  to  such  a  degree  as  to  be 
deprived  of  an  independent  standing.  There  is  no  means  of 
discovermg  what  the  intuitions  would  dictate  of  themselves, 
J?  or  aU  purposes  of  logical  certainty,  therefore,  they  mast  be 
put  out  of  account ;  regard  must  be  had  solely  to  observation, 
and  experience.  ^ 

Our  Knmvlcdge  is  Limited  hy  our  SensibUitiex 

19  We  are  able  to  know  what  things  affect  our  various 
sensibilities,  or  what  may  be  compounded  of  these :  and 
our  knowledge  extends  no  farther. 

We  have  a  certain  number  of  sensibilities,  namely,  in  the 
Senses  (Passive),  and  in  the  Muscles  (Active)  ;  and  when 
any  of  these  is  affected  we  have  knowledge  or  experience- 
we  know  sight,  sounds,  touches,  tastes,  smells,  and  various 
organic  affection^ ;  we  know  resistance  and  movement 
We  know  various  emotional  states,  love,  anger,  fear,  &c 
We    have   many   experiences   from  the    discrimination  and 


/ 


^^ 


\ 


\ 


14  FIRST  PUINCIPLES  OF  LOGIC. 

the  aereemont  of  onr  varions  states.  In  tW,  we  hare 
our  aPXt  of  the  knowable.  We  can  then  --b^ne  a  num- 
ber of  primitive  feelings  into  a  constructive  agSff'*'  «f 
when  we  attain  to  the  idea  of  an  orange,  or  of  »  ■"»°- 
I  of  thTentiTe  -lobe.  But  we  cannot  by  any  effort  pass 
out t  SeTomJa^s  of  these  primitive  sensibilities.  Supposing 
the  universe  to  contain  powers  and  properties  that  do  not  im 
prirone  or  other  of  oo'r  senses,  as  -W^'^^^^' ^^^''^'^^^: 

thoushts,Ld\oliti'ons;  and  we  can  know  nothing  beyond. 

FIRST  PRINCIPLES  OF  LOGIC. 

20  In  Logic,  there  are  certain  general  principles,  consti- 
tuting it  a  Wence  properly  so  called  and  lying  at  the 
foundation  of  its  practical  rules  and  methods. 

These  principles  are  variously  expressed.     They  ^ Jern^^^ 
Laws   of  Thought,  and  fundamental  Axioms  of  K^asonmg. 
Som  embracing  these  highest  of  all  g-e-ht.es  jh^       pene 
trate  into  every  science,  and  fromlaymg  down  rules  on  sc  en- 
tS^method,  Logic  has  been  designated  *  scientia  scientxarum 
—the  science  that  comprehends  all  sciences. 
The  First  Principles  may  be  arranged  thus :— 
I.  The  Principle  of  Consistency,  or  Necessary  Tratlk 
li.  The  Principles  of  Deduction.! 
lli.  The  Principle  of  Induction.  1 

L^Prmciple  of  Consistency— Necessary  Trnthr 
21    It  is  a  fundamental  requisite  of  reasoning,  as  well  as 
of  communication  by  speech,  that  what  is  affirmed  in  one 
form  of  words  shall  be  affirmed  in  another. 

Lanf^uage  often  contains  equivalent  expressions  for  the  same 
fart  There  are  synonvmous  names  as  *  round,  circular ;  a 
lound  tSis  the  same  as  a  circular  thing  *  Matter  is  heavy, 
"Ztter  glvit^^^  are  the  same  fact  in  different  words  ;  if  tho 
oris  true  so  is  the  other,  by  virtue  of  mere  consistency. 
Z.in  there  are  forms  that  enable  us  to  affirm  many  separate 
ffin  one  sweeping  statement ;  instead  of  affirming  m  detail, 
Merciry^oves  i  al  ellipse,  Venus  moves  in  an  ellipse,  &c, 


PKINCIPLE  OF  CONSISTENCY. 

we  can  put  forth  the  one  condensed  affirmation— all  the  planets 
have  eUiptic  orbits.  Having  advanced  this  general  statement, 
we  are  required  by  consistency  to  maintain  each  separate 
particular,  the  orbit  of  Saturn  is  elliptical,  and  so  on. 

It  18  obvious  that  without  this  consistency,  there  could  be 
no  intelligent  communication  between  one  human  being  and 
another.  Unless  the  affirraer  adheres  to  his  affirmation,  how- 
ever he  may  vary  the  language,  no  one  can  divine  what  he 
means  ;  there  is  no  possibility  of  discussion  or  reasoning. 

To  these  self-consistent,  although  variously  worded,  affirma- 
tions IS  apphed  the  descripion  *  Necessary  Truth.*  *  All  matter 
IS  heavy,  therefore  any  one  piece  of  matter  is  heavy '  is  called 
a  necessary  inference.  A  more  exact  designation  would  be 
an  equivalent,  implicated,  or  self-consistent  assertion. 

There  is  a  vital  contrast  between  passing  from  one  form  to 
another  form  of  expressing  the  same  fact,  and  passing  from 
one  fact  to  another  distinct  fact.  When  we  say— because  both 
A  and  B  are  mortal,  therefore,  A  is  mortal— we  merely  repeat 
ourselves  ;  when  we  say,  bec8,use  A  is  mortal,  therefore  B  is 
i^rtal— we  make  the  affirmation  of  one  fact,  the  ground  of  an 
aflirmation  of  a  different  fact.  In  order  to  the  one  leap,  we 
need  only  to  know  the  meaning  of  language ;  in  order  to  the 
other,  we  must  consult  the  facts  of  the  world. 

The  supposition  has  been  advanced  that  truths  of  implica- 
tion   or  consistency,  inappropriately  called  *  Necessary,*  are 
drawn  out  from  their  equivalent  statements  by  a  peculiar 
innate  power  of  the  mind,  distinct  from  the  powers  of  observing 
the  order  of  nature  ;  that  without  a  special  instinct  they  could 
not  be  evolved,  nor  reposed  in  with  the  absolute  credence  that 
we  give  to  them.     There  are  no  sufficient  grounds  for  the  sup- 
position.    We  should  be  disposed  to  consistency  of  statement, 
without  any  special  instinct.     The  impossibility  of  carrying  on 
intercourse  hy  language,  on  any  other  footing,  compels  us  to 
be  consistent  m  our  statements  ;  at  least  up  to  a  certain  point, 
for  we  are  not  always  so.     There  is  no  instinct  needed  but  the 
broad  instinct  of  self-preservation  ;  were  it  not  for  this  we 
should  probably  care  very  little  about  observing  the  conditions 
of  necessary  truth.     If  we  could  go  on  as  well  by  maintaining 
an  opinion  m  one  form  of  words,  while  denying  it  in  another, 
there  appears  to  be  nothing  in  our  mental  constitution  that 
would  secure  us  against  contradicting  ourselves.     Our  facul- 
ties as  laid  down  by  those  philosophers  that  derive  all  our 
knowledge  from  experience   alone,  taken   together  with  our 
practical   necessities,  soem   quite   sufficient  to  make  us   ad- 
2 


FIRST   PKINCIPLES   OF   LOGIC. 

here  to  our  statements  under  all  variety  ot  forms  and  expres- 
sions.* 

22  There  are  certain  maxims  of  Consistency  known  by 
the  title  '  Laws  of  Thought ';  they  are  the  principles  of 
Identity^  Contradiction,  and  Excluded  Middle, 

The  principle  of  Ideyitity  is  given  in  the  form  "A  is  ^'^'^^ 
thing  is  what  it  is  ;  man  is  man.  Accordmg  to  Plato,  ine 
Idea  is  equal  to  itself."  ^        i  x  j       j«« 

Properly  speaking  this  is  not  the  case  contemplated  under 
the  principle  of  Consistency  ;  it  is  not  the  same  fact  m  other 
languacre,  but  the  same  fact  in  the  same  language.  That  the 
same  meaning  expressed  by  the  same  word  or  words,  is  the 
same,  would  appear  to  be  an  utter  superfluity  of  affirmation  ; 
wbat  we  want  to  be  guarded  against  is  mistaking  the  same 
fact  in  a  different  form  of  language. 

This  obvious  criticism  is  evaded  by  giving  the  law  an  inter- 
pretation  that  supposes  difference   in   the  statement.      The 
meaning  is  said  to  be  that  the  thing  A,  although  differently 
worded,  is  still  A  ;  which  is  merely  an  awkward  way  of  stating 
the  general  maxim  of  Consistency.     If  A  equals,  or  includes 
a  b,  c,  d,  &c.,  then  we  may  say,  in  slightly  different  words,  A 
is  equal  to  the  whole  series  of  what  it  includes ;  a  whole  is  the 
Bun^of  its  parts;  a  complex  attribute  is  the  aggregate  of  the 
component  attributes. 

The  Principle  of  Contradiction,  *  The  same  thing  cannot  be 
A  and  not- A  ;'  this  room  cannot  be  both  hot  and  not-hot,  that 
is  cold  Consistency  requires  that  when  we  affirm  a  definite 
fact  we  do  not  at  the  same  time  deny  it ;  having  made  an 
assertion,  we  are  to  abide  by  that.  The  pnnciple  may  be  carried 
one  step  farther.  By  the  law  of  Relativity,  every  thing  that 
can  be  thought  of,  every  affirmation  that  can  be  made,  has  an 
opposite  or  counter  notion  or  affirmation  ;  to  the  thing  that 
we  call  a  *  straight'  line,  there  corresponds  a  negative  or  oppo- 
site called  a  'bent'  or  crooked  line.  Now  thorough-going 
consistency  requires  that  when  we  affirm  a  certain  thing  to  bo 

•  Only  some  of  the  a  priori  philosophers,  as  Leibnitz,  contend  for  tho 
existence  of  an  intuitive  faculty  in  order  to  apprehend  these  judgments  of 
mere  consistency.  Kant,  and  others  atter  him.  confine  the  characteristic^ 
of  necessity,  and  of  intuitiye  origin  to  certain  fiV^f^^^'f  Judgments,  where 
the  two  things  given  are  distinct,  and  not  mutually  i^lPl^cated  facts.  It  was 
the  peculiarity  of  Kant  to  maintain  that  there  are  such  synthetic  judgmenta 
a  priori  transcending  our  actual  experience :  he  instanced,  m  ^particulw. 
the  proposition  that  *  two  straight  lines  cannot  enclose  a  space. 


CONTILADICTION  AND   EXCLUDED   MIDDLE. 


17 


a  straight  line,  we  must  be  prepared  also  to  deny  that  it  is  a 
bent  line  ;  when  we  call  this  man  wise,  we  must  also  deny  that 
he  is  foolish.  This  is  an  equivalent  form  that  plays  a  great 
part  in  Logic.  Viewed  thus,  the  Law  of  Contradiction  has  a 
pregnant  meaning,  which  can  hardly  be  said  of  the  Law  of 
Identity. 

The  Principle  of  Excluded  Middle,   *  A  thing  must  either  be  or 
not  be ;'  *of  contradictories  one  must  be  true,  and  the  other  false.' 

This  law  grew  out  of  the  distinction  of  propositions  into 
those  of  total,  or  universal,  and  those  of  partial  or  particular 
quantity— all  men  and  some  men.'  When  a  proposition  of 
universal  quantity  is  opposed  by  one  of  particular  quantity, 
the  opposition  is  not  thorough-going ;  there  is  not  a  perfect 
and  entire  contrariety.  Perfect  contrariety  is  between,  *  all  men 
are  mortal '  and  'no  men  are  mortal ;'  partial  or  incomplete  con- 
trariety is  'all  men  are  mortal,'  * ^owe  men  are  wo^  mortal ;' 
and  *  no  men  are  mortal,'  *  some  men  are  mortal.'  Between 
this  last  species  of  opposition,  there  is  no  middle  affirmation ; 
if  one  is  not  true,  if  it  is  not  true  that  all  men  are  mortal,  then 
it  must  be  true  that  some  men  are  not  mortal ;  we  have  no 
third  alternative.  But  in  the  thorough-going  contrariety— 
*  all  diamonds  are  precious,'  *  no  diamonds  are  precious,'  there 
is  a  middle  ground  of  compromise  ;  the  fact  may  be  that  some 
diamonds  are  precious  and  some  not.  Thus,  the  Law  of 
Excluded  Middle  is  an  incident  of  partial  or  incomplete  con- 
trariety. It  was  enunciated  by  Aristotle  as  following  from  the 
classification  of  propositions  according  to  quantity.  It  is  too 
much  honoured  by  the*dignity  of  a  primary  law  of  thought. 

The  Principle  of  Consistency,  inadequately  rendered  by  these 
Laws  of  Thought,  may  be  assigned  as  the  basis  of  the  logical 
department  entitled  *  Immediate  Inference'  (as  opposed  to 
Mediate  Inference  or  Syllogism),  *  Inferences  improperly  so 
called,'  *  Equivalent  Propositional  Forms.'  Whatever  be  the 
general  designation,  the  details  are  fully  agreed  upon ;  the 
doctrine  of  the  Conversion  of  Propositions  is  one  of  the  leading 
topics. 

First  Principles  of  Deduction, 

23.  In  Deduction,  there  is  the  application  of  a  general 
proposition  to  a  particular  case  conjing  under  it. 

The  following  is  a  deduction  :— *  All  arsenic  is  poison  ;  now 
this  substance  is  arsenic  ;  therefore,  this  substance  is  poison.' 
This    is    something    more    than    consistency,    implication,  or 


18 


FIRST  PRINCIPLES  OF  LOGIC, 


equivalence  of  phraseology.  There  would  be  equivalence  of 
ai&rmation  in  saying  *  all  arsenic  is  poison  ;  therefore,  some 
arsenic  is  poison.*  In  the  present  case,  however,  we  have 
another  step  to  take  ;  we  need  a  second  and  distinct  assertion, 
*  this  substance  is  arsenic,*  before  we  can  conclude,  *  this  sub' 
stance  is  poison.  Instead  of  deriving  an  affirmation  from  a 
prior  affirmation,  by  change  of  language,  wo  derive  an  affirma- 
tion from  two  prior  affirmations  ;  and  these  have  to  be  related 
one  to  another  in  a  proper  form,  in  order  that  we  may  draw 
the  conclusion. 

This  process  is  called  Mediate  Inference ;  there  being  an 
intermediate  link  or  stepping-stone  between  the  primary  pro- 
position and  the  conclusion.  We  cannot,  by  mere  Consistency, 
resolve  *  All  arsenic  is  poison  *  into  *  the  substance  in  this 
bottle  is  poison  ;  *  *  no  matter  is  destructible,'  into  *  no  ether 
is  destructible  * ;  there  is  in  both  cases  a  missing  link.  Until 
we  show  that  the  substance  in  the  bottle  is  arsenic,  and  that 
ether  is  matter,  we  cannot  draw  the  special  conclusions  above 
given, 

24.  The  Axiom,  or  First  Principle,  at  the  basis  of  De- 
duction, is  expressed  in  a  variety  of  forms,  which  are 
reducible  substantially  to  two  : — 

(1.)  Whatever  is  true  of  a  whole  class  is  true  of  what  can 
be  brought  under  the  class. 

(2.)  Things  co-existing  with  the  same  thing  co-exist  with 
one  another. 

There  are  corresponding  forms  for  negative  reasoning. 

The  first  form  is  the  one  suitable  to  the  exposition  of  the 
syllogism.  It  sets  forth  the  deductive  type  of  reasoning,  as 
consisting  of  a  general  principle  brought  to  bear  upon  a  case 
or  cases,  found  to  come  under  it. 

The  second  form  can  be  shown  to  be  equivalent  to  the  first. 
It  has  the  advantage  of  making  prominent  the  mediate  charac- 
ter of  deductive  inference,  so  as  to  contrast  it  with  immediate 
inference,  or  mere  identical  propositions  under  the  Law  of 
Consistency.  Two  things  not  known  in  themselves  to  co- 
exist, are  shown  to  co-exist  by  each  co-existing  with  some  third 
thing.  Mere  consistency  will  not  include  this  case.  The 
principle  is  admitted  as  soon  as  it  is  understood  ;  but  solely 
because  each  one's  experience  bears  it  out. 

The  obverse  forms,  for  negative  reasoning,  are — (1)  What 
19  denied    of  a  whole   class  is  denied  of  whatever  can    be 


AXIOMS   OF  DEDUCTION. 


19 


brought  under  the  class ;  (2)  One  thing  co-existing  with  a 
second  thing,  with  which  second  thing  a  third  thing  does  not 
co-exist,  is  not  co-existent  with  that  third  thing. 

25.  The  Axioms  of  Deduction  suppose  the  Uniformity 
of  Natura 

This  is  obvious,  if  the  axioms  are  based  on  experience.  We 
have  observed,  in  a  large  number  of  instances,  that  things  con- 
cidmg  with  the  same  thing  coincide  with  one  another ;  but 
we  have  not  observed  it  in  all  instances ;  we  have  not  observed 
it  in  what  took  place  before  we  were  born,  in  what  is  beyond 
our  reach,  or  in  what  is  still  to  happen.  Yet,  from  the  cases 
we  have  observed,  we  do  not  hesitate  to  extend  the  principle 
to  the  unobserved  cases.  We  thus  assume  that  'nature  is 
uniform ;  *  that  what  we  find  to-day,  all  circumstances  being 
the  same,  we  shall  find  to-morrow. 

Agam,  we  may  deny  that  the  axioms  are  experimental,  and 
call  them  intuitive.  The  case  is  not  altered.  The  intuition 
still  supposes  nature's  uniformity  ;  the  thing  intuitively  con- 
ceived and  believed  is  not  true,  unless  nature  be  uniform. 
Thus,  on  either  supposition  as  to  our  knowledge  of  the  Logical 
(and  Mathematical)  Axioms,  the  truth,  still  deeper,  and  more 
comprehensive,  is  that  nature  is  uniform.  The  so-called 
axioms,  therefore,  are  not  ultimate  principles ;  they  are  only 
secondary,  proximate,  or  derivative ;  they  proceed  from  a  stem 
bearing  other  branches  besides  them.  If  they  are  true,  more  is 
true.  The  wider  principle  will  next  be  stated,  for  the  sake  of 
its  other  consequences. 

First  Principle  of  Induction. 

26.  When  we  infer  from  a  fact  known,  to  another  un- 
known, we  make  a  real  inference,  for  which  there  must  be 
some  guarantee. 

The  sole  guarantee  is  the  Uniformity  of  Nature. 

Putting  a  piece  of  wood  into  the  fire  and  seeing  it  consumed, 
we  infer  that  another  piece  will  be  consumed  in  like  manner. 
This  is  to  take  for  granted  that  what  has  happened  will,  in  the 
same  circumstances,  happen  again;  in  other  words,  that 
Nature  is  Uniform. 

The  Uniformities  of  Nature  fall  under  (1)  Uniformities  of 
Co-existence,  and  (2)  Uniformity  of  Succession.  It  is  a  uni- 
formity of  Co-existence  that  *  inert  matter  gravitates,*  that 
the  distinctive  property  of  matter  called  *  Inertness*  is  asso- 


rsw^ 


20 


FIRST  PRINCIPLES   OF  LOGia 


LAW   OF  CAUSATION. 


21 


ciated,  throngli  all  nature  at  all  times,  with  the  property  of 
weight  or  Gravitation. 

The  evidence  for  Uniformities  of  Co-existence  is  special 
observation  of  each  separate  uniformity.  From  seeing  two 
things  coupled  together  in  a  few  instances,  we  cannot  presume 
that^hey  are  always  coupled  together ;  we  must  observe  the 
coupling  in  various  times,  places,  and  circumstances.  If,  after 
a  sufficient  search,  we  find  no  single  contradictory  instance, 
we  affirm  the  union  to  prevail  through  all  nature. 

27.  In  Uniformiti^.s  of  Succession,  there  has  been  dis- 
covered a  la2V  of  Uniformity  that  shortens  the  labour  on 
enquiry  in  this  department.  It  is  called  the  Law  of  Cause 
and  Etfect,  or  Causation.     We  may  express  it  thus  : — 

*  Every  event  is  uniformly  preceded  by  some  other  event  :* 
*  To  every  event  there  is  some  antecedent,  which  happening, 
it  will  happen.' 

To  say  that  *  Every  effect  must  have  a  cause,'  is  begging  thg 
question  ;  the  word  cause  implies  an  effect,  and  the  word 
effect  implies  a  cause.  The  correct  mode  of  expression  is,  *  To 
every  event  there  corresponds  a  prior  event,  which  happening, 
it  will  happen  ;  and  which  failing,  it  will  not  happen.''  '  The 
antecedent  may  be,  and  often  is,  a  whole  assemblage  of  circum- 
stances ;  as  in  the  case  of  Health,  an  effect  depending  on 
many  conditions. 

Since  there  are  effects  produced  by  a  plurality  of  Causes,  the 
principle  of  Uniformity  is  limited  and  qualified  by  that  circum- 
stance.  Thus,  Death  may  be  caused  by  starvation,  by  a 
violent  blow,  by  poison,  &c.  It  is  therefore  proper  to  say 
that  given  any  of  these  conditions  in  sufficient  amount,  death 
will  follow  ;  but  the  occurrence  of  death  does  not  prove  that 
there  has  been  starvation ;  it  proves  only  that  one  of  the 
producing  agencies  has  been  present.  In  the  Inductive 
enquiry  into  nature,  all  the  causes  that  may  produce  each 
effect  are  sought  out. 

From  the  Law  of  Causation,  we  deduce  consequences  such 
as  these  : — *  If  the  cause  be  absent,  the  effect  will  be  absent'— 
*cessante  causa,  cessat  et  effectus,'  *If  the  cause  be  present 
the  effect  will  be  present,'  *  Whatever  agent  cannot  be 
removed  without  the  cessation  of  the  effect,  mlist  be  the  cause 
or  part  of  the  cause,'  'Whatever  agent  can  be  removed 
without  the  cessation  of  the  effect  is  not  the  cause,'  *The 
cause  and  effect  vary  proportionately.' 


These  various  aspects  or  implications  of  the  Law  of  Causa- 
tion are  the  maxims  serving  to  eliminate  and  to  prove  cause 
and  effect  in  the  phenomena  of  nature. 

28.  The  Law  of  Uniform  Causation  appears  in  a  form 
still  more  pregnant  with  consequences,  namely,  the  Law  of 
the  Persistence,  Conservation,  Correlation,  or  Equivalence 
of  Force. 

This  is  a  generalization  only  recently  effected. 

Galileo  and  Newton  may  be  considered  as  having  established 
the  Law  of  the  Persistence  or  Conservation  of  Mechanical 
Force,  that  is,  force  applied  to  matter  in  masses.  If  one  ball 
strikes  another  and  puts  it  in  motion,  the  force  imparted  to 
the  second  is  exactly  what  is  lost  to  the  first. 

Lavoisier  established  the  persistence  of  ponderable  matter, 
showing  that  no  atom  of  matter  could  be  destroyed,  and  none 
created.  In  burning  and  in  evaporation,  the  particles  merely 
change  their  positions;  they  do  not  abandon  their  material 
properties  of  inertia  and  gravity. 

In  the  present  day,  evidence  has  been  obtained  to  show  that 
other  forces  besides  mechanical  force,  namely,  Heat,  Chemical 
Force,  Electricity,  Nerve  Force,  have  the  same  numerical 
persistence;  they  can  neither  be  created  nor  destroyed; 
They  can,  however,  be  mutually  converted,  at  a  definite  rate. 
Heat  can  give  birth  to  Mechanical  Force  ;  Chemical  Force  can 
evolve  Heat;  Electricity  is  convertible  into  all  the  other 
modes.  In  this  conversion,  nothing  is  lost,  and  nothing  is 
created  ;  when  heat  becomes  a  mechanical  prima  mover  in  the 
steam  engine,  it  disappears  as  heat.  When  mechanical  force 
is  seemingly  destroyed,  as  when  a  cannon  ball  spends  itself  on 
an  unyielding  mass  of  stone,  the  whole  momentum  of  the  ball 
is  transformed  into  heat ;  at  the  place  of  encounter,  both  the 
ball  and  the  stone  are  raised  in  temperature,  exactly  in  propor- 
tion to  the  momentum  arrested. 

This  great  law  of  the  quantitative  persistence  of  Force,  or 
Momentum,  deserves  an  eminent  place  in  the  Inductive  Logic. 
It  encompasses  and  pervades  all  the  natural  sciences,  each 
one  of  which  is  but  a  partial  development  of  it. 

NATURE   AND   CLASSIFICATION   OF  KNOWLEDGE. 

29.  Knowledge  is  made  up  of  affirmations  respecting 
the  order  of  the  world.  These  affirmations  are  the  subject 
of  Belief,  of  which  the  ultimate  criterion  is  Action. 


fi 


22 


NATURE  AND  CLASSIFICATION   OF  KNOWLEDGE. 


Twice  two  is  four ;  the  son  rises  and  sets ;  Tmsupported 
bodies  fall  to  the  ground ;  heat  causes  water  to  boil ;  animal 
bodies  are  nourished  by  food  and  air  ;  harmony  is  agreeable 
to  the  mind  : — are  affirmations,  or  Knowledge,  respecting  the 
tiniverse.  We  believe  them,  and  show  our  belief  by  acting  on 
them.  When  we  desire  water  to  boil,  we  apply  heat ;  which 
is  onr  belief  of  the  affirmation. 

30.  The  first  requisite  of  Knowledge  is  that  it  shall  be 
true. 

An  Affirmation  is  true  when,  on  actual  trial,  it  corresponds 
to  the  fact.  This  is  the  direct  proof.  Indirectly,  we  may 
test  the  truth  of  affirmations  by  comparing  one  with  another. 
Wherever  there  is  contradiction,  there  must  be  falsehood. 

31.  Knowledge  is  either  Particular  or  General, 

An  Affirmation  respecting  a  certain  individual  thing,  as 
*  this  house  is  stable,*  *  Caesar  was  brave,'  *  a  certain  patient 
will  not  recover ' — is  a  particular  or  individual  affirmation ; 
it  is  limited  to  one  subject.  An  affirmation  respecting  a  whole 
class  or  species  of  things — as  *  an  erection  is  stable  when  tlie 
line  of  the  centre  of  gravity  falls  within  the  base*;  *all  great 
generals  are  brave  ' ;  *  the  stiffi3ning  of  the  limbs  is  a  sign  of 
death  * ; — are  general  affirmations ;  they  extend  to  instances 
beyond  number. 

32.  Owing  to  the  frequent  recurrence  of  the  same  things 
and  the  same  processes,  we  can  attain  to  numerous  genera- 
lities. 

If  every  individual  thing  in  nature  were  throughout  unique, 
resembling  no  other  thing,  each  would  need  a  law  to  itself. 
If,  instead  of  a  common  substance  *  water  *  in  all  seas,  rivers, 
and  fountains,  there  were  a  thousand  different  substances,  we 
should  have  to  multiply  affinnations  accordingly.  If,  instead 
of  the  sixty-three  elementary  bodies  known  to  us  at  present, 
the  globe  were  made  up  of  six  thousand  elements  with  their 
compounds,  there  would  be  a  great  increase  in  the  bulk  of  our 
knowledge.  If  instead  of  sixtj-three,  there  had  been  six,  we 
should  have  been  able  to  comprehend  all  physical  knowledge 
in  comparatively  few  affirmations. 

33.  It  is  desirable  to  attain  knowledge  in  the  highest 
possible  degree  oi  generality. 


TRUTH  AND  GENERALITY. 


23 


The  reason  is  cbviotis.  A  general  affirmation  is  a  great 
many  particular  affirmations  in  one.  It  is  a  vast  economy  of 
the  human  understanding.  A  general  law  places  us  at  a 
commanding  height,  where,  by  one  glance,  we  can  survey  a 
wide  array  of  facts.  The  law  of  Gravity,  the  law  of  the  Per- 
sistence of  Force,  the  law  of  Definite  Proportions  in  Chemistry, 
the  law  of  Relativity  in  Mind,— -severally  comprehend  thou- 
sands of  individual  affirmations. 

34.  The  perfect  form  of  knowledge  is  Scienck 
The  peculiarities  of  Science  are  these : — 

I.  It  employs  special  means  and  appliances  to  render 
knowledge  true. 

The  uninstructed  man  is  apt  to  make  affirmations  without 
taking  the  trouble  to  test  them.  The  scientific  man,  on  the 
other  hand,  not  only  avails  himself  of  the  common  means  of 
proof,  but  employs  an  express  machinery  for  testing  all  the 
knowledge  in  his  own  department.  This  machinery  is  to  a 
certain  extent  common  to  all  knowledge,  and  all  science ;  and 
to  a  certain  extent,  it  is  special  to  each  science.  The  common 
machinery  is  embraced  in  Logic. 

35.  IT.  Knowledge,  in  the  form  of  Science,  is  made  as 
general  as  possible. 

Science  does  not  refuse  individual  facts,  provided  they  are 
true  ;  on  the  contrary,  it  collects  as  many  such  facts  as  pos- 
sible. But  considering  the  enormous  sweep  and  vantao^e 
ground  of  generalized  facts,  science  pushes  the  generalising 
process  to  the  utmost  limits.  A  few  isolated  facts  carefully 
ascertained  to  be  true,  would  be  valuable  in  themselves,  but 
they  would  not  constitute  a  science. 

36.  III.  A  Science  embraces  a  distinct  department  of 
the  world,  or  groups  together  facts  and  generalities  that 
are  of  a  kindred  sort. 

It  appears,  on  investigation,  that  the  operations  of  the  world 
are  different  in  their  nature,  and  need  to  be  differently  studied. 
Ihe  forces  that  maintain  the  motions  of  the  heavenly  bodies, 
are  different  from  combustion,  magnetism,  or  vegetable  and 
animal  growth.  The  functions  of  the  mind  scarcely  resemble 
anything  else.  Hence  the  affirmations  or  truths  respecting 
the  world  fall  into  distinct  departments  ;  and  there  is  an  evi- 
dent propriety  in  observing  the  distinction,  and  in  classing 
kindred  facts  together.      To  class  together  facts  about  the 


w 


fi 


11 


24        NATURE   AND  CLASSIFICATION   OF   KNOWLEDGF. 

planets,  and  fa^jts  about  the  human  mind,  could  only  perplex  the 
understanding. 

37  IV  A  Science  has  a  certain  order  or  arrangement  of 
topics,  suitable  to  its  ends  in  gathering,  in  verifying,  and  in 
coramuuicating  knowledge. 

Besides  bringing  together  the  facts  and  generalities  relative 
to  each  division  of  phenomena,  a  science  must  present  its 
materials  in  a  fitting  arrangement.  ^ 

This  arrangement  varies  in  the  difierent  sciences,  btill,  in 
all  of  them,  Attention  must  be  given  to  the  following  pomts- 

m  To  nroceed  from  the  more  easily,  to  the  less  easily 
known.  If  any  fact  or  generaUty  depends  upon  or  presup- 
poses  another,  that  other  should  be  stated  first  in  order. 

(2)  Whatever  is  requisite  for  proving  any  doctrine  should 
Drecede  what  is  to  be  proved.  In  concatenated  or  deductive 
sciences,  like  geometry,  each  affirmation  depends  ^Pon  some 
that  go  before  f  and  the  evolution  is  thus  methodical  and  sys- 

*^?3)' The  meanings  of  all  terras  should  be  distinctly  given 
before  they  are  made  use  of.  It  is  usual  to  commence  with 
the  definitions  of  leading  terms. 

38  The  classification  of  the  Sciences  is  in  accordance 
with  the  foregoing  views.  In  the  first  place,  it  follows  the 
division  of  nature  into  departments,  and  m  the  second 
place,  it  follows  the  order  of  relative  simplicity  and  ot 
mutual  dependence  in  those  departments. 

If  each  different  process  of  nature  were  entirely  separate 
from  the  others,  there  would  be  no  special  order  of  the  sciences. 
But  the  distinct  powers— gravity,  heat,  animal  growth,  mind, 
&c.,  are  to  a  great  degree  intermingled  m  their  workmgs 
Moreover,  all  phenomena  whatever  are  subject  to  laws  ot 
Quautity,  and  these  can  be  studied  apart  from  any  one  class  ot 
thin^rs  ;  hence,  such  laws  are  a  preparation  for  all  the  depart- 
ments. Nor  is  this  the  only  way  that  one  science  paves  the  way 
for  another.  Accordingly,  there  is,  among  the  several  sciences, 
an  order  of  dependence  that,  to  a  certain  degree,  determines 
their  succession  to  the  learner,  and  their  gradual  evolution 
under  the  hands  of  scientific  enquirers. 

39.  The  Sciences  are  either  Abstract  or  Concrete. 
The  Science  of  Mathematics,  which  treats  of  quantity,  with- 
out referring  to  any  particular  kind  of  quantity,  as  length, 


OEDEE  OF  THE   SCIENCES. 


25 


y^ 


weight,  heat,  Ac,  is  called  an  Abstract  Science.  With  one 
exception,  it  is  the  most  abstract  of  all  the  Sciences ;  the  pro- 
perties treated  of  are  the  most  general  of  all  properties ;  and 
they  are  discussed  in  the  highest  degree  of  separation  from 
concurring  attributes. 

On  the  other  hand.  Zoology,  which  classifies  and  describes 
one  great  department  of  actual  or  concrete  things — the  whole 
Animal  Kingdom — is  a  Concrete  Science. 

Tiie  science  that,  in  point  of  abstractness,  rivals  Mathema- 
tics is  Logic  itself.  The  First  Principles  of  Logic,  as  above 
laid  down,  including  the  law  of  Consistency,  the  law  of  Deduc- 
tion, the  law  of  Uniformity,  are  paramount  over  every 
science  ;  they  are  wider  than  even  the  laws  of  quantity. 

Next  to  quantity,  the  most  general  attribute  of  natural 
things  is  motion.  All  material  bodies  may  pass  into  motion — 
motion  in  mass  (molar  movement)  or  motion  in  molecule 
(molecular  movement)  or  both.  Now  the  laws  of  motion  may 
be  laid  down  without  reference  to  any  particular  objects- 
Hence  there  may  be  an  abstract  science  of  Motion,  for  which 
the  name  might  be  Abstract,  Theoretical,  or  Rational 
Mechanics;  the  designation  now  accepted  is  'Kinematics.* 
The  principles  of  motion,  as  applied  to  actual  bodies — solids, 
liquids,  and  gases— constitute  the  departments  of  Concrete 
Mechanics,  which  have  appropriate  names. 

The  Abstract  is  also  the  simple,  the  concrete  is  usually  the  com- 
plex. When  what  is  true  of  the  Abstract  is  not  also  true  of  the 
concrete,  the  reason  is  an  incident  and  not  a  necessity.  What  is 
true  in  the  Abstract  really  means  truth  in  the  concrete;  the 
abstract  is  merely  a  name  for  the  concrete  under  agreement.  A 
law  true  in  the  abstract  would  be  a  contradiction,  if  it  were  not 
true  in  the  concrete  also.  But  in  the  concrete,  there  may  be 
counteracting  forces,  so  that  the  real  point  is  to  contrast  a 
power  working  alone  with  a  power  working  in  company.  The 
abstract  law  of  motion — the  persistence  of  a  body  in  its  present 
state,  fails  in  the  concrete,  because  of  friction,  or  of  opposing 
obstacles;  the  tendency  to  persist  is  compounded  with  other 
influences,  and  we  have  to  calculate  the  result  of  the  composition. 
Self-interest  working  alone  would  have  certain  consequences ;  as 
an  element  of  a  compound,  it  is  no  longer  accountable  for  the 
whole  effect. 

The  Abstract  Sciences  properly  precede  the  corresponding  Con- 
crete Sciences. 

40.  For  the  purposes  of  the  present  day,  the  Sciences 
may  be  classified  as  follows  :— L  Logic,  IL  Mathematics, 
III.  Mechanics  or  Mechanical  Physics,  IV.  Molecular  Phy- 


26  NATURE  AND  CLASSIFICATION  OF  KNOWLEDGE. 

sics,  V.  Chemistry,  VI.  Biology,  VII.  Psychology.  In 
every  one  of  these,  there  is  a  distinct  department  of  pheno- 
mena ;  taken  together,  they  comprehend  all  known  pheno- 
mena ;  and  the  order  indicated  is  the  order  from  simple  to 
complex,  and  from  independent  to  dependent,  marking  the 
order  of  study  and  of  evolution. 

I.  Logic  embraces,  as  has  been  seen,  the  most  fundamental 
and  universal  of  all  principles — Consistency,  Deduction,  and 
Uniformity.  It  reposes  upon  nothing  more  fundamental  than 
itself,  and  it  gives  foundation  to  all  the  other  sciences.  There 
can  be  no  science  without  assuming  all  the  data  of  Logic, 
whether  avowedly  or  not. 

II.  Mathematics  is  the  abstract  science  of  Quantity,  and  the 
laws  of  Quantity,  in  every  possible  combination. 

III.  Mechanics,  or  Mechanical  Physics,  or  Mechanical 
Philosophy,  is  the  science  of  Motion,  as  regards  bodies  in 
mas8y  and  of  Force,  which  is  the  momentum  of  moving  masses. 
There  is  an  abstract  or  theoretical  department  (Kinematics), 
comprising  all  the  laws  of  the  Equilibrium,  and  of  the  Move- 
ments, of  matter  iu  mass,  without  reference  to  any  special 
class  of  things.  The  Concrete  applications  of  these  laws 
embrace  Astronomy,  or  the  Celestial  Motions,  the  kindred 
subject  of  Falling  Bodies  on  the  Earth,  Statics,  Hydrostatics, 
Dynamics,  Hydrodynamics,  Acoustics. 

IV.  Molecular  Physics  refers  to  the  molecular  movements 
and  arrangements  of  material  bodies.  It  comprises  the  Mole- 
cular Cohesions  and  Adhesions,  as  operative  in  the  structure 
of  Solids,  Liquids,  and  Gases  ;  Heat ;  Light ;  Electricity. 

V.  Chemistry  is  a  continuation  of  Molecular  Physics,  having 
more  especial  reference  to  the  Combinations  and  Decomposi- 
tions, named  chemical,  and  characterised  by  great  accompanying 
changes  of  properties. 

The  branch  of  Science,  long  known  as  Natural  Philosophy, 
comprises  both  Mechanical  Physics  and  Molecular  Physics,  but 
excludes  Chemistry.  An  equally,  if  not  more,  suitable  arrange- 
ment would  be  to  treat  Chemistry  as  a  part  of  Molecular 
Physics  ;  into  which  it  shades  by  imperceptible  gradation.  In 
point  of  fact,  Chemical  action  is  inseparably  implicated  with 
Heat  and  with  Electricity,  although  these  subjects  can  be,  in 
exposition,  detached  from  Chemistry. 

Mechanical  Physics  and  Molecular  Physics,  taken  together, 
exhaust  all  the  fundamental  aspects  of  the  great  doctrine  of 
the  Persistence,  Conservation,  or  Correlation  of  Force, 


CLASSIFICATION   OF  THE  ABSTRACT  SCIENCES.  27 

VL  Biology  enters  upon  an  entirely  new  field  of  pheno- 
mena, the  phenomena  of  Life,  or  of  Living  Bodies,  involving 
an  organised  structure,  with  perpetual  evolution  and  repr(> 
duction.  This  science  is  posterior  to  the  foregoing,  inasmuch 
as  living  bodies  come  under  all  the  laws  of  Mechanical  and  of 
Molecular  Physics,  in  addition  to  their  own  specific  laws  as 
living  bodies. 

Biology  is  divided  into  Vegetable  and  Animal  Biolotry  •  the 
one  exhaustmg  the  structure,  classification,  and  description  of 
Plants,  the  other  referring  to  Animals,  Botany,  Zooloffv. 
Human  Anatomy  and  Physiology,  are  the  concrete  depart! 
ments  of  Biology,  and  its  leading  divisions  for  study.  There 
can  scarcely  be  such  a  science  as  Abstract  Biology  ;  the  laws 
ot  lite  cannot  be  given  in  separation  from  living  veo-etables  and 
animals.  The  nearest  approach  to  a  division  into  Abstract 
and  Concrete,  is  the  distinction  between  Physiology—Veffetable 
and  Animal-^nthe  one  hand,  and  the  classification  and  de- 
tailed description  of  Plants  and  of  Animals  on  the  other 

VIL  Psychology,  or  the  Science  of  Mind,  is  a  unique  de- 
partment  of  natural  phenomena.  Its  terminal  position  in  the 
order  of  the  Sciences  is  owing  to  two  circumstances.  In  the 
tirst  place,  It  is  a  subject  of  great  complication,  aggravated  bv 
an  especial  amount  of  corrupting  bias.  Hence  the  student 
does  weU  to  come  prepared  with  a  scientific  discipline,  such  as 
IS  best  furnished  in  the  previously  ennumerated  sciences. 
Secondly,  although  the  mind  proper—the  subjective  conscious- 
"^!uT'^^  ''''''1''®  subject,  yet  a  material  organism  is  allied 
with  it  throughout,  and  therefore  should  be  known  as  so  allied 
JNow  the  material  organism  falls  under  the  last  part  of  Bioloffv* 
namely  Human  Physiology.  ^^* 

These  seven  branches  contain  the  laws  of  every  known  pro- 
cess m  the  world,  whether  of  matter  or  of  mind ;  and  set  forth 
those  laws  m  the  order  suitable  for  studying  and  comprehend- 
ing them  to  the  greatest  possible  advantage.  No  phenomenon 
can  be  strange  to  any  one  thoroughly  conversant  with  those 
subjects.  Properly  speaking,  the  laws  of  the  phenomena  mi^ht 
be  comprehended  under  four  heads  :— Molar  Mechanics,  Mole- 
''"J'^^r  fu''^^"^''^  <^^''  Physics),  Biology,  Psychology.  Logic 
and  Mathematics  are  merely  aids  to  the  better  comprehension 
ot  the  actual  things. 

Astronomy  was  detached,  by  Auguste  Comte,  from  its  usual 
position  under  Mechanics,  and  made  one  of  the  primary  depart- 
ments. His  reason  w^as  that  it  deals  with  the  great  fact  Gravity 
—a  distinct  and  specific  phenomenon,  unlike  everything  els^ 


k 


fi 


tit 


< 


28 


NATURE  AND  CLASSIFICATION  OF    KNOWLEDGE. 


PRACTICAL   SCIENCES. 


29 


I: 


and  capable  of  being  developed  apart,  merely  with  the  aid  of 
Mathematics  and  abstract  Mechanics.  Although  the  position 
thus  given  to  the  subject  may  be  thought  unnecessarily  pro- 
minent, yet  the  reason  contains  an  undoubted  and  highly  illus- 
trative fact.  The  gravitating  action  is  peculiar  and  distinct ; 
it  operates  in  the  celestial  bodies  uncomplicated  with  any  other 
actions,  giving  Astronomy  a  character  of  remarkable  simpli- 
city as  regards  the  forces  at  work. 

41.  The  Concrete  Departments  include  various  additional 
subjects — as  Meteorology,  Mineralogy,  Geology,  Geography, 
— no  one  of  which  involves  any  operation  but  what  i? 
expounded  in  the  Fundamental  or  Departmental  Sciences. 

In  each  of  these  branches,  a  certain  group  of  locally  allied 
phenomena  is  separated  for  special  study.  Meteorology,  treats 
of  the  Atmosphere,  all  whose  phenomena  are  regulated  by 
the  laws  of  Mechanical  and  of  Molecular  Physics.  The  same 
may  be  said  of  Mineralogy  ;  there  is  no  natural  agent  at  work 
in  the  formation  of  minerals,  but  what  is  discribed  in  the 
fundamental  departments  last  named.  The  special  aim  of  the 
subject  is  to  provide  a  systematic  mode  of  classifying  and 
describing  mineral  bodies,  so  that  they  may  be  recognised  and 
understood.  Geology  involves  Biology,  in  addition  to  Physics ; 
its  localit-j  is  the  crust  of  the  globe,  so  far  as  accessible.  Geo^ 
graphy  is  the  science  of  the  Earth's  surface — and  is,  like  the 
two  foregoing,  a  descriptive  science,  but  containing  no  new 
laws  of  phenomena. 

Among  Concrete  Sciences  related  more  particularly  to 
mind,  we  may  class  the  Science  of  Society,  Politics,  or  Sociology, 
which  applies  the  laws  of  Mind  to  human  beings  aggregated 
in  Society.  Another  example  is  Philology,  or  the  theory  of 
Universal  Language,  together  with  the  Classification  of  the 
Languages  now  or  fonnerly  spoken. 

42.  We  have  not  yet  exhausted  the  branches  of  know- 
ledge designated  Sciences.  There  remain  the  Practical 
Sciences. 

The  final  end  of  all  knowledge  is  Practice,  or  the  guidance 
of  conduct.  There  are  numerous  departments  of  practice, 
according  to  the  needs  of  human  beings ;  and  every  one  of 
these  reposes  upon  knowledge  more  or  less  accurate.  Another 
name  for  practice  is  Art. 


iff 


Now,  accordmg  to  the  quality  of  the  knowledge  at  com- 
mand. Art  may  be  empirical  or  it  may  be  scientific.  An 
empirical  art  proceeds  solely  upon  the  knowledge  gained  in 
the  exercise  of  the  art  itself.  All  arts  were  empirical  before 
science  began ;  as  for  example.  Agriculture,  Navigation,  and 
Metallurgy.  There  are  still  some  empirical  arts,  as  the  greater 
part  of  Medicine. 

Art  becomes  scientific,  when  science  is  brought  to  bear 
u^Tt^\  Navigation  is  a  remarkable  instance;  being  aided 
by  Mathematics,  Mechanics,  Astronomy,  Optics,  and  Meteoro- 
logy. Engineermg,  Building,  Machinery,  Dyeing,  and  the 
range  of  Manufactures  generally,  are  arts  founded  on  Science, 
and  may  be  called  Scientific  Arts,  or  Practical  Sciences. 
Another  group  (connected  more  with  mind),  includes  Ethics, 
Logic  (in  its  practical  aspect),  Esthetics,  Rhetoric,  Grammar, 
Jl^ducation,  Politics,  Jurisprudence,  Law,  Pohtical  Economy. 

Several  of  the  subjects  last  named  might  be  viewed  either 
as  Theoretical  Concrete  Sciences,  or  as  Practical  Sciences. 
Ihis  would  depend  upon  whether  they  were  constructed  most 
upon  the  one  type  or  upon  the  other.  Thus,  Politics  might  be 
arranged  as  a  methodical  body  of  political  doctiines  consecu- 
tively  evolved  from  primary  truths  or  data,  like  Mechanics, 
Chemistry,  or  Psychology.  It  might  also  be  arranged  with  a 
predominant  regard  to  the  ^political  end,  and  might  take  the 
form  of  a  series  of  maxims  or  directions  for  the  art  of  o-ovem- 
ment,  more  or  less  supported  by  scientific  doctrines  and 
general  reasonings.  A  similar  remark  applies  to  Political 
Economy,  Jurisprudence,  and  Ethics.  , 

43.  In  a  Practical  Science,  the  knowledge  is  selected  and 
arranged  purely  with  reference  to  the  object  in  view.  The 
definition  of  a  Practical  Science  is  its  End. 

This  makes  a  great  difference  as  respects  choice  of  topics, 
between  a  Theoretical  Science  (Abstract  or  Concrete)  and  a 
Practical  Science.  In  the  first,  the  knowledge  imparted  per- 
tains exclusively  to  one  department  of  natural  phenomena- 
Motion,  Life,  Mind,  &c.  In  the  second,  the  knowledge  is 
selected  froni  one  or  more  theoretical  sciences,  and  set  forth  in 
the  order  suited  to  the  end  in  view.  In  a  theoretical  science 
we  obtain,  in  the  most  succinct  and  intelligible  shape,  the  en- 
tire body  of  existing  information  relating  to  one  group  of 
kindred  phenomena;  the  knowledge  being  applicable  to 
several  arts,  but  not  specially  applied  to  any.     In  a  practical 


utms^a 


1 


30 


NATURE  AND  CLASSIFICATION  OF  KNOWLEDGB. 


science,  the  information  conveyed  is  kept  in  subservience  to 
the  purpose  of  the  art. 

That  the  definition  of  a  Practical  Science  is  its  End,  was  a 
point  greatly  insisted  upon  in  the  Aristotelian  treatises.  Thus,  in 
Ethics,  we  have  to  ascertain  first  the  telos,  the  ethical  end ;  on 
which  turns  the  chief  difierences  of  opinion  on  the  subject. 
Logic,  in  so  far  as  being  a  theoretical  science,  is  defined  by  its 
natural  department ;  as  a  practical  science,  or  an  art  (whether 
empirical  or  scientific),  it  must  be  defined  by  its  end.  (See 
also  Appendix  A,  and  Liductive  Logic,  Book  III.) 

DIFFERENT  VIEWS   OF  THE  DEFINITION  OR  PROVINCE  OF 

LOGIC. 

44  Logic  has  been  termed  (I.)  the    Art  of  Reasoning 
and  (II.)  the  Art  and  Science  of  Reasoning. 

The  first  is  Aldrich's  definition  ;  the  second  is  Whatcly*8 
amendment.  In  both  forms,  there  is  an  admission  of  the 
practical  character  of  Logic  ;  in  the  second  form,  the  practice 
is  said  to  be  founded  on  Science ;  in  other  wordij,  Logic  is  a 
Practical  Science. 

45.  The  term  *  Reasoning  *  is  insufficient,  as  being,  first 
susceptible  of  more  than  one  interpretation,  and,  secondly 
too  narrow  for  the  admitted  scope  of  Logic. 

Reasoning  may  mean  Deduction  solely,  or  it  may  mean 
Inference  as  a  whole,  which  is  Deduction  together  with  Induc- 
tion. In  the  narrower  acceptation.  Logic  would  be  confined 
to  Deductive  Reasoning,  or  Syllogism  ;  in  the  wider  accepta- 
tion, it  comprises  Induction  also.  The  narrower  meaning  has 
been  the  most  usual  in  Logical  treatises,  but  in  scarcely  auy 
one  is  it  consistently  adhered  to.  Either  under  the  title  of 
Induction,  or  as  Applied  Logic,  matters  pertaining  to  Induction 
have  been  introduced  by  Whately,  Hamilton,  Thomson,  and 
others. 

Again,  taken  in  its  widest  sense,  the  term  Reasoning  is  still 
too  narrow.  We  always  find,  in  books  on  Logic,  subjects  not 
comprised  under  the  term  Reasoning:  as  Classification, 
Definition,  and  Division  ;  all  which  are  amenable  to  rules,  and 
may  be  performed  well  or  ill.  We  apply  the  epithet  *  logical ' 
to  a  definition,  as  well  as  to  an  argument. 

46.  III.  Logic  has  been  described  as  *  the  Science  of  the 
Laws  of  Thought.* 


LAWS  OP  THOUGHT. 


31 


This  definition  remedies  the  narrowness  of  the  foreffoinff  in 
respect  of  the  use  of  the  word  Reasoning.     *  Thought  'is  lar^e 
enough  to  cover  all  the  processes  admitted  into  Loffic      It. 
however,  does  more ;  it  includes  in  its  meaning  all  the  intel- 
lectual  processes,  being  co-oxtensive  with  intelligence  itself. 
Memory  and  Imagination  would  be  departments  of  thought. 
Consequently,  the  word  has  to  be  narrowed  in  its  signification, 
to  what  18  termed  *  Discursive^  or  *  Elaborative '  Thought,  the 
faculties  concerned  in  the  scientific  operation,  or  in  the  attain- 
ment of  truth ;  which  faculties  may  be  summed  up  in  the  two 
-Abstraction  and  Reasoning.     The  power  called  Abstraction 
covers  those  portions  of  the  field  of  Logic  that  Reasoning  in 
Its  widest  meaning  does  not  cover. 

Even  with  this  limitation,  the  title  »Laws  of  Thought'  is 
liable  to  other  objections.  In  particular,  it  points,  by  an 
obvious  interpretation,  to  Fsychologij  rather  than  to  Lo^Ic. 
The  Laws  of  Thought,  or  of  Thinking,  would  appear  most 
naturally  to  indicate  the  laws  of  the  rise  and  succession  .of  our 
thoughts  as  explained  in  Mental  Science ;  in  other  words,  the 
laws  of  the  Association  of  Ideas. 

This  difficulty  can  be  met  only  by  arbitrary  interpretations 
of  Laws  of  Thought.'  By  some,  the  phrase  is  qualified  by 
the  word  *FormaV  which,  however,  does  not  relieve  the 
perplexity.  Do  the  *  Laws  of  Thought »  mean  Thought  as  it 
18,  or  Thought  as  it  ought  to  be  ?  If  *  Thought  a^  it  ?s,'  then 
the  subject  is  pure  psychology ;  if  *  Thought  a^  it  ought  to 
be,  there  must  be  supplied  some  principle  for  checking  or 
controlling  the  spontaneous  thinking  of  the  mind,  which 
principle  IS  the  all-important  element  of  the  case,  and  needs  to 
be  exphcitely  stated, 

Hardly  any  amount  of  explanation  will  convert  into  a  ffood 
Definition  a  phrase  of  such  ambiguous  and  uncertain  scope  as 
the  Laws  of  Thought.'  When  the  proper  limitations  are 
supplied,  there  can  be  found  some  other  phraseology  more 
suitable  to  indicate  what  is  intended.  If  the  meaning  is 
Thought  as  it  ought  to  be'— Right  or  Corrected  Thinking  — 
a  standard  must  be  assigned,  which  standard  can  be  nothinc^ 
but  the  standard  of  what  is  true  and  false;  » the  end  of  thouffht? 
Hamilton  remarks,  is  '  truth.' 

47.  IV.  Logic  is  defined  (Port  Royal  Logic)  'the  Science 
of  the  operations  of  the  understanding  in  the  pursuit  of  truth.' 

Here  three  things  are  implied.  First,  Logic  is  a  department  of 
practice,  scientifically  conducted,  that  is,  a  Practical  Science. 


32      DIFFERENT   VIEWS   OF  THE   DEFINITION   OF  LOGIC. 

Secondly,  whereas  every  Practical  Science,  and  every  Art, 
whether  scientific  or  not,  mast  have  an  End,  the  end  of  the 
science  of  Logic  is  the  attainment  of  Truth.  Thirdly,  the 
means  employed  in  this  pursuit  is  an  enquiry  into  the  opera- 
tions of  the  human  understanding. 

The  two  first  positions  can  hardly  be  controverted.  Logic, 
no  doubt,  has  a  certain  theoretic  aspect,  to  be  considered  pre- 
sently, but  its  chief  aim  must  ever  be  practical.  •  Had  the  sub- 
ject not  been  wanted  as  an  aid  to  the  search  of  truth,  it  would 
never  have  been  called  into  existence. 

The  third  position — that  the  means  in  Logic  consists  in  an 
enquiry  into  the  operations  of  the  Understanding — admits  of 
one  criticism.  This  may  be  a  means,  but  is  not  necessarily 
the  sole  means. 

48.  The  foregoiDg  definition  is  modified  by  distinguish- 
ing between  two  kinds  of  truths : — namely  those  known 
immediately f  intuitively,  or  by  direct  consciousness ;  and 
those  known  by  the  mediation  of  other  truths. 

The  distinction  is  fundamental  and  important.  Facts  of 
present  consciousness,  as — I  am  hungry,  I  hear  a  sound,  I  am 
pleased,  I  am  speaking, —  are  amenable  to  no  laws  or  rules ;  they 
are  final  and  conclusive  of  themselves.  We  cannot  escape  from 
them,  we  cannot  be  more  or  less  convinced  of  them  by  any 
method  of  procedure.  They  are  the  ultimate  data  of  each 
one's  knowledge. 

The  other  class  of  truths,  by  far  the  most  numerous,  are 
known  not  by  direct,  immediate  intuition,  or  consciousness, 
but  by  the  medium  of  some  other  facts,  themselves  immediate. 
That  the  sun  has  risen  is  a  mediate  or  indirect  truth  ;  what  is 
immediate  is  the  sensation  of  light,  and  from  that  immediate 
fact^  we  infer  or  believe  the  other  fact,  *  the  sun  is  above  the 
horizon.'  That  I  feel  cold  is  an  immediate  truth,  that  another 
person  feels  cold  is  a  mediate  inference  ;  the  immediate  fact 
being  certain  sensations  of  sight,  or  of  sound,  with  which  I 
have  learnt  to  connect  the  fact  of  feeling  cold.  All  the  feel- 
ings and  thoughts  of  other  beings  are  known  to  us  in  this 
way. 

Everything  that  is  transacted  in  our  absence  must  be  known 
mediately,  if  known  at  all.  And  as  intuitive  knowledge  is 
confined  to  time  present,  all  knowledge  of  the  past  and  of  the 
future  is  necessarily  mediate. 

Now,  a  mediate  truth  is  properly  an  Inference.  When  a 
thing  is  known,  not  in  itself,  but  by  some  second  thing  related 


-418^1 


IMMEDIATE   OD   INFERRED   TRUTHa 


33 


J^of  •  1  ^I'^'^Y^^^^T^'"'^^  ""^  m^evvedi ;  and  the  immediate 
fact  IS  the  Proof  or  E  vidonce  of  the  fact  so  inferred.  The  fact; 
that  the  air  is  below  32  deg.  Fahrenheit,  is  inferred  from 
the  visible  phenomenon  of  falling  snow;  the  snow  is 
the  medium  of  inference,  the  proof  or  the  evidence  that  the 
air  IS  cold  ;  the  melting  of  the  snow  would  be  the  proof  that 
the  air  is  becoming  warmer. 

All  such  inferences  suppose  a  sure  link  of  connexion  between 
different  phenomena.  If  A  is  the  evidence  of  B,  A  and  B 
must  be  known  as  joined  together  in  the  nature  of  things. 
JMow,  in  order  to  our  assurance  of  such  connecting  links 
certain  processes  ha^'e  to  be  gone  through--namely,  Observa-' 
tion,  Induction,  or  Deduction.  In  performing  these  processes 
we  are  liable  to  commit  mistakes ;  we  need  a  number  of 
precautions  ;  and  these  precautions  are  the  rules  of  Logic. 

As  regards  Immediate  Truths,  no  such  precautions  or  rules 
are  necessary.  The  chief  mistake  that  we  are  liable  to  on 
their  account  (and  the  mistake  is  a  frequent  source  of  error) 
IS  the  confounding  of  an  immediate  truth  with  an  inferred 
truth  We  are  apt  to  say  that  we  are  immediately  conscious 
ot  what  we  only  infer.  The  most  notable  instance  is  our 
belief  that  we  see  distance  ;  whereas,  in  fact  (according  to 
Berkeley  and  the  majority  of  scientific  men),  we  do  but  infer 
distance  ;  our  immediate  consciousness  is  only  of  colour  and  of 
the  tension  and  the  movements  of  ocular  muscles,  which  are 
signs  of  distance,  but  are  not  themselves  the  fact  of  distance. 

Thus,  while  there  are  certain  things,  admitted  by  all  to  be 
matters   of  intuition,   or  immediate   consciousness,  such   as 
our  sensations  and  emotions  in  their  primitive  character;  and 
certain    other    things    equally    admitted  to   be    matters   of 
mference,  or  mediate  cognition,  such  as  the  feelings  of  other 
men,  the  facts  of  testimony,  and  the  generalizations  of  science ; 
—there  is,  as  often   happens,  a  middle   ground,  or   margin,' 
where  intuition  and  inference  are  blended  and  confused,  and 
where  what  is  accounted  intuition  by  one  man  may  be  called 
inference  by  another.     This  happens  with  some  of  the  most 
celebrated  questions.     The  existence  of  the  Deity  is  reckoned 
by  some  to  be  an  intuition,  or  an  immediate  revelation  of 
consciousness,  a  judgment  a  priori;    by  others  an  inference 
from  design,  or  a  judgment  a  posteriori :  while  most  commonly 
it  IS  viewed  as   both   the  one   and  the   other.      Again,  our 
perception  of  a  material  world  is  accounted  an  intuition  by 
Keid  and  Hamilton  ;   while  others  deny  it  to  be  intuitive  in 
Che  sense   intended.      In   fact,   the    controverted    question* 


I 


i 


,tirt. 


34      DIFFEKENT   VIEWS   OF  THE   DEFINITION   OF  LOGIC. 

relating  to   the   Origin  of  our  Knowledge  all  lie  upon  the 
doubtful  margin  of  intuition  and  inference. 

49.  As  Logic  deals  with  truths  of  Inference  solely, 
the  definition  (according  to  Mill,  amending  the  foregoing 
definition),  should  be  '  the  science  of  the  operations  of  the 
understanding  that  are  subservient  to  the  estimation  of 
Evidence.' 

The  estimation  of  Evidence  must  unquestionably  be  accounted 
the  main  function  of  the  Logician.  It  is  his  business  to  lay  down 
the  tests  of  true  and  false,  with  a  view  to  the  establishment  of 
the  true. 

Whether  the  Logician  should  give  suggestions  as  to  dis- 
covery, or  as  to  the  modes  of  arriving  at  suggestions  to  be 
verified  by  the  logical  tests,  is  an  open  question.  Mr.  Mill 
does  not  expressly  include  this  in  his  definition,  but  in  the  title 
of  his  work  he  couples  with  the  *  Principles  of  Evidence  *  the 
*  Methods  of  Scientific  Investigation.' 

50.  In  the  present  work,  Logic  is  viewed — 
First,  as  a  Theoretical  Abstract  Science. 

Secondly,  as  the  Practical  Science  of  Proof  or  Evidenca 
Thirdly,  as  a  body  of  Method  auxiliary  to  the  search 
for  Truth. 

First.  Logic,  as  we  have  seen,  lays  down  the  most  funda- 
mental laws  of  all  affirmation,  and  deduces  inferences  from 
these  laws,  embodying  them  in  suitable  formulas.  In  this 
view,  it  is  the  parallel  of  Mathematics,  being  equally  a  theo- 
retical science,  although  greatly  inferior  to  Mathematics  in  the 
extent  and  variety  of  its  developments  and  apph  cations.  The 
evolution  of  syllogistic  forms  may  be  regarded  as  a  theorizing 
process ;  these  forms  being  systematically  deduced  from  the 
supreme  laws,  or  axioms,  of  Deduction.  From  the  Inductive 
law  of  Causation,  in  like  manner,  are  deduced  inferences,  con- 
vertible into  canons  of  inductive  elimination. 

From  regarding  Logic  in  this  theoretical  aspect,  the  older 
logicians  distinguished  Logica  docens,  the  *  teaching*  and  specu- 
lative side,  from  Logica  uteris,  the  *  guiding '  and  practical  side. 
In  recent  times,  De  Morgan  and  Boole  may  be  considered  as 
exemplifying  the  theoretical  development,  and  as  illustrating 
forcibly  the  parallelism  between  Logic  and  Mathematics — the 
abstract  sciences  by  pre-eminence. 

Secondly.  Logic  is  the  Practical  Science  of  Proof  or  Evi- 
dence.    The  conclusions  of  Theoretical  Logic  are  of  value  in 


LOGIC  AS   THE  SCIENCE  OF  PROOF. 


35 


discnmmatmg  between  truth  and  falsehood,  between  sufficient 
and  insufficient  evidence.  This  is  the  useful  part  of  Syllogism, 
of  Inductive  Elimmation,  of  the  theory  of  Definition,  and  so 
on.  ihe  immense  theoretical  developments  of  De  Morgan  and 
Boole  pass  beyond  the  known  applications  of  Logic  in  the 
present  state  ot  our  knowledge;  although,  like  the  Conic  Sec- 
tions, which  lay  unused  for  two  thousand  years,  these  elaborate 
tormul89  may  one  day  be  turned  to  practical  account 

In  the  present  work,  the  laws  of  Evidence  are  regarded  in 
their  widest  compass,  or  as  embracing  alike  Deduction  and 
Induction.  The  main  reasons  are— that  Induction  is,  properly 
speaking,  the  foundation  of  all  knowledge  ;  that  errors  are 
frequent  m  the  Inductive  processes,  and  are  as  much  amenable 
to  rules  and  corrections  as  errors  of  Deduction;  and  that  the 
utility  of  a  Logic  strictly  confined  to  Deduction  is  comparatively 
small,  so  much  so  that  writers  on  the  science  seldom 
confine  themselves  to  this  department.  (For  a  full  considera- 
tion of  the  confficting  opinions  as  to  the  Province  of  Loffic,  see 
Appendix,  B.)  ^ 

Thirdly.  Logic  is  a  body  of  Method,  or  Procedure.  It  may 
without  impropriety  give  an  account  of  all  known  processes 
that  aid  the  understanding,  whether  in  proving  or  in  evolving 
truth  ;  provided  always  that  these  are  of  a  general  kinc^ 
adapted  to  all  science  or  knowledge  as  such,  and  not  mixed  up 
with  the  technical  specialities  of  the  separate  sciences. 

There  are  various  admitted  uses  of  Logic  that  fall  under 
Method.  One  of  these  is  expressed  by  Hamilton  as  *  the  ren- 
dering explicit  in  the  statement,  whatever  is  implicit  in  the 
thought.'  In  ordinary  reasonings,  there  are  frequent  omissions 
or  ellipses  ;  and  in  cases  of  difficulty  or  obscurity,  these  omis- 
sions need  to  be  supplied. 

The  second  point  belonging  to  Method  is  the  arranging  of 
an  argument  or  chain  of  reasoning  into  the  form  that  best 
discloses  to  the  mmd  its  conclusiveness  or  inconclusiveness. 
Ihis  is  one  great  use  of  the  Syllogism.  But  it  is  not  confined 
to  syllogism.  The  Inductive  canons  give  a  full  and  precise 
account  of  all  the  possible  modes  of  proving  a  fact  inductively  • 
and  by  reducing  any  given  proof  under  its  proper  heads,  we 
see  better  what  it  amounts  to.  By  the  same  canons,  we  are 
also  taught  what  sort  of  proofs  we  ought  to  look  out  for  and 
produce  in  any  given  instance. 

Once  more.  There  are  certain  modes  of  presenting  to  the 
mmd  all  the  known  facts  and  premises  of  a  subject,  such  as  to 
suggest  the  conclusions  involved,  and  to  bring  into  explicit 


36 


DIVISIONS   OF  LOGIC. 


AJiTS   OF  OBSERVATION. 


37 


statement,  what  is  implicit  and  latent.  This  is  a  positive  aid 
to  discovery. 

The  Laws  of  the  Association  of  Ideas  may  be  applied  to 
assist  both  in  Deductive,  and  in  Inductive  discoveries.  The 
great  end  of  Deductive  Science  is,  from  a  given  number  of 
data,  whether  facts  or  principles,  to  evolve  the  greatest  number 
of  truths  ;  and  the  intellectual  forces  are  greatly  assisted  by 
adopting  certain  forms  of  procedure. 

We  shall  resume,  in  a  final  Appendix  note,  all  the  bearings 
of  Logical  Method,  as  an  Art  of  Discovery. 

DIVISIONS  OF  LOGIC. 

51.  In  the  discovery  and  verification  of  knowledge,  there 
are  four  cardinal  operations  ;  one  relating  to  Facts,  and  the 
others  to  the  Generalizing  of  Facts.  They  are,  I.  Observa- 
tion, including  Experiment :  IL  Definition,  or  Abstrac- 
tion ;  III  Induction  ;  IV.  Deduction. 

Observation, 

52.  If  there  were  rules  of  observing  common  to  all 
sciences  and  subjects,  Observation  would  be  a  part  of  the 
Inductive  Logic. 

For  ascertaining  matters  of  fact,  which  must  be  the  ground- 
work  of  all  scientific  doctrines,  we  must  have  recoui-se  to 
Observation  and  Experiment.  As  regards  the  material  world, 
this  supposes  the  exercise  of  the  Senses;  as  regards  the 
Bubject-mind,  it  supposes  Self-consciousness. 

Of  all  the  cardinal  processes.  Observation  is  the  least 
adverted  to  in  Logical  systems.  If  it  were  wholly,  as  it  is  in 
part,  a  matter  of  pure  intuition,  it  must  be  for  ever  excluded 
from  Logic.     In  reality,  however,  it  is  something  more  than 

intuition.  . 

What  we  term  a  *fact,'  or  an  *  observation  is  seldom  an  ab- 
solutely single  or  individual  conscious  impression.  We  speak 
of  the  fact  that  high  water  at  Leith  follows  high  water  at 
London  by  a  certain  definite  interval ;  but  this  is  far  beyond 
any  individual  impression  upon  our  senses.  It  is  a  generahty 
of  considerable  compass,  the  resnlt  of  the  comparison  of  many 
separate  observations.  It  is  a  fact  only  by  reference  to  some 
higher  generality— to  the  laws  of  tidal  succession  over  the 
globe.  There  is  a  process  of  induction  requisite  in  order  to 
establish  such  a  fact ;  and  all  the  securities  for  soundness  in 


the  inductive  proofs  are  called  into  play.  So  the  fact  that  the 
barn-door  hen  brings  forth  her  young  in  the  egg  is  an  induc- 
tive generality  ;  innumerable  observations  have  contributed  to 
its  establishment.  Only,  there  are  generalities  still  wider,  of 
which  it  is  an  individual  constituent;  but  the  difierence  is 
merely  the  difference  of  lower  and  higher  degrees  of  generaliza- 
tion. 

We  come,  in  the  last  resort,  to  observations  that  are  strictly 
individual.  Such  "are  historical  incidents  ;  the  taking  of  Jeru- 
salem was  an  individual  fact.  So,  the  details  of  scientific 
observation  are  individual  acts  of  sense  and  attention.  They 
are  not,  however,  intuitions  ;  for  when  we  say  we  observe  the 
the  needle  pointing  to  the  north,  we  include  with  the  impres- 
sion made  on  our  senses  a  number  of  inferences  from  previous 
knowledge.  It  is  from  previous  knowledge  that  we  know 
we  are  looking  at  a  needle,  and  that  its  direction  is  north. 
The  simplest  observation  is  thus  a  niixture  of  intuition  and 
inference  ;  and  our  habit  of  joining  the  two  is  one  cause  of 
error  in  the  act  of  observing. 

There  must  be  in  all  observation  (of  the  material  world)  an 
exercise  of  the  senses;  accuracy  of  observing  is  accuracy  of 
sense  discrimination.  Now  the  delicacy  of  the  senses  is  partly 
natural,  partly  the  result  of  their  exercise  upon  the  special 
objects.  The  astronomical  observer  is  trained  in  the  observa- 
tory ;  the  physicist  and  chemist  in  the  laboratory ;  the  anato- 
mist in  the  dissecting  room ;  the  naturalist  in  the  field,  or  the 
museum  ;  the  medical  student  in  the  hospital. 

Besides  the  discrimination  by  the  senses,  a  good  observer  is 
trained  to  avoid  delusive  mixtures  of  inference  with  observa- 
tions. He  is  also  indoctrinated  in  certain  artificial  rules  and 
precautious  for  attaining  the  highest  possible  accuracy ;  such 
as  the  repetition  and  comparison  of  observations,  the  striking 
of  averages,  the  elimination  of  causes  of  bias  in  the  instru- 
ments ;  to  these  are  added  certain  mathematical  formulsB  of  Pro- 
bability, which  contribute  still  farther  to  the  certainty  of  observed 
facts.  Still,  these  rules  are,  for  the  most  part,  peculiar  to  the 
different  subjects. 

It  is  in  likd  manner  a  special  accompaniment  of  each  de- 
partment to  know  what  to  observe ;  to  select  from  a  miscellane- 
ous group  the  circumstances  in  point.  The  ongoings  of  a 
nation  are  multitudinous  as  the  sands  of  the  sea  shore ;  the 
politician  or  historian  knows  what  to  fix  attention  upon  and 
to  record  as  political  facts,  the  data  of  political  science.  The 
designations  applied  to  the  power  of  political  observation  are 


* 


% 


..-."  iSLL 


38 


DIVISIONS    OF  LOGIC. 


ANALYSIS. 


39 


'  appropriate  knowledge,  a  sagacions  and  discriminating  judg- 
ment, and  analytical  reasoning.'  No  art  or  rules  can  impart 
the  intellectual  attributes  thus  described. 

Useful  illustrations  might  be  given  of  the  errors  in  observa- 
tion habitually  comn\itted  by  untutored  minds.  Still,  the  best 
training  even  for  general  observation  would  be  a  training  in 
some  one  department.  Every  educated  person  should  know 
something  of  the  practical  manipulation  of  at  least  one  of  the 
sciences  of  observation  or  experiment — such  as  a  Natural 
History  Science,  Physics,  Chemistry,  or  Physiology. 

Certain  logicians,  in  dissenting  from  the  inclusion  of  Induc- 
tion in  the  sphere  of  Logic,  have  remarked  that  the  rules  of 
Induction  must  be  special  to  the  separate  sciences.  This  is  a 
repetition  of  the  remark  just  made  as  to  observation.  But  the 
cases  are  not  the  same.  The  methods  of  Induction  do  not 
differ  in  the  different  sciences,  as  the  methods  of  Observation 
differ.  Induction  in  Astronomy  is  the  same  as  Induction  in 
Chemistry,  in  Physiology,  or  in  Psychology  ;  the  distinctions 
in  the  Inductive  problem  are  distinctions  that  do  not  divide 
the  Inductive  sciences.  There  may  be  a  common  logic  of 
Induction,  although  not  of  Observation, 

Definition. 

53.  Definition  is  a  process  of  generalizcUion,  confined  in 
its  scope  to  a  single  property,  or  a  group  of  properties 
treated  as  a  unity. 

This  is  the  first  and  simplest  of  the  generalizing  processes. 
When  a  number  of  particular  things  are  compared  and  assimi- 
lated on  some  single  property,  as  round,  white,  heavy,  pungent, 
the  result  is  a  notion,  whose  expression  in  any  way  is  Defini- 
tion. The  notion  may  be  complex,  or  may  express  several 
points  of  agreement,  as  for  example  *  life ' ;  but  if  these  are 
given  as  united  or  grouped,  they  are  still  regarded  as  a 
notion. 

The  operation  of  generalizing,  with  a  view  to  the  Notion, 
assumes  a  succession  of  aspects — Classification,  Abstraction, 
General  Naming,  Definition.  We  assume  the  last  as  the  repre- 
sentative designation  of  the  whole  series. 

It  is  in  this  department  that  we  see  the  assimilating  and 
generalizing  process  in  its  simplicity  and  purity.  In  the  de- 
partment next  to  be  named,  generalization  occurs,  but  con- 
joined with  other  operations. 

Reference  v/ill  often  be  made  in  the  sequel  to  the  operation 


il 


designated  *  Analysis ;'  and  as  the  process  is  essentially  allied 
to  the  generalizing  of  the  Notion,  a  brief  explanation  is  hero 
given. 

Analysis  is  an  adjunct  and  a  result  of  Abstraction.  The  sepa- 
ration expressed  by  the  term  is  of  two  kinds.  The  first  is  the 
separation  of  concrete  substances,  as  in  the  analysis  of  a  water, 
which  separates  the  saline  bodies  and  impurities  contained  in 
the  water.  This  is  often  a  very  subtle  operation,  demanding 
extreme  knowledge,  and  delicate  manipulation.  It  is,  how- 
ever, an  actual  separation;  the  constituents  are  laid  hold  of 
and  exhibited  apart.  ' 

The  second  kind  of  Analysis  is  the  analysis  following  on 
Abstraction.  It  is  purely  mental :  the  constituents  cannot  be 
exhibited  apart.  When,  by  abstraction,  we  can  think  of  the 
distinct  properties  named  weight,  liquidity,  transparency, 
retracting  power,  solvent  power,  we  divide,  or  analyze,  in  our 
minds,  the  concrete  called  water  (pure),  into  separate 
properties,  although  these  cannot  subsist  in  separation. 
Water  admits  of  being  classed  in  many  groups  ;  every  classifi- 
cation making  what  is  termed  an  attribute  of  water.  The 
concrete  *  water,'  is  thus  a  complexity,  an  aggregate,  or  a 
compound,  of  many  powers  ;  and  when  these  are  stated 
m  separation,  the  concrete  is  analyzed,  abstractively  or  men- 
tally,  not  really,  "^ 

Analysis  thus  grows  out  of  generalization,  being  merely  a 
phase  or  attribute  of  it.  Every  act  of  classifying  or  general, 
izmg  necessarily  tends  to  abstractive  separation  of  this  nature 
When  we  class  a  shilling  with  round  bodies,  with  white 
bodies,  with  bodies  of  a  certain  diameter,  with  bodies  made  of 
silver,  with  bodies  stamped  as  coin— we  analyze  the  concrete 
shiUing  into  the  attributes  or  abstractions,  round,  white,  size, 
material  constitution,  coin.  * 

In  the  elimination  of  causes,  or  productive  agents,  which  is 
a  part  of  the  Inductive  problem,  a  preparatory  analysis  is 
essential  in  order  to  isolate  in  the  mind  the  various  antecedents 
that  are  to  be  tested.  When  a  certain  impure  water  is  found 
to  produce  disease  the  water  is  analyzed  in  the  first  instance  : 
and  not  till  the  different  substances  contained  in  it  are  found 
out,  can  we  enter  on  the  enquiry  what  particular  ingredient  is 
the  noxious  one.  This  is  to  apply  concrete  analvsis.  Again, 
when  we  enquire  into  the  cause  of  the  slaking  of  "quicklime  by 
water  we  must  analyze  in  our  mind  the  inseparable  properties 
Ot  water :  we  must  distinguish  its  solvent  property  from  its 
chemical  affinity,  and  then  proceed  to  enquire  which  of  these 

3 


4 


40 


DIVISIONS   OF  LOGIC. 


ORDER  OF   TOPICS  IN  LOGIC. 


41 


two,  or  of  any   other  properties,  is  the  antecedent  in  the 


slaking  of  the  lime. 


Induction, 


54.  Induction  is  the  generalization  of  conjoined  proyer- 
ties,  on  the  observation  of  individual  instances. 

In  an  induction,  we  always  deal  with  a  proposition,  op 
concurrence  of  two  facts  or  properties :  as  opposed  to  the 
notion,  which  may  consist  of  a  single  property.  *Iron  takes  on 
the  magnetic  property,*  is  a  proposition  made  up  of  two 
conjoined  notions — iron  and  magnetic  property.  One  of  these 
notions  singly  could  be  defined,  but  could  not  be  matter  for  an 
Induction. 

The  circumstance  common  to  Definition  and  to  Induction  is 
generalization.  A  single  isolated  instance  may  be  a  preposi- 
tional conjunction,  but  not  an  induction.  *  This  magnet  ia 
made  of  iron '  is  not  an  induction :  it  fails  as  being  only  an 
individual  fact. 

The  largest  part  of  scientific  enquiry  consists  in  arriving  at 
these  inductive  generalizations.  The  notion  is  useful  chiefly 
as  the  constituent  of  the  inductive  proposition. 

Deduction. 

55.  Deduction  is  the  application  or  extension  of  Induc- 
tion to  new  cases. 

When  a  general  proposition  is  arrived  at,  the  next  operation 
is  to  bring  it  to  bear  on  new  instances.  By  help  of  the 
inductive  methods,  we  are  satisfied  that  *  iron  is  a  magnetic 
substance ;'  and  we  apply  the  proposition,  as  occasion  requires, 
to  individual  specimens  of  iron.  Thus  the  collective  iron  of 
the  earth  comes  under  the  sweep  of  the  proposition ;  which 
then  indicates  the  cause,  or  a  cause,  of  the  earth's  magnetism. 

It  is  the  Deductive  process  that  has  been  developed  into  the 
forms  of  the  Sylw)QISM. 

Since  Observation  is  not  made  a  part  of  Logic,  the  subject 
is  comprised  under  the  three  heads— Definition,  Induction, 
Deduction.  There  would  be  no  radical  inconvenience  in  ex- 
pounding the  subject  in  this  order,  beginning  with  Definition 
and  ending  with  Deduction.  Probably,  if  Logic  were  now  studied 
for  the  first  time,  or  if  the  science  had  followed  out  its  Socratic 
commencement,  this  would  have  been  Regarded  as  the  natural 


order  Circumstances,  however,  have  led  to  the  inverted  order 
— DeductioD  Induction,  Definition.  Although  Aristotle  himself 
cultivated  all  parts  of  the  subject,  yet  his  chief  labours  were 
concentrated  m  the  Syllogism,  and  his  followers  took  up  this 
department  to  the  total  exclusion  of  Induction,  and  of  Defini- 
tion (as  a  generalizing  process).  In  the  re-introduction  of 
these  omitted  branches,  they  have  been  made  to  follow,  and  not 
to  precede  the  Syllogism. 

Another  reason  for  the  inverted  order  is  the  elementary 
character  of  the  formal  Deductive  process ;  it  being  possible 
to  explain  that  process  without  alluding  to  the  Inductive 
methods  for  attaining  the  general  propositions. 

Under  every  arrangement,  a  preliminary  portion  of  Logic  is 
occupied  with  the  elements  or  constituents  of  knowledge— the 
Notion  and  the  Proposition.     A  fall  account  has  to  be  given  of 
all  the  diverse  forms  assumed  by  these  elements  in  the  varioua 
departments  of  information  or  science. 


ll 


KNOWLEDGE  WITHOUT  LANGUAGE. 


BOOK  I. 

NAMES.  NOTIONS.  AND  PROPOSITIONS. 


CHAPTER    I. 
NAMES  OR  TERMS. 

1.  There  may  be  ^-o^^leige  .without  J^^^l^^^l 
All  the  truths  considered  in  Logic,  are    liuths  expresse 

""th!  knowledge  that  guides  the  lower  animals  is  unconnected 

a  he  '^nowieagev       ^.  ,^    their  senses  the  things  about 

Tu*^      Id  fhe  observationT^e  remembered  in  sensible  forms. 

Tt'^^h  that'^ve:  I^^^^^^^  the  herbage  for  food,  the  ^ima  s 

to  be  preyed  u^n,  are  known  and  sought  after,  by  the  sole 

euidance  of  sense  impressions.  y.   , 

Wnman  beines  have  numerous  experiences  of  the  same  Inna, 

sensible  appearances  and  "^ov^'"^"*^  >  *°  f„^  "^^^'J*"  ' 

the  sieht  of  the  surface  at  once  suggests  the  next  blow. 

Fvfninahiehly  intellectual  profession,  as  the  Practice  of 
Phtfc  The  c£ummation  of  skiU  requires  a  large  sense 
i-nysic,  luB  bevond  the  scope   of  language.       Ihe 

language 'cl  convey,  stored  up.  without  verbal  expression,  in 

*'ffi  It^l^g:,  Wevr'sufficient  for  the  individual,  can 
be  only  toT  very 'limited  degree,  and  with  difficulty,  com- 


43 


^^n.?^  ^-  °*^f ™-  ^  *™**  impression,  strictly  speaking 
.^fv  ^  ^  "^"T*'^,  communicated  at  all.  Indirectlyrone 
individual  can  be  of  use  to  others,  by  bringing  them  witWn 
reach  of  the  objecte  that  they  need  to  knL.°  The  oW  can 
Th^int'  T°^  *°  food,  water,  or  shelter,  in  the  first  i^Lce! 

.^Zi;  ntt   !^f-       "^"emenU,  or  outward  actions,  there  is  the 

n«11  T'^u""'  ^?'"^f^  possessed  by  human  bdngs,  and  t^ 
a  small  extent  by  animals.  °  ' 

Such  communication  is  obviously  restricted  to  personal 
nf  ^'■^nnlf'  ?  '  '^  °u'  ^°  ^parted,  is  lost.     The  tact  and  skill 

The  most  signal  failure  in  communication  unassisted  by 
names,  ,s  in  the  attempt  to  convey  easily  our  discoveries  of 
Z  ■  •  ^  or  resemblance.  In  order  to  teich  another  man  the 
similarity  detected  among  a  number  of  scattered  things,  in  the 
point  of  giving  warmth,  we  should  have  to  direct  his  Attention 
nl=  K  /.  one  after  another,  that  he  might  feel  the  like- 
ness  by  the  actual  comparison.  How  immensely  superior  is 
the  instrumentality  of  the  names-sun,  fire.  aniLd  bodiesi 
„ftw^  ""P  P"""^''  °^  connecting  each  of  these  names, 
r/ln.^  ''°"""°''  ""^^  '  ^°^'  *'^«  discovery  is  made  known 

Oil)  OJlCQt 

This  is  the  primary  fact  constituting  the  value  of  names  in 
general  knowledge.  A  generality  is  a  discovery  of  likeness, 
and  nothing  more  Now,  the  most  rapid  and  ready  mode  of 
nZe  Ihf  '"'^  discoveries  is  to  appTy  to  them  f  common 
name     1  he  name  '  tree   designates  a  feature  of  community  in 

wrln"" w.°^ ^^""^V  "^^ '^' °^ "'^ ^^^  "^'"e « connexion 
with  all  such  things  makes  known  the  community,  the  '  one  in 

the  many  '  of  the  Platonic  philosophy. 

The  higher  operations  of  Reasoning  often  bring  together 
groups  of  these  genei-alities.  A  simple  product  in  multiplica- 
tion-eight  times  nme  makes  seventy-two.-contains  the  fol- 
lowing generahtaes,-e.ght.  nine,  mnltiple.  equality,  seven,  ten, 

ittT^u''^-  .?T  5'*''°"^'^  ^^^"^  ">«''*  be  sevei^Uy  attain! 
able,  by  the  method  of  confronting  the  particulars,  yet,  without 
names  or  signs,  the  union  of  them  in  the  muliplying  operation 
would  surpass  the  power  of  the  strongest  intellect.  By  sense 
alone  we  might  see  that  two  rows  of  three,  joined  in  one 
would  make  the  row  of  six  ,  but  we  would  not  it  a  glance^! 
cover  that  seven  and  eight  would  make  fifteen. 

Ihns  when  truths  are  expressed  in  language,  they  can  not 


M 


t 


1 


-v 


a 


NAMES  OE  TEKM8. 


•\ 


only  be  communicated  and  d^cussed ;  ^^^^T-^^^J^jtS 
»rT^ISnn"o'exprSfed:"at  knowledgeof  any 
V  T.rbeUScted  to  the  tests  and  methods  of  Logic, 
kind  can  be  ^^'^J^.^tea  conveyed  in  language, 

2.  Every  portion  f/r^^^'^?ff  or  disbelief,  takes  the 
everything  propounded  for  beliet  or  a  ,  _ 

form  called,  in  Grammar,  a  Sentence ,  in  i^o^io,  <» 

"a"  Proposition  mentions  two  things,  and  is  therefore 
mide  UD  of  at  least  two  names.  ,,    „  „ 

"t  Inot  impart,  by  ^^i^^ --S^^fs^Z] 
ledge,  without  uttermg  ^l'**;^^^^^";^"  ^  ^eutenie  is  called, 
which  alway s  conUms  a  no^^  and  verb^  A^^^.^^ 

L'l.l'iK/r  The  Subject  is  tbe  thing  spoken  about  ^he 

Predicate  the  ^^j^^^^^Zp'Zii'^t^^C^^  ^^  >  A 
names  '  John,      sun,     wma,      °°      •  j^ber  sentences  m 

give   no   information     they  constitute  ^^^_ 

Grammar,  nor  propositions  in  Logic^     They  nee 
bined,  in  a  certain  way,  .^^l^.  °*f,!/.TX  house  faces  the 
Hhe  sun  shines,'  '  the  wind  ^^  ™'    /^    "ositions.   They 
sea,'-are  pieces  of  information,  ««°^"7%P^°P^„,e  than  two. 

=s;  *  shines/  '^^^-^^^^^^^^^^  words  put  to- 

We  farther  remark  that  any  *J^^^^^.^^  ^  sentence,  a 

getber  do  not  amount  to  an  f  ^/^^^^'.^^.ed  '^         or  false, 
^roposition-somethmg  that  eanj^e  ^^f^f,;^^ 
believed,  or   disbelieved  p    John   tree       sn,^^    ^^^ 

.wind  terror  tempest,'  ^tris  a  peS^  the  wording 

tences  or  affirmauons    J^^^^^.^^^E^^^  J^^^^S 

and   grammar   of  all  i"*^^^^^,  7''  i^^comes   expressive  of 
which   a.  it   f^tion'/rf^^ 
Tow ''  tV^b  w^^i^  b^^^^^^^  others  into  a  sentence ; 

lonstitutes  the  Gapula  of  the  P^o^l^X^ded  merely  into  the 

While  the  Sentence  m  Gfnamar  is  ^^!^^^^^ 
two  parts,-Subiect  .^^^  Pred.^te--^^e^^^^^^^^^      .  i>  ^^^^^^^ 

•is  yellow;'  iu  LopC  ,^^%^^^^!l^r^^^^  and  the 

divided  into  the  attribute  of  the  pi^dicate,    yei       , 


PARTS  OF  THE  PROPOSITION. 


45 


bmdmgr  word  or  copula  *  is ; '  the  attribute—*  yellow*  is  the 
logical  predicate.  A  proposition  in  Logic,  then,  consists  of 
subject  (gold,)  predicate  (yellow,)  and  copula  (is.) 

In  affirmations  containing  but  two  names,  the  copula  is  to 
be  sought  in  the  form  of  the  verb.     *  John  speaks,'  contains 
a  noun  and  a  verb ;  and  the  verb  *  speaks'  has,  of  its  own 
nature  as  a  verb,  the  power  of  affirming.     Neither  two  nouns, 
John  lawyer,'  nor  a  noun  and  an  adjective  'gold  heavy,' 
would  give  any  knowledge  without  a  third  word  as  copula ; 
but  we  have  many  propositions  where  a  noun  and  a  verb  (in 
a  single  word)  contain  a  complete  affirmation,  « baby  walks, 
food  nourishes,'  *  Sirius  twinkles.' 
In  these  last  forms,  we  can  distinguish  subject  and  predi- 
cate  by  our  grammatical  knowledge ;   the  noun   is  subject^ 
the  verb  is  the  grammatical  predicate,  and  unites  in  itself  the 
logical  predicate  and  the  logical  copula  of  affirmation.     Also 
m  such  forms  as  'gold  is  heavy,'  we  are  guided  by  grammar. 
We  know  that  an  adjective,  as  *  heavy,'  is  never  a  subject,  and 
must  therefore  be  the  predicate.     The  noun  can  be  both  a 
subject  and  a  logical  predicate ;— *  gold  is  a  metal,'  *  Csesar  is 
emperor  contain  each  two  nouns,  one  being  subject  and  the 
other  predicate ;  which  is  which  may  be  usually  determined 
in  JLnghsh  by  the  order ;  the  subject  being  given  first.    When 
the  order  is  inverted  for  Rhetorical  effect,  we  must  judc^e  bv 
the  meaning  and  the  context.  .  ^     &       ^ 

The  fact  cannot  be  too  soon  laid  to  heart,  that  the  predicate 
is  usually  larger  in  meaning  than  the  subject ;  it  applies  to 
many  other  things  besides  the  one  spoken  of  at  the  time. 
iTold  IS  heavy,' but  not  the  only  heavy  thing;  'heavy'  ap- 
plies to  other  substances  besides  gold.  '  Woody  fibre  is  not 
tt  to  eat,  leaves  us  free  to  affirm  that  there  are  many  things  not 
tit  to  eat,  as  well  as  woody  fibre.  Hence,  subject  and  predi. 
cate  m  affirmation,  are  7iot  necessarily  co-extensive ;  in  point  of 
tact,  they  are  very  seldom  co-extensive. 

3  There  are  various  motives  or  reasons  for  commencioff 
Logic  with  an  examination  of  Names. 

(1).  It  has  now  been  seen  that  a  Proposition,  the  final  con- 
stituent  of  Logic  the  logical  form  of  all  knowledge,  is  made 
up  of  Names.  The  characters  of  propositions,  therefore,  can- 
not  be  given  without  referring  to  their  component  names. 

(2).  In  the  use  of  Names  are  involved  numerous  sources  of 
error,— pitfalls  and  snares  ;  and  it  is  one  function  of  Loffic  to 
jfive  warning  of  these. 


X 


46 


NAMES   OB.  TEBUS. 


SINGCLAB  AND   GENERAL  NAMESL 


47 


(3).  An  examination  of  the  existing  vocabularies  of  mankind 
is  the  readiest  clue  to  the  universe  of  existing  things.  A 
language,  if  fully  developed,  indicates  all  the  things  that  the 
persons  speaking  it  have  taken  notice  of ;  these  may  or  may 
not  be  everything  that  the  world  contains,  but  they  are  every- 
thing brought  to  light  by  the  combined  observation  of  many 
men  through  many  ages.  Now,  it  is  found  useful,  in  laying 
down  the  scheme  of  a  comprehensive  Logic, — a  code  of  Evi- 
dence and  of  Methods  for  all  kinds  of  knowledge — to  survey 
and  reduce  to  heads  the  whole  universe  of  ascertained  things. 
The  vocabulary  of  the  most  advanced  and  cultivated  people, 
or  of  several  peoples  combined,  is  the  best  available  aid  to  this 
operation. 

In  an  advanced  language,  we  find  names  for  the  heavenly 
bodies,  and  their  revolutions,  and  changes ;  names  for  large 
objects  on  the  earth — sea,  mountain,  river,  Ac. ;  names  for 
separate  material  substances — water,  stone,  iron,  gold,  wood, 
ivory ;  names  for  powers  and  forces, — wind,  weight,  heat ; 
names  for  living  bodies — plants  and  animals ;  names  for  the 
bodily  parts  and  functions  of  human  beings  ;  names  for  men- 
tal functions — pleasure,  pain,  will,  thought;  names  for  the 
social  facts  of  humanity — king,  law,  punishment,  property, 
crime ;  names  for  the  numerous  exercises  and  functions  of 
mankind — husbandry,  trade ;  and  so  on.  Now  the  names  give 
the  clue  to  the  various  objects  named.  Again,  we  have  names 
and  forms  of  speech  indicating  agreement  among  things — 
generic  or  common  words,  as  star,  solid,  heat,  power,  pleasure 
— which  show  us  that  natural  facts  frequently  recur.  Farther 
we  have  names  that  imply  other  names  ; — ruler-subject ; 
up-down  ;  whence  we  learn  that  the  world  contains  mutually 
connected  things. 

4.  A  name  is  defined,  in  the  first  instance,  *a  mark  at- 
tached to  a  thing  to  enable  it  to  be  spoken  about.* 

In  giving  names  to  objects,  the  end  primarily  sought  is 
communication  and  discourse.  Once  invented,  names  have 
the  additional  function  of  aiding  the  solitary  thinker,  in  re- 
calling, fixing,  and  arranofing  his  thoughts. 

It  is  remarked  by  Mr.  Mill,  as  a  corrective  to  the  unguarded 
views  of  Locke  and  others,  that  names  are  the  names  of  Things, 
and  not  of  the  Ideas  of  things.  The  word  *  sun '  is  the  mark  of  the 
object  called  by  that  word,  and  not  simply  the  name  of  our  thought 
or  idea.  To  suppose  that  names  are  names  of  ideas  alone  is  a 
species  of  idealism,  confounding  together  the  object  and  the  sub- 
ject.   The  Thing  itself  (if  an  object)  is  determined  by  our  sensa- 


tions, or  what  we  call  our  experience  of  actuality;  the  Idea  is 
purely  subjective ;  it  is  a  menttd  element  strictly  so  called. 

5.  For  the  purposes  of  Logic,  Names  have  regard  to 
Generality  and  to  Relativity  ;  in  correspondence  with 
the  two  foundations  of  knowledge — Agreement  and  Differ^ 
cnce. 

Names  may  be  variously  classified.  They  may  be  divided 
philologically  into  languages,  as  English,  French,  Hebrew. 
They  may  be  divided  for  rhetorical  purposes  into  plain  and 
figurative  ;  the  figurative  class  containing  species — Hyperbole, 
Irony,  &c., — opposed  to  Logic,  as  departing  from  truth  for 
the  sake  of  the  feelings. 

There  is  also  a  division  of  Names  under  grammar,  namely,  the 
Parts  of  Speech,  which  may  be  looked  upon  as  in  great  part  a  logical 
division.  Thus,  the  Noun  may  be'al ways  the  subject  of  a  proposition, 
and  is  often  a  predicate.  The  Adjective  has  two  logical  functions ; 
— it  may  be,  and  frequently  is,  a  predicate ;  and,  secondly,  it  is  the 
specifying  designation  of  a  genus  expressed  by  a  noun;  man 
(Noun),  genus,  white  (Adjective)  man,  species.  The  Verb  has  the 
important  logical  function  of  affirmation  or  predication ;  there  can 
be  no  proposition  without  a  verb ;  '  fire  hums,  '  honey  is  sweet.* 
The  remaining  parts  of  speech  possess  no  logical  function. 

NAMES  CLASSED  ACCORDING  TO  GENERALITY. 

6.  In  classing  Names,  with  reference  to  Generality  (or 
Agreement),  the  fundamental  distinction  is  between  Singu- 
lar Names  and  General  Names,* 

The  process  of  generalization,  through  the  tracing  of  agree- 
ment, is  a  thoroughly  scientific  or  logical  process.  Now, 
whether  for  a  general  notion  (as  *  liquid  *),  or  for  a  general 
proposition  (*  liquids  find  their  level  *),  the  names  employed  are 

•  In  the  foundations  of  knowledge.  Discrimination  or  Relativity  may  be 
supposed  to  have  the  priority  ;  we  discriminate  first,  and  trace  agreements 
in  difference  afterwards.  On  this  view,  the  classification  by  Relativity 
might  properly  precede  the  classification  by  generality.  In  reality,  how- 
ever, we  cannot  treat  either  without  the  other  being  implicated ;  the 
relative  couple,  light-dark,  is  understood  by  us  only  as  generalized 
upon  many  recurrences  of  the  transition :  we  do  not  go  back,  for  our 
typical  notion  of  the  phenomenon,  to  the  first  occasion  when  we  experi- 
enced the  shock  of  transition,  or  before  we  had  identified  several  recurring^ 
shocks.  There  is,  therefore,  no  special  disadvantage  in  beginning  with 
generality :  we  being  aware  that  there  could  be  no  notion  of  either 
individual  or  general,  without  prior  shocks  of  discrimination  or  relativity. 
Whichever  of  the  two  facts  is  under  consideration,  the  other  must  be 
tacitly  supposed. 


/ 


48 


NAMES  CLASSED  ACCORDING  TO  GENERALITY. 


CONNOTATIVE  NAMES. 


49 


general  names.  Moreover,  the  individuals  that  have  to  be 
identified  and  compared  in  order  to  the  generals,  must  also  have 
their  names  as  individuals, — *  the  Rhine,*  *  the  Caspian  sea.* 

7.  A  Singular  or  Individual  Name  is  a  name  applicable 
to  one  thing.  A  General  Name  is  applicable  to  a  number 
of  things,  in  virtue  of  their  being  similar,  or  having  some- 
thing in  common. 

Xerxes,  Bucephalus,  Sirius,  Teneriffe,  the  Alps,  England, 
Rome,  Notre- Dame,  Koh-i-noor,  are  Singular  names;  they 
designate  each  one  individual  object. 

Man,  horse,  star,  mountain,  kingdom,  city,  building,  gem, 
are  general  names ;  they  apply  each  to  an  indefinite  number 
of  things   having   a   certain  likeness   or   community   among 

themselves. 

The  Singular  Name  may  be  of  various  forms.  One  form, 
exhibited  in  the  above  examples,  is  a  single  meaningless  mark 
or  designation  appropriated  to  the  thing.  *  Xerxes,'  *  Sirius  * 
have  no  function  but  what  might  be  served  by  any  other 
distinctive  utterance  applied  to  the  objects  indicated.  A 
modification  of  this  form  is  seen  in  the  many-worded  designa- 
tions of  individual  men  and  women,  John  Davidson  Ross ; 
Maria  Anne  Louisa  Brown  ;  David  Smith,  of  George  Street, 
York.  A  plurality  of  words  must  be  resorted  to,  because 
John,  Maria,  Brown,  &c.,  are  used  in  naming  a  great  many 
individuals,  and  are  therefore  not  distinctive.  Such  names 
furnish  the  least  possible  information  about  the  persons  named. 
They  do  not  necessarily  indicate  human  beings  ;  horses,  dogs, 
ships,  &c.,  receive  designations  from  the  same  class  of  words. 

Another  form  of  the  siugular  name  is  seen  in  such  examples 
as  *  the  reigning  Pope,'  *  Her  Britannic  Majesty's  minister  at 
Berlin,'  *  the  discoverer  of  America,'  *  the  high-priest  of  Baal,* 
*  the  youngest  of  the  family,'  '  the  pinnacle  of  Europe,'  *  the 
vault  of  heaven.'  These  are  severally  applicable  to  individuals, 
but  they  suppose  previous  generalities,  combined  so  as  to 
restrict  the  meaning  to  definite  individuals.  They  are  signifi- 
cant although  also  singular  ;  and  the  significance  grows  out  of 
the  generalities. 

Collective   names,  as   nation,   army,   multitude,    assembly, 
universe,  are  singular  ;  they  are  plurality  combined  into  unity. 
But,  inasmuch  as  there  are  many  nations,  armies,  assemblies, 
the  names  are  also  general.     There  being  but  one  *  universe, 
that  term  is  collective  and  singular. 

Names   of    Material— earth,    stone,   salt,   mercury,    water, 


flame,-are  singular.  They  each  denote  the  entire  collection 
of  one  species  of  material.  If  Spa^e  and  Time  be  not  regarded 
as  abstractions,  they  fall  under  the  present  class. 

8.  General  Names  are  said  to  be  Connotative ;  that  is 
they  denote  objects,  and  connote  or  imply  attributes    or 
points  of  community  among  objects.  ' 

As  a  mere  mark,  a  name  has  no  power  beyond  simply  denot- 
ing or  pomtmg  out  its  object;  Sirius  suggests  the  star  of 
that  name ;  London  has  no  other  function  than  to  make  us 
thmk  of  the  object  named.  But  the  general  name,  the  result 
of  assimilation,  denotes  the  individuals,  and  coniioies  or  im- 
plies a  certain  similarity  among  them,  in  other  words,  a  com- 
mon  attribute.  The  word  *  star'  denotes  any  star  in  the  firma- 
ment, and  implies  or  connotes  the  similarity  pervading  the 
stars ;  the  word  ^  metropolis '  is  the  name  denoting  London, 
Pans,  Benm,  and  also  declaring  that  all  those  separate  objects 
have  pomts  of  resemblance ;  the  resemblance  is  the  common 

A  n  ^  ^  ^°^®'  ^^^  *^®  connotation  of  the  general  name 

All  Class  names,  therefore,  being  general  names,  are  conno- 
tative names  :— man,  animal,  plant,  tree,  metal,  mountain,  sea. 
kingdom,  government,  factoiy,  circle,  virtue. 

Besides,  the  general  or  class  nouns.  Adjectives  are  to  be  held 
as  connotative  :-for  example,  white,  square,  wise,  virtuous. 
Ihese  are  generalized  names  ;  they  are  given  to  a  plurality  of 
things  agreeing  m  a  certain  way.  They  each  denote  particular 
objects  (the  noun  being  supplied)  ;  they  cmnote  or  imply  a 
community  m  these  objects.  They  are  signifipant  and  not 
meaningless  names. 

Adjectives  are  obviously  products  of  the  generalizing  process 
no  less  than  class  nouns.  The  same  generalization  is  often  ex- 
pressed both  as  a  noun  and  as  an  adjective,— circle,  round  or 
circular  ;  colour,  coloured ;  weight,  weighty. 

The  Umitation  to  this  practice  belongs  to  the  nature  of  the  thmgs. 

w/r'/r''  °^  ^^  ^^i'""*^^"  ^^  ^  ^^^^  *^«  appUcation,  afd 
mcrease  the  meanmg  of  a  noun ;  *  wise  men'  are  fewer  in  nuiiber 
and  more  numerous  m  attributes  than  men.  Now,  in  order  that  a 
noun  may  take  on  the  whole  meaning  of  an  adjective,  that  mean- 
ing must  be  a  hmited  one ;  it  must  be  expressive  of  only  one  or  a 
few  attributes.  *  Men'  can  take  the  quahfications  signified  by  the 
adjectives  'wise;  ^old,'  *  tall,"  virtuous.'     If,  however,  we  were 

,-n  ^T  ^.^f"*'!^  ?r  ^^^  ?.*"'  '  ^°^««''  *^«^«  ^e  no  objects 
m  nature  that  could  take,  m  addition  to  their  own  attributes,  aU 
those  possessed  by  horses.  When  adjectives  are  formed  from  such 
classes-commonly  called  natural  kinds— they  are  used  only  in  a 
select  or  partial  meaning.     '  Golden  '  means  either  made  of  gold 


M 


Ill 


50 


NAMES  OR  TERMS. 


or  possessing  the  salient  and  striking  attribute  of  gold;  'feline* 
signifies  only  one  single  feature  of  the  genus  '  fel ;'  *  human'  is  some 
peculiar  attribute  of  mau. 

Sometimes  a  general  name  is  explained  as  being  the  name 
of  a  class ;  *  man'  the  name  of  the  class  men.     But  the  word 

*  class '  has  two  meanings — the  class  definite,  and  the  class  in- 
definite. The  class  definite  is  an  enumeration  of  actual  indi- 
viduals, as  the  Peers  of  the  Realm,  the  Oceans  of  the  globe, 
the  known  Planets.  The  individuals  of  these  classes  have  a 
certain  likeness  or  common  character  ;  while,  in  addition  to 
this,  they  are  all  known  and  enumerated.  The  question 
whether  a  certain  object  belongs  to  the  class,  might  be  settled 
in  two  ways  ;  first,  by  its  possessing  the  class  likeness,  secondly, 
by  its  being  found  in  the  enumeration.  The  shortest  way  of 
ascertaining  whether  a  given  person  is  a  peer  of  the  realm 
would  be  to  look  for  his  name  in  the  Peerage.  At  all  events, 
this  dispenses  with  the  method  of  judging  by  means  of  class 
marks. 

The  class  indefinite  is  nnenumerated  : — such  classes  are 
stars,  planets,  gold-bearing  rocks,  men,  poets,  virtuous.  These 
classes  contain  individuals  known  and  many  more  unknown. 
There  is  no  complete  list  whereby  to  test  any  supposed  indi- 
vidual. The  sole  criterion  is  the  class  attribute  or  likeness. 
Whether  a  newly-discovered  heavenly  body  be  a  star  or  a  planet 
is  to  be  decided  by  finding  its  characters.  If  it  is  a  fixed  body, 
we  class  it  with  stars,  if  it  circles  round  a  fixed  star,  we  class 
it  with  planets. 

In  this  last  acceptation  of  the  word,  class  name  and  general 
name  are  identical.  The  class  name  denotes  an  indefinite 
number  of  individuals,  and  connotes  the  points  of  community 
or  likeness.  The  genei*al  name  does  the  very  same  thing. 
The  designation  '  wise  men'  is  a  class  name  and  also  a  general 
name.  But  in  the  acceptation  of  an  enumerated  and  finished 
list,  the  class  name  is  not  the  same  as  the  general  name ;  it 
provides  an  additional,  and  exceptional  test  of  the  claims  of 
individuals  to  belong  to  the  class.  *  T hales  is  one  of  the 
seven  wise  men '  exemplifies  the  class  definite  ;  *  Socrates  is 
wise  *  sets  forth  the  class  indefinite,  known  only  by  the  mean- 
ing of  the  general  name. 

9.  The  contrast  designated  by  the  words  '  denote*  and 

*  connote,  *  corresponds  to  Hamilton's  distinction  between 
quantity  in  Extension  and  quantity  in  Covipixhension. 

The  denotation  of  a  general  term,  the  individuals  that  it 


EXTENSION  AND   COMPREHENSION. 


51 


applies  to,  IS  designated  by  Hamilton,  its  Extension,  or  extent 
lUe  denotation  or  Extension  of  the  term  *man'  is  the  whole 
population  of  human  beings.  The  connotation  or  Compre- 
hension is  the  community  of  attributes,  or  points  of  agreement, 
making  up  the  characters,  marks,  or  definition  of  men— animal 
nie,  anatomical  peculiarites,  mental  endowments,  &c. 

Ihe  two  facts— denotation  or  extension,  and  connotation  or 
comprehension— are  reciprocally  opposed ;  the  greater  the  one 
the  less  the  other.     The  term  *  animal '  has  a  greater  denota. 
tion  or  extension  than  the  term  *  man ; '  it  includes  all  men, 
and  the  population  of  brutes  besides.     It  has  so  much  the  less 
connotation,  or  comprehension ;  it  connotes  only  the  points 
common  to  animals,  which  are  much  fewer  than  the  points 
common  to  men  ;-animal  life  in  general,  without  distinctive 
organized  forms.     On  the  other  hand,  the  term  *  wise  men' 
denotes  less,  has  less  extent,  than  the  term  men ;  it  applies 
only  to  a  selection  of  men.     It  connotes  or  comprehends  all 
the  more ;  to  the  connotation  of  men  it  adds  the  attribute  con- 
noted by  *  wise. 

Mr    De  Morgan  has  dwelt  at  great  length,  and  expressed  in  a 
variety  of  forms,  the  distinction  between  Extension  and  Compre- 

HTr??^^^w^*^l*''.^..^fP*^•-^^    ^^«   ^^^^^^^  it   out,   like 
Hamilton,  into  syllogistic  forms. 

r.f^?.  ^^^arJ^s  that  Terms  are  used  in  four  different  senses.    Two 

ot  tnese  he  caUs  objective,  as  directed  to  the  external  object.     The 

nrst  are  terms  expressing  an  individual  standing  alone,  or  out  of 

^rTS'^^'''' ''''  relationship  with  any  other  individual ;  as  John. 

man.     Ihe  second,  the  name  of  an  individual  quality,  forming  part 

of  or  residing  in,  the  individual  object,  as  the  term  •  human,' or  as 

ammal,    when  applied  to  man.      The  author  considers  that  the 

ordinary  syllo^sm  ha^  reference  to  these  terms,  which  he  calls 

terms     of  the  first  intention,'  and  also  arithmetical.      The  usual 

term  of  a  proposition  is  to  declare  some  objects  to  be  mcluded  in. 

or  to  be  excluded  from,  some  other  objects ;  or  to  affirm  or  den? 

of  them  some  quahty  m  the  form  now  stated—'  men  are  animals? 

Jongs  are  human.'  ^^ 

The  two  other  senses  of  Terms  are  called  by  the  author  subjective, 
Ihe  tLTst  18  to  represent  a  class,  or  collection  of  individuals,  named 
after  a  qimlity  common  to  all  :  these  are  Mill's  connotative  class 
names.  The  second  represents  the  attribute  of  the  class  apart,  in 
other  words  the  abstraction  as  conveyed  by  the  abstract  name, 
in  snort,  m  these  subjective  meanings,  explicit  notice  is  taken  of 
the  fact  of  'generaUty'  or  'generalization;'  the  one  in  the 
concrete  and  the  other  in  the  abstract  designation 

It  may  be  remarked  on  the  distinction  between  these  objective 
and  subjective  meanings,  that  it  hardly  involves  any  serious 
diflerence.     Unless  the  objective   terms  were  confined  to  proper 


52 


NAMES  OR  TERMS. 


names,  they  are  terms  having  generality,  and  that  generality 
(perhaps  more  expressly  brought  into  the  foreground)  is  all  that  is 
indicated  by  the  subjective  terms  for  class  and  attribute.  Take 
the  author's  illustration  of  all  the  four — man,  human,  mankind, 
humanity — the  two  first  objective,  the  two  second  subjective ;  the 
difference  between  *  man  '  and  *  mankind  '  is  impalpable  ;    while 

*  humanity  *  is  merely  the  abstract  noun  of  the  adjective  '  human.* 

The  real  distinction  is  between  the  class  and  the  class  attribute. 

For  'extension  and  comprehension,*  Mr.  De  Morgan  employs 
the  terms  'extent'  and  'intent,'  also  'scope'  and  'force.'  He 
farther  draws  attention  to  an  important  distinction  in  the  modes 
of  combining  terms  of  extension  and  terms  of  comprehension  res- 
pectively.    When  terms  of  extension  are  combined,  as  '  man'  and 

*  brute,'  there  is  an  arithmetical  summation  of  individuals ;  this  he 
calls  aggregation.  When  two  terms  expressing  attributes  combine, 
as  'white'  and  'polished,'  it  is  not  an  arithmetical  sum  or 
aggregate,  but  a  joint  inherence  of  quality  in  a  common  subject; 
to  this  he  applies  the  name  composition.  He  remarks  that  we  have 
not  a  good  English  designation  for  the  separate  parts  of  a  com- 
pound in  this  last  sense.  The  word  '  part '  refers  to  extension. 
The  words  '  constituent '  and  *  element '  are  a  nearer  approach  to 
the  idea,  but  do  not  exactly  hit  it. 

Boole,  in  his  system,  expresses  aggregation  by  the  sign  of 
addition,  man  -f-  brute,  x  -f-  y ;  and  composition  by  a  product, 
white  X  polished,  x  y ;  and  conducts  his  manipulation  throughout 
in  conformity  with  these  suppositions. 

10.  The  final  result  of  the  generalizing  process  is  the 
Abstract  Name.  This  is  an  elliptical  form  of  speech, 
highly  useful,  but  also  greatly  abused. 

Such  names  as  motion,  weight,  breadth,  roundness,  white- 
ness, melody,  sweetness,  roughness,  polarity,  wisdom,  justice, 
beauty,  are  called  abstract  names,  as  signifying  qualities  or 
attributes  without  reference  to  the  things  that  possess  the 
qualities.  They  seem  to  separate  the  points  of  community  of 
agreeing  objects,  from  the  objects  themselves,  an  operation 
impossible  in  fact,  and  even  in  thought,  but  supposed,  by  a 
kind  of  fiction,  to  be  possible.  They  give  the  meaning  ex- 
pressed by  the  connotation  of  the  corresponding  class  desig- 
nations— moving  things,  heavy  things,  broad,  round,  white, 
&c.,  but  they  drop  entirely  the  denotation. 

The  abstract  name,  although  occurring  in  all  languages,  is 
not  absolutely  required  for  ordinary  speech  ;  nor  indeed  for 
science.  The  meaning  to  be  conveyed  can  always  be  given, 
although  not  so  shortly,  by  means  of  general  or  class  names. 
The  name  *  motion  *  expresses  what  is  meant  by  *  moving 
things ; '  the  farther  effect  of  it  is  to  limit  the  consideration 


ABSTRACT  NAMES. 


53 


to  this  one  feature  of  the  things  in  question ;  it  amounts  to 
saying  *  moving  things  in  so  far  as  moving,'  or  with  reference 
to  the  one  circumstance  common  to  them  all,  and  not  to  any 
other  circumstance  that  may  attach  to  particular  individuals. 
So  *  justice' expresses  the   same  meaning  as  'just  actions; ' 
the  only  existing  fact  corresponding  to  the  term  is  the  class 
J  just  actions.'     There  is  no  such  thing  in  the  universe  as 
justice  by  itself;  we  cannot  point  to  a  disembodied  justice. 
The  term  signifies  *just  actions,'  with   a  peculiar  stress  or 
emphasis  put  upon  the  features  of  agreement ;  'just  actions  in 
so  far  as  just,  or  viewed  solely  with  reference  to  their  being 
just.'     The  proposition  ^Justice  commands  respect^*  is  the  same 
proposition  as  'just  persons  are  respected  persons,'  with  a 
more  emphatic  indication  than  the  class  names  seem  to  give, 
that  the  causation  refers  solely  to  the  points  common  to  'just 
persons,'  and  to  *  respected  persons.'     *  Just  persons  so  far  as 
just  are  respected  persons  so  far  as  respected.'     *  Beauty  gives 
pleasure '  is  equal  to  '  beautiful  things  (in  so  far  as  beautiful) 
are  things  pleasant   (in   so   far  as  pleasant).'     There  is  no 
'beauty 'in  the  abstract  giving  'pleasure'  in  the  abstract ; 
such  a  supposition  is  the  old  error  of  Realism,  scarcely  yet  ex- 
tinct.    *  Mind  is  the  cause  of  force '  can  mean  only  *  beings 
possessing  mind,  in  so  far  as  possessing  mind,  are  the  cause  of 
moving  things  considered  as  moving.'     'Mind'  is  inseparable 
from  certain  actual  beings  called  persons,  beings  mentally  en- 
dowed, &c. ;  and  '  force  '  is  an  abbreviation  for  moving  things, 
the  cause  of  other  moving  things,  in  so  far  as  moving. 

A  great  power  of  abbreviation  is  given  by  abstract  terms, 
which  is  probably  the  motive  for  introducing  them  so  largely 
into  common  speech.  This  is  apparent  from  the  circumlocu- 
tions necessary  for  avoiding  them. 

The  abuse  of  abstract  names  is  exemplified  in  the  almost 
irresistible  tendency  they  have  to  suggest  the  existence  of 
things  in  the  abstract.  We  are  led  to  suppose  from  the  use 
of  the  terms  Time,  Space,  Mind,  that  there  is  something  in 
nature  called  Time,  apart  from  things  enduring ;  something 
in  Space  different  from  things  extended  and  the  free  move- 
ments of  extended  things ;  something  named  Mind,  distinct 
from  beings  exerting  mental  functions. 

An  important  logical  exercise,  for  detecting  the  fallacies 
nursed  under  abstract  names,  is  to  translate  abstract  proposi- 
tions into  the  equivalent  propositions  made  up  of  general 
names,  not  abstract.* 

•  *  If  the  student  of  philosophy  would  always,  or  at  least  m  cases  of 
jmportancr,  adopt  the  rule  of  throwing  the  abstract  language  in  which  it 


111 


54 


NAMES   OR  TERMS. 


POSITIVE  AXD  NEGATIVE  NAMEa 


>i 


i 


In  contrast  to  abstract  names,  all  general  names,  or  class 
names,  are  termed  Concrete  names  :  they  express  the  agree- 
ment among  things,  not  as  an  impossible  detached  fact, 
but  in  the  actual  state  of  the  case,  namely,  as  the  things  that 
possess  the  agreement.  All  class  nouns,  as  man,  tree,  star, 
and  all  adjectives,  as  brave,  tall,  lustrous, — are  concrete  general 
names.     Every  connotative  name  is  thus  a  concrete  name. 

We  must  not  confound,  as  is  sometimes  done,  a  general 
name  with  an  abstract  name.  A  general  name  is  opposed  to 
an  individual  or  singular  name ;  an  abstract  name  is  opposed 
to  a  concrete  name,  whether  general  or  individual.  Tho 
abstract  *  whiteness  *  is  opposed  to  the  general  designation 
'  wbite  things,'  and  through  it  to  every  particular  white  thing. 

The  Abstract  name  cannot  possess  the  double  function  of  the 
general  name, — denoting  a  thing  and  connoting  the  similarity 
of  things  ;  it  may  be  said,  as  by  Mr.  Mill,  to  denote  the  simi- 
larity, or  the  common  attribute,  and  to  connote  nothing. 
There  is,  however,  nothing  gained,  anywhere  in  Logic,  by  such 
a  designation.  The  Abstract  name  is  the  last  product  of 
generalization ;  alike  the  facility  and  the  snare  of  general 
expression. 

It  is  a  consequence  of  the  generalizing  process  that  there 
should  be  names  of  lower  and  higher  generality,  as  English- 
man, European,  man,  animal,  organized  being  ;  circle,  curve, 
geometrical  figure,  extended  thing.  These  successive  gener- 
alities play  a  great  part  in  science,  and  lead  to  many  technical 
designations  which  have  to  be  considered  in  Logic ;  but  their 
suitable  place  is  in  the  following  chapter,  on  the  Notion,  or 
Concept. 

11.  The  second  group  of  Names,  viewed  for  Logical  ends, 
embraces  those  connected  with  Kelativity. 

The  essential  Relativity  of  all  knowledge,  thought,  or  con- 
sciou.^ness,  cannot  but  show  itself  in  language.  If  everything 
that  we  can  know  is  viewed  as  a  transition  from  something 
else,  every  experience  must  have  two  sides  ;  and  either  every 
name  must  have  a  double  meaning,  or  else  for  every  meaning 
there  must  be  two  names.  We  cannot  have  the  conception 
*  light,*   except  as  passing  out  of  the  *  dark  ;*    we  are  made 

is  80  frequently  couched  into  a  concrete  form,  he  would  find  it  a  powerful 
aid  in  dealing  with  the  obscurities  and  perplexities  of  metaphysical  specu- 
lation. He  would  then  see  clearly  the  character  of  the  immense  mass  of 
nothings  which  constitute  what  passes  for  philosophy.'  (Bailey's  Letters 
on  the  Mind,  vol.  ii.  p.  159.) 


55 


conscious  in  a  particular  way  by  passing  from  light  to  dark, 
and  from  dark  to  light.     The  name  *  light '  has  no  meaning 
without  what  IS  implied  in  the  name  *dark.*  -  We  distinguish 
the  two  opposite  transitions,  light  to  dark,  and  dark  to  light, 
and  this  distinction  is  the  only  difference  of  meaning  in  the 
two  terms;  Might    is  emergence  from  dark;    '  dark  '  is  emer- 
gence from  light.     Now,  the  doubleness  of  transition  is  likely 
to  occasion  double  names  being  given  all  through  the  universe 
ot  thin^ ;    languages  should  be  made  up,  not  of  individual 
names,  but  of  couples  of  names.     When  we  refer  to  the  actual 
ca^e  we  find  a  very  great  prevalence  of  couples,  but  we  can 
hardly  call  it  universal.     We  have  such  instances  as  heat-cold 
motion-rest,  up-down,  light-heavy,  thick-thin,  hard-soft,  rich- 
poor,  lite-death,  parent-child,  ruler-subject ;  and  we  must  en- 
quire how  far  the  system  extends,  and,  if  short  of  universaUtv, 
wtiy  it  is  so.  * ' 

12.  The  great  distinction  of  Names  founded  on  Eela- 
tivity  IS  expressed  by  Positive  and  ^Negative  names. 

tilr  Tw'i^f  ^?S^^?'*^y  '?*?  *^^  principle  of  universal  rela- 
n^Z'  .  ^-P^^,  ^?''*'''^  ^""^  Negative'  is  the  best  we  have,  but 
the  term  'negative'  mclmes  too  much  to  the  idea  of  deficiencv  or  ab 

Now  ft'r ">  -i*^°-*  *^-  P^^ence  of  a  corresprnd^nTopS 
Now  the  negative  of  a  real  quahty  is  as  much  real  as  the  positive  • 

Heat  and  cold,  or  the  transitions  cold-heat,  and  heat-cold,  are 
equaUy  real  or  present  experiences.  ' 

The  terms  ♦  Relative '  and  '  Correlative »  are  also  too  limited  for 
the  purpose ;  they  are  too  much  confined  to  complex  relationships 
as,  parent-child,  teacher-scholar,  mover-moved  "^^^^^ps, 

««i?fi*nf.^  iT  """"^^xf '  *b«  one  most  easily  ad;pted  to  the  univer- 
sahty  of  relation  is  the  first-'  Positive  and  Negative ; '  which  we 
shall  adopt  with  the  understanding  that  <  negative '  haslws  a 

st^JwT'Vr  ^T  ,*^r   'P««iti^e-'     So  Ixplained,  it  may  be 

stretched    to   the^  hole  length   of  universal  relativity.      Under 

Eelative    and  ;  Correlative,'  will  be  explained  certain  special  rel^ 

tionships,   growmg  out  of  the  compUcated  arrangements  of  the 

Mr.  Mill  expresses  the  nature  of  Positive  and  Negative  in 
the  following  terms:-' To  every  positive  concrete  name,  a 
corresponding  negative  one  might  be  framed.  After  ^ivin^  a 
name  to  any  one  thing,  we  might  create  a  second  name  which 
should  be  a  name  of  all  things  whatever,  except  that  parti- 
cuar  thmg  or  things.  These  negative  names  are  empfoyed 
^  henever  we  have  occasion  to  speak  coUectively  of  all  things 
other  than  some  thing  or  cla^s  of  things.     Thus  not^white  dl 


ft 


NAMES   OR  TERMS. 


notes  all  things  whatever  except  white  things  ;  and  connotes 
the  attribute  of  not  possessing  whiteness.*  '  Names  which  are 
positive  in  form  are  often  negative  in  reality,  and  others  are 
really  positive  though  their  form  is  negative.  The  word  in- 
convenient for  example,  does  not  express  the  mere  absence  of 
convenience ;  it  expresses  a  positive  attribute,  that  of  being 
the  cause  of  discomfort  or  annoyance.  So  the  word  unpleasant, 
notwithstanding  its  negative  form,  does  not  connote  the  mere 
absence  of  pleasantness,,  but  a  less  degree  of  what  is  signified 
by  the  word  painful,  which  is  positive.  Idle  on  the  other  hand, 
is  a  word  which,  though  positive  in  form,  expresses  nothing 
but  what  would  be  signified  either  by  the  phrase  not  working,  or 
by  the  phrase  not  disposed  to  work ;  and  sohcr^  either  by  not 
drunk,  or  not  drunken.* 

Thus  far  Mr.  Mill.  Mr.  de  Morgan  carries  the  distinction  to 
the  length  of  a  mode  of  universal  relativity.  He  says : — *  Let  us 
take  a  pair  of  contrary  names,  as  man  and  not-man.  It  is  plain 
that  between  them  they  represent  everything  imaginable,  or 
real,  in  the  universe.  But  the  contraries  of  common  language 
usually  embrace,  not  the  whole  universe,  but  someone  general 
idea.  Thus,  of  men,  Briton  and  alien  are  contraries  :  every  man 
must  be  one  of  the  two,  no  man  can  be  both.  Not-Briton  and 
alien  are  identical  names,  and  so  are  not-alien  and  Briton.  The 
same  may  be  said  of  integer  and  fraction  among  numbers,  peer 
and  commoner  among  subjects  of  the  realm,  male  and  female 
among  animals,  and  so  on.  In  order  to  express  this,  let  us  say 
that  the  whole  idea  under  consideration  is  the  universe  (mean- 
ing merely  the  whole  of  which  we  are  considering  the  parts) 
and  let  n^mes  that  have  nothing  in  common,  but  which  be- 
tween them  contain  the  whole  idea  under  consideration,  be 
called  contraries  in,  or  with  respect  to,  that  universe.  Thus  the 
universe  being  mankind,  Briton  and  alien  are  contraries,  as 
are  soldier  and  civilian,  male  and  female,  &c.  ;  the  universe 
being  animal,  man  and  brute  are  contraries,  &c.' 

Mr.  de  Morgan  here  supplies  what  is  requisite  to  the  pre- 
cise definition  of  Positive  and  Is  egative.  It  is  not  strictly 
correct  to  say  that  *  not- white  *  means  everything  in  nature 
except  white  things  ;  a  more  limited  universe  is  supposed  at 
the  time,  probably  the  universe  *  colour  ;'  and  the  meaning  of 
not- white  is  black,  red,  green,  yellow,  blue,  &c.  Sometimes  a 
still  smaller  universe  may  be  intended,  the  universe  of  white, 
black,  and  the  shades  of  grey ;  the  prismatic  colours  being  ex- 
cluded ;  in  which  case  not- white  means  black  and  grey. 

When  a  term  is  ambiguous,  one  mode  of  rendering  it  pre- 


TJNIVEKSE   OF   THE  PROPOSITION. 


57 


cise,  18  to  name  the  opposite  of  what  is  meant.  The  term 
civil  has  many  meanings ;  ifc  is  opposed  to  natural,  to 
military,  to  ecclesiastical,  to  uncivil  or  discourteous,  and  so  on 
I  he  same  purpose  is  served  by  stating  what  higher  universe  i^ 
present  to  the  mind  of  the  speaker.  If  the  universe  be  the 
condition  of  human  beings  in  relation  to  one  another,  *  civil  * 
means  organized  into  human  society  ;  if  the  universe  be  the 
departments  of  government,  *  civil*  is  known  to  exclude 
military  and  ecclesiastical ;  if  the  universe  be  manners  or  ad- 
dress, civil  IS  understood  in  that  connexion. 

Thus  of  the  three  things— the  universe  or  genus  of  the 
speaker,  the  positive,  and  the  negative- we  cannot  know  one 
witiiout  knowing  the  others.  Any  ambiguity  in  one  is  reme- 
died  by  stating  a  second  ;  it  matters  not  whether  that  second 
be  the  contrary  or  the  entire  universe.  In  common  speech, 
we  are  usually  able  to  assign  the  universe  from  the  context  or 
occasion.  In  discussing  the  origin  of  human  society,  we  see 
that  the  words  *  civil »  and  *  natural '  are  employed  to  divide 
the  universe  of  man's  condition  in  respect  of  society  When 
we  do  not  know  the  subject  of  discourse,  we  are  still  made 
aware  of  what  a  term  means,  if  the  opposite  happens  to  be  ^ven. 
as  *  civil,*  *  not  rude.*  fe      "» 

13.  In  those  cases,  where  a  universe  contains  bnt  two 
members,  the  one  is  the  complete  negative  of  the  other 
This  is  the  most  marked  form  of  contrariety. 

Heat-cold,   light-dark,    high-low,    straight-bent^    good-evil 
pleasure-pam,  virtue-vice,  health-disease,  man-brute,  are  com- 
plete and  emphatic  contraries  ;  the  negative  of  one  member  is 
the  affirmation  of  the  other ;  the  affirmation  of  one,  the  nega- 
tive of  the  other.  ° 

14  When  a  universe,  or  higher  genus,  contains  many 
members,  the  contrariety,  although  no  less  real,  becomes 
amused. 

*  Red  *  in  the  universe  colour  is  not  negatived  by  any  single 
colour,  but  by  a  plurality  of  colours.  Jf  we  are  dividing 
colours  according  to  the  Newtonian  spectrum,  *  not-  red  *  means 
eix  ^colours.  In  a  full  enumeration  of  shades  of  colour,  *  not- 
red  would  be  a  list  of  many  scores  of  individuals.  The 
contrariety  is  then  difiused  and  pointless.  *  Not  an  English- 
man '  leaves  us  in  a  wide  sea  of  possibilities ;  the  universe 
being  natives  of  different  countries. 


r/j, 


68 


KAMES   OE  TEBMS. 


i 


::^i 


15.  Language  contains  various  modes  of  expressing 
opposition  or  negation. 

(1)  In  certain  prominent  instances,  separate  names  are 
given  to  the  contraries ;  as  in  many  of  the  examples  already 
quoted.  Our  language  contains  perhaps  some  hundreds  of 
couples  of  contrary  names  :  young-old,  wise-foolish,  brave- 
cowardly,  rising- falling,  good-evil,  sweet-bitter,  rough-smooth, 
health-disease. 

(2)  There  are  certain  general  modes  of  stating  negation. 
The  chief  is  the  prefix  not : — not-cold,  not- well,  not  a  fish, 
not-metal,  non-electric. 

The  prefixes  *  un,'  *  in,'  and  the  suffix  *  less,'  are  also  used : 
unknown,  incomprehensible  ;  heedless,  blameless. 

The  purpose  is  also  served  by  various  circumlocutions  — 

*  everything  but,*  *  all  but,'  *  all  that  remains  when  one  is 
withdrawn.'  These  last  forms  express  accurately  the  real 
process  of  negation  when  disguised  by  plurality  of  contraries ; 
a  universe  is  assumed,  the  given  positive  is  subtracted  from 
that  universe,  and  what  remains  is  the  negative  or  opposite. 

*  All  the  simple  bodies  except  the  metals '  explains  the  meaning 
of  not-metal,  in  the  universe  *  simple  body.'  *  All  the  parts  of 
speech  except  the  noun,'  is  the  full  renderiug  of  *  not  a  noun,* 

*  not-noun.' 

16.  The  Negative  of  a  real  property  or  thing  is  also  real. 

If  a  negation  be  simply  the  remainder  when  one  thing  is 
subtracted  from  a  universe  containing  more  than  one,  such 
negation  is  no  less  a  positive  reality  than  the  so-called  positive. 
In  fact,  positive  and  negative  must  always  be  ready  to  change 
places ;   positive  up,  negative  dovm ;   positive  down,  negative 

MJ9. 

There  are  certain  circumstances,  where  one  side  seems  to  be 
positive,  by  a  special  propriety  ;  as  when  we  express  fullness, 
abundance,  or  presence,  as  opposed  to  deficiency,  or  absence. 

*  Wealth-poverty,'     *  debt-credit,'     *  plus-minus,'    *  full-empty,* 

*  strong-weak,'  *  living- dead,'  *  knowledge-ignorance,*  *  fruitful- 
barren,'  *  something-nothing,* — these  seem  to  give  us  on  the  one 
side  a  truly  positive  conception,  on  the  other  side,  a  truly 
negative  ;  the  reversal  of  the  terms  would  seem  harsh,  un- 
natural, distorted.  Yet,  in  all  such  cases,  the  negation  is  a 
real  and  definable  phenomenon ;  a  genuine  experience  of  the 
human  mind,  although,  in  most  instances,  a  less  agreeable 
experience.     The  position  of  being  in  debt  is  a  real  fact  or 


THE  HIGHEST  UNIVERSE. 


69 


state,  with  characteristic  features ;  there  is  an  assignable  uni- 
verse,  the  universe  of  pecuniary  circumstances ;  we  subtract 
from  that  total  the  cases  called  being  *out  of  debt,*  *  solvent,* 
and  we  find  as  a  remainder  cases  of  *  being  in  debt ;'  the  two  are 
mutually  opposed  ;  we  might  call  either  positive,  and  the  other 
negative.  Any  awkwardness  in  the  free  transposition  of  the 
epithets  arises  from  the  imperfection  already  noticed  as 
attaching  to  those  epithets,  considered  as  names  for  universal 
relativity.  They  are  frequently  used  with  more  limited  and 
special  associations,  such  as  to  give  a  greater  seeming  pro- 
priety to  the  employment  of  *  positive  '  for  the  conditions  ex- 
pressed by  abundance,  wealth,  credit,  strong,  pleasurable, 
good,  than  to  the  employment  of  *  negative  '  for  those  condi- 
tions. 

The  highest  universe  of  all  must  contain  at  least  two  things, 
mutually  explaining,  and  equally  real.     This  remark  is  neces- 
sary, because  a  fallacy  is  often  committed  by  using  the  forms 
oflanguage  where  there  is  no  longer  a  reality  to  correspond. 
Thus  matter-mind,  or  more  correctly    extended-unextended, 
---object-subject--signify  a  real  couple,  mutually  explaining. 
The  denial  of  matter,  extension,    or  the  object-world,  is  the 
affirmation  of  mind,  the  subject- world.     Up  to  this  point,  we 
are  m  the  region  of  real  and  actual  experience.      There  is  a 
transition  familiar  to  us,  between  certain  states  of  conciousness 
called  matter,  and  other  states  called  mind :   we  know  both, 
by  mutual    contrast;     while  our    knowledge   can    ascend    no 
higher.      Still,  language  can  take  a  flight  beyond.      We  can 
m  words,  sum    these  two  facts  together— mind  and  matter, 
subject  and  object;    we  can  even  use  a  single  term  as  the 
equivalent  of  this  sum— Universe,  Existence,  Absolute;  but  our 
knowledge  is  not  advanced  by  the  step.     There  is  nothing 
correlative  to  the  supposed  universe,  existence,  the  absolute ; 
nothing  affirmed,  when  the  supposed  entity  is  denied.     Matter 
we  can  conceive,  because  of  its  real  opposite,  mind ;  but  *  exist- 
ence '  has  no  real  opposite. 

Granting  for  a  moment,  that  there  were  such  a  thing  as 
non-existence,  to  give  reality  to  existence,  what  is  to  prevent 
us  from  summing  these  two  together,  giving  a  name  to  the 
sum,  and  insisting  on  the  reality  of  this  new  entitv,  with  a 
correlative  reality ;  and  so  on  withoutend  ?  We  must  obviously 
stop  somewhere ;  and  the  proper  point  is  the  highest  couple 
that  generalization  can  carry  us  to.  This  is  to  conform  to  the 
essential  relativity  or  doubleness  of  knowledge.  An  absolute 
unity  IS  not  knowledge,  but  an  unmeaning  phrase. 


60 


NAMES  OR  TERMS. 


RELATIVITY  UNIVERSAL. 


In 


17.  Many  Special  Relationships,  apart  from  nniversal 
relativity,  are  involved  in  the  processes  of  nature,  and  in 
the  relationships  of  living  beings.  From  these,  we  have 
numerous  relative  terms. 

In  the  act  of  communicating  motion,  there  is  a  thing  moving 
and  a  thing  moved,  something  striking,  and  something 
struck.  In  support,  there  is  a  supporter  and  a  thing  sup- 
ported. Attraction  and  repulsion  require  two  things ;  the 
attracting  and  the  attracted.  Heat  and  hght  emanate  from 
some  body  and  operate  upon  other  bodies.  Acid  is  relative 
to  alkali  or  base  ;  both  to  a  neutral  salt. 

Procreation  implicates  parents  and  offspring.  Male  is  cor- 
relative with  female  ;  the  name  *  male '  has  no  meaning  by 
itself;  we  must  understand  *  male  *  and  *  female  *  by  the  same 
indivisible  act  of  intelligence.  The  fact  that  they  express  is  a 
complex  fact ;  both  parties  are  concerned  in  it ;  the  part  of 
one  cannot  be  separated  from  the  part  of  the  other. 

*  Lock  *  and  *  key  *  are  correlative  terms  of  this  kind.  We 
cannot  understand  or  explain  a  key  without  the  mention  of  a 
lock,  nor  a  lock  without  a  key. 

The  complex  structure  of  human  society  contains  many 
situations,  where  two  parties  mutually  enter.  Such  are  sove- 
reign-subject, master-servant,  buyer-seller,  debtor-creditor,  ac- 
cuser-accused, teacher-pupil,  doctor-patient,  churchman- dissen- 
ter. These  are  cases,  not  of  universal,  but  of  special,  relativity, 
and  deserve  to  be  considered  apart  from  the  more  fundamental 
relationships  inherent  in  knowledge. 

All  active  verbs  are  correlative  from  the  very  necessity  of 
their  structure.  An  agent  supposes  something  to  act  upon  ; 
unless  viewed  in  act,  it  has  no  meaning.  A  conqueror  that 
never  conquered  anybody  is  an  absurdity. 

It  is  commonly  said,  with  reference  to  the  great  problem 
of  the  Perception  of  a  Material  World,  that  knowledge  *  sup- 
poses a  mind  knowing,  and  a  thing  known ';  which  is  inter- 
preted as  proving  that  there  is  a  mind  apart  from  matter.  In 
truth,  however,  it  proves  only,  that,  in  the  act  of  knowledge, 
as  in  every  other  act,  there  is  a  mutual  participation  of  two 
things.  Whether  these  things  can  exist  as  separate,  detached, 
and  independent  entities,  is  a  distinct  enquiry. 

18.  The  meaning  of  every  object  of  knowledge  enlarges 
with  the  enlargement  of  its  negatives  or  contraries. 

Gold,'  in  the  universe  *  simple  body  *   means  the  opposite. 


61 


or  exclusion  of  the  other  sixty-two  simple  bodies.  If  ten  more 
elements  be  discovered,  there  will  be  ten  more  exclusions  or 
opposites  *  Health'  to  a  rustic  means  the  absence  of  a  certain 
number  of  familiar  diseases— catarrh,  rheumatism,  dyspepsia 
measles,  &c. ;  to  a  hospital  nurae,  it  has  a  still  wider  meaniuff  ' 
to  an  institutional  writer  on  Medicine,  it  means  the  exclusion 
ot  upwards  of  a  thousand  diseases. 

There  is  no  escape  from  the  principle  of  universal  relativity. 
Intlu'   •Ki°*'  ?X'^'^'}'^^^P^  mentioning  a  thing,  so  aa  to  be 
mtel  gible,  without  implicating  some  other  thing  or  thines 
equally   intelligible.     One  might  suppose  that  a  chair  is  In 
absolute   and  unconnected  fact,  not  involving  any  opposite 
contrary,   or  correlative  fact.      The  case  is  quite   otherwise! 
Ibe   chair  is   immediately   opposed   to   vacuity,  and   to  the 
physical  and  mental  condition  of  the  person  suffering  from  its 
absence.     It  may,  according  to  the  circumstances,  have  a  still 
^eater  compass  of  opposition,  and  so  a  still  wider  meaning  • 
it  may  be  opposed  to  a  table,  a  bed,  a  footstool.     It  may  have 
Btill  farther  oppositions  ;  the  reference  may  be  to  the  universe 
seat  ;  m  which  it  would  be  opposed  to  a  'stool,'  « a  bench,' 
a    sofa      an  ottoman,'  &c.     The  full  meaning  would  then  he 
I  do  not  want  a  *  stool,'  *  sofa,'  &c.,  but  a  ch^ir. 


CHAPTER   n. 

CLASSES,  NOTIONS,  OR  CONCEPTS. 

1.  These  designations  signify  generalization  applied  t» 
single  properties,  or  to  groups  of  properties  regarded  as 
units  or  wholes.  &        v*  a« 

r2^^  *'''°fwl*  ''«°  P^'P^f tions.  ^hich  are  generalized 
cm,.iples,  with  the  affirmation  (or  denial)  of  coincidence. 

We  may  identify  and  generalize  a  nnmber  of  things  under 
a  ungle  pomt  of  comrannity,  as  'round,'  'heat,'  '  polarity ' 
In  the  concrete  these  generalities  are  named  classes— '  round 
thmg^,  'hot  thmgs,'  '  polar  things.'  When  the  point  of  com- 
mnnity   is   spoken  of  vx  the  abstract,— ' roundness, '  'heat' 


I  'l 


62 


CLASSES,  NOTIONS,  OB  CONCEPTS. 


polarity, — the  abstraction  is  called  a  general  notion,  a  general 
concept,  and  often   simply  a  notion,   or  concept ;  the  terms 

*  notion'  and  *  coDcept'  being  regarded  as  more  applicable  to 
a  generalized  property,  than  to  a  single  concrete  objeck  The 
phrase  *  abstract  idea*  is  an  equivalent  expression,  for  the 
common  property  of  a  class. 

It  is  impossible  to  confound  these  classes,  or  notions,  having 
only  a  single  feature  in  common,  with  propositions,  which 
must  have  at  least  two  things.  But  many  classes  have  more 
than  one  feature  in  common ;  as  *  metals,'  which  agree  in  four 
or  five  points.  The  class  '  man  '  has  a  still  greater  number  of 
points  of  agreement.  In  such  instances,  the  distinction  between 
the  class,  or  the  general  notion,  and  the  proposition,  appears 
to  be  done  away  with.  It  no  longer  turns  upon  the  number 
of  common  properties,  but  upon  the  manner  of  expressing  their 
conjunctions.  In  the  class,  the  conjunction  of  the  properties 
in  a  group  is  assumed ;  there  is  no  question  raised,  as  to 
whether  they  are  conjoined.  In  the  proposition,  this  is  treated 
as  open  to  doubt,  and  the  doubt  is  met  by  a  positive  assurance, 
in  the  form  of  a  distinct  affirmation,  backed  up,  if  need  be,  by 
proof  or  evidence. 

The  following  are  examples  of  the  generalized  Proposition, 
involving  two  notions  linked  together  by  affirmation  (or  dis- 
joined by  denial).  *  The  circle  contains  the  largest  area  within 
a  given  circumference  ' ;  *  heat  is  convertible  into  mechanical 
force  ' ;  *  the  metals  are  the  bases  of  salts.*  In  every  one  of 
these  there  are  two  distinct  general  classes  or  notions  ;  the  class 

*  circle*,  with  the  class  or  notion  *  largest  area  in  a  given 
circumference  * ;   the  class  or  notion   *  heat  *  and  the  notion 

*  convertible  into  mechanical  force  * ;  the  class  *  metals  ',  and 
the  class  *  bases  of  salts.'  But  the  existence  of  two  notions 
does  not  exhaust  the  force  of  the  proposition.  There  is  farther 
the  information  that  the  two  in  each  case  do,  or  do  not,  go  to- 
gether. A  hearer  is  supposed  to  be  in  ignorance  or  in  doubt  as 
to  whether  the  notions  *  circle  *  and  *  maximum  of  area  '  are 
coincident ;  and  the  proposition  sets  this  doubt  at  rest,  so  far 
as  affirmation  can  go. 

Obviously,  it  is  only  the  affirmative  or  conjunctive  proposi- 
tion that  can  ever  be  confounded  with  the  double-propertied 
class ;  the  negative  proposition  declares  the  disjunction  of 
things. 

The  nature  of  the  Class,  Notion,  or  Concept,  has  been 
unavoidably  brought  out  under  *  Names,'  and  more  especially 
under  names  grounded  on  generality. 


ONE   OB  MANY  CLASS  FEATURES.  63 

thl  ir^'**''.u"l°^  ^  ^'°S'®'  '^divisible  impression  on  the  mind 
the  things  that  agree  in  it,  and  in  nothing  besides  ar^cL^e' 

a  tint" Teh'  °  """""""^ '  '""'y ^^''^  onl/^'srgleSs 
attribute,      bach   classes   are    numerons.     The   proplrties— 

transparent  hard.  soft,  elastic,  brittle,  long,  sanarefwiaaid 

agreement  there  are  communities  of  thing?  comDrisino- 
these  several  indi.  dual  features,  and  no  others  ,^nd  ZTwf 
all  treated  as  simple  effects.  •  ■' 

vA^^f  ^  ^'^  ''■^f '^'.  *'''™^'^  "P""^  ™«re  than  oue,  but 
yet  not  many,  points  of  community. 

A  good  number  of  classes  have  two  points  in  common  A 
house  IS  (])  an  artificial  erection,  (2)  for  the  purpoTof  ;het 
tenng  hvmg  bemgs  or  things  belonging  to  them  A  u,^r,  I 
(1)  an  assemblage  of  inhabired  building?,  (2)  ^  a  c~n 

•Mt"^^"  example  of  a  triple-propertied  class,  we  may  cite 
in^  Wil7  r'".  ^rrnl  '''■:«^'li«t-g°i«hable  function"!^F^t 
tio^'  .^'"'/°^»«°'-  Chemical  Affinity  has  also  a  triple  M 
heat.'~  proportions,  change  of  properties,  production  of 

The  long  received  definition  of  'Inflammation'  enumerates 
four  properties— Heat.  Redness.  Swelling.  Pain.        ''°™®™'*^ 

,•  ^J^f^^  are  certain  Classes  grounded  upon  a  large  and 

ndefinite  number  of  common  features.    These  are  t'ermed 

by  pre-eminence,  real  Kinds,  Injivue  Species,  lowest  SI 

„(•  *A  ^*  «'°g'enes8,  in  some  of  these  instances,  is  relative  to  the  nanal  ™„rfl 
a  special  „%  Igiren'inlTder/tion^-^L  Se)   "'rAt^J^jl'^ 

W  .n.gle.     In  many  notions,  this  specific  difFerence  fs  complex      ^       ^ 


\ 


Ifi 


64 


CLASSES,  NOTIONS,  OE  CONCEPTa 


GEADES   IN  CLASSIFICATION. 


65 


The  simple  bodies  of  Chemistry — Oxygen,  Sulphur,  Silicon, 
Sodium,  Tin,  Gold,  &c. — have  each  a  series  of  distinctive  pro- 
perties. The  number  actually  known  is  considerable  ;  and 
there  may  bo  many  unknown.  There  are  from  ten  to  twenty 
properties  given  in  the  usual  account  of  Oxygen ;  and  about  as 
many  in  the  description  of  Iron,  and  of  Gold. 

Again,  in  the  Vegetable  world,  we  have  classes  founded  on 
a  great  number  of  common  properties.  The  classes  termed 
*  Species,'  in  the  peculiar  sense  of  Species  in  the  Natural  His- 
tory Sciences,  have  a  great  many  characters ; — many  com- 
mon peculiarities  in  form,  in  mode  of  growth  and  development, 
chemical  products,  &c.  A  full  account  of  the  British  Oak 
would  extend  to  at  least  twenty  or  thirty  characters. 

Still  more  in  the  Animal  Kingdom,  have  we  the  aggregation 
of  many  features  in  the  same  class.  The  properties  common 
to  the  species  *  Elephant '  are  very  numerous  ;  a  full  enumera- 
tion of  the  bodily  and  mental  peculiarities  of  the  species  would 
require  perhaps  fifty  to  a  hundred  designations.  The  common 
properties  of  the  class  *  man '  are  still  more  numerous. 

It  is  in  these  three  great  departments — the  Mineral,  Veget- 
able, and  Animal  Kingdoms, — that  we  have  the  culminat- 
ing instances  of  plural  properties.  The  greatest  complications 
known  apart  from  these  do  not  pass  beyond  a  small  number 
of  properties.  The  most  intricate  disease,  for  example,  can 
usually  be  characterized  by  not  more  than  five  or  six  distinctive 
features. 

5.  Classes  are  of  higher  or  lower  Generality  ;  whence 
arises  a  system  of  Grades,  with  a  nomenclature  expressive 
of  the  relation  of  each  class  to  those  above,  and  to  those 
below  it  The  same  is  true  of  the  corresponding  Abstmc- 
tions. 

The  names  '  genus '  and  '  species  *  express  a  single  step 
of  the  gradation; 

The  class  *  man  *  has  a  certain  degree  of  generality ;  it  is 
co-extensive  with  the  human  race,  and  connotes  or  compre- 
hends the  points  of  similarity  among  human  beings,  the  terms 
of  communion  for  admission  to  the  class.  The  class  *  animal* 
is  still  wider;  including  human  beings  and  a  great  many  other 
members  besides— the  whple  of  what  is  termed  the  *  brutes.* 
The  wider  class  is  called  » genus/  with  reference  to  the  nar- 
rower, the  *  species.'  Bqt  there  are  classes  wider  still ;  *  or- 
ganized beings*  cpn^prise  animals  and   plants  j  and  if  thin 


wider  class  were  termed  a  *  genus,*  animals  and  plants  would 
be  species  under  it.  The  yet  higher  genus  *  material  bodies,' 
would  have,  as  species,  organized  bodies  and  inorganic  sub- 
stances ;  and  so  on. 

Justice  is  included  in  the  wider  class  *  virtue  ;*  virtue  in  the 
still  wider,  « human  conduct.'  *  Reason*  is  a  species  in  the 
genus  intellectual  power ;  *  which  last  is  a  species  in  the 
higher  genus  *  mental  endowment.* 

Circle  is  a  species  in  the  genus  *  curve  line.' 
Geometry  is  a  species  in  the  genus  Mathematics ;  Mathe- 
matics IS  a  species  in  the  still  higher  genus  *  science.* 

If  we  bad  no  other  terms  of  gradation  but  the  two— crenus 
and  species— obtained  from  Greek  philosophy,  we  should 
have  to  keep  shifting  them  up  and  down  the  scale  ;  and  thev 
would  express  nothing  but  the  relationship  of  the  two  classes 
indicated  ;  the  genus  would  always  be  wider  or  more  general 
than  the  species.  But  in  Natural  History,  where  there  is  a 
great  range  of  successive  gradations,  a  series  of  terms  has 
been  adopted  to  correspond  to  the  entire  compass  of  the  scale, 
and  each  is  retained  for  a  distinct  grade ;  *  genus'  and  » species' 
Demg  faxed  at  a  certain  stage,  and  kept  always  the  same.  Man 
horse,  dog,  cat,  are  Species,  and  are  never  anything  else  ;  the 
gmdes  next  above  them  are  Genera  and  nothing  else. 

In  Botany,  for  example,  there  are  four  permanent  leading 
grades,— Classes,  Families  or  Natural  Orders,  Genera,  and 
bPECiEs.  The  Dicotyledons  are  a  Class ;  Banunculaceoe,  is  a 
J^amily  or  Natural  Order;  A^iemone  a  genus;  Anemone  neiiio- 
>-05a  (wood  anemone),  a  species.  In  particular  cases,  inter- 
mediate  grades  are  inserted.  Classes  are  divided  into 
sub-classes;  Natural  Orders,  are  divided  and  sub-divided 
successively  into  Sub-orders,  Tribes,  Sub-tribes,  Divisions,  Sub- 
divisions;  geneva,  into  Sub- genera.  Sections,  Sub  •sections;  Species 
may  have  under  them  Varieties.  The  carrying  out  of  these 
snb-di  visions  to  the  full  would  make  fourteen  grades. 
,  ^?°|?^^»  ^^®  primary  divisions  or  sub-kingdoms,  Verte- 

brata  Mollusca,  &c,are  sub-divided  into  Classes  (as  Mammalia), 
bUB-CLAssEs  (Monodelphia),  Orders  (Primates),  Sub-ordeus 
CbmnadoB),  Genfjra  (Ape),  Species  (Chimpanzee). 

Beyond  the  Natural  History  departments,  and  one  or  two 

other  exact  sciences  of  classification,  as  Diseases,  the  terms 

genus     and  *  species*  retain     their  mobile  character.      In 

Law,  cnme  would  be  a  '  genus '  to  the  particular  kinds  of  crime 

—treason,    murder,   manslaughter,    theft,   libel,  perjury,  &c. 

iCight    is  a  genus  to  the  several  kinds  of  right;  itisaspeciea 


66 


CLASSES,  NOTIONS,   OR  CONCEPTa 


^ 


I 


under  the  higher  genus  *  claim,'  or  requisition.     (G.  C.  Lewifl, 

*  Explanation  of  Political  Terms,'  p.  7). 

6.  On  the  principle  of  Eelativity,  every  class  has  its 
CORRELATIVE  ckss  or  classes ;  every  real  notion  has  a  co- 
relative  notion,  also  real. 

Little  more  needs  to  be  said  on  this  head.  The  principle  of 
Relativity,  if  true  at  all,  must  be  true  without  reservation  or 
exception.  We  cannot  form  a  class,  without  dividing  the 
universe  into  two  halves,  one  half  within  and  one  half  without ; 
when  we  indicate  the  class  *  round'  in  the  universe  *  plane 
figure,'  we  imply  certain  other  figures,  as  triangular,  oval, 
spiral,    &c.,    which  are  the   correlative    group.        The    class 

*  virtue '  supposes  another  class,  according  to  the  universe  of 
the  speaker  ;  if  that  universe  be  actions  relating  to  morality  or 
to  good  and  evil,  the  negative  or  co-relative  class  is  *  vice.'  If 
plants  be  spoken  of,  the  class  to  be  excluded  or  denied,  may 
be  animals,  or  may  be  all  material  bodies.  The  class  *  bitter 
tastes,'  if  in  the  universe  *  sensations  of  taste,'  co-relates  with 

*  sweet,  astringent,'  Ac,  or  all  tastes  except  bitter  ;  if  the 
universe  be  *  sensation,'  the  remaining  sensations  of  taste,  and 
all  the  sensations  of  all  the  remaining  senses,  are  the  correlative, 
the  things  excluded  when  *  bitter  tastes'  are  mentioned,  the 
things  brought  forward  when  bitter  tastes  are  excluded. 

In  like  manner,  every  abstract  idea  must  have  its  correlative 
or  counterpart,  which  must  be  a  reality  if  the  idea  it-self  is  a 
reality.  Length  (in  the  universe  *  dimension  ')  is  opposed  by 
Breadth  and  Thickness.  If  *  justice '  be  a  real  notion,  there 
must  be  a  reality  corresponding  to  injustice.  'Affinity'  is  op- 
posed either  to  *  neutrality  '  or  to  *  repulsion,'  or  to  both.  If 
there  be  a  distinct  meaning  in  *  force,'  there  must  be  some 
distinct  opposite ;  and  the  meaning  changes  as  the  intended 
opposite  changes  ;  it  may  be  force  as  opposed  to  inactivity, 
quiescence,  or  force  as  opposed  to  matter. 

THE  NOTION   UNDER  THE  GUISE   OF  THE   PROPOSITION. 

7.  In  many  instances,  propositions  appear  to  give  know- 
ledge, but  in  reality  do  not ;  the  intention  being,  not  to 
conple  two  distinct  things  in  affirmation,  but  merely  to  in- 
dicate a  Class,  Notion,  or  Concept.  This  is  a  source  of 
much  confusion  and  fallacy. 

In  the  sentence,  *  a  triangle  is  a  three-sided  figure,'  there  i« 


VERBAL  PROPOSITIONS. 


67 


the  form  but  not  the  reality  of  predication;  in  the  sentence 
W^ildTh'  "  l'.'  '^"  ofgreateststabilityV  thereisbo^^^^^^^^^ 

t\TX  ?'  "'•  '^^-  ^^  ^\^''^  ^«^^'  ^^^*  ^«  couple,  by 
the  affirmation,  is  a  name  and  a  thing ;  we  eive  a  lesson  in 

mming,  or  else  give  the  meaning  of  a  name.  ^  In  Ve  second 
case,  we  couple  two  distinct  thin'gs;  we  declare  a  fact  t  the 
inl'of  l^f  ''  "r"^^'  saj^ng  that  wherever  we  find  a  build! 
lT,httlt^n^^^  ^^'^^^  -^  ^^-  ^  «^-^^-^  of  the 

The  instance  first  quoted~a  triangle  is  a  three-sided  figure 
ZFf^^  \  ?'^^  ""^^^^  ^^  predications  in  form;  they  are 
orZt^v'"r  ?^oP°^^*^o^«»'  ^definitions,'  and  also  *  analytical' 
or    exphcative    propositions  or  judgments.     Thus,  *  Justice 

1^%^^"^^  ^"^  T""^  ?°^  *^^^^  ^^^>'  i«  a  verbal  proposition! 
definition,  or  analytic  judgment;  it  tells  us,  that  when  the 
Jact—  giving  any  one  their  due'— occurs,  the  single  word  to 
«ame  i  by  is  /justice;'  and,  conversely,  whef  thlword 
If  tnvl  V'  n '"'T?f '  the  fact  signified  is  otherwise  expressed 

to  «;.]  ?  •  ^^  '3  '^^^  propositions  teach  us  the  name 
to  apply  to  a  given  thmg;  on  the  other  side,  they  t«ach  the 
meaning  of  a  given  name.  ^ 

«f  J^fl'"''''*''''"  u*^^  *^''^  propositions  in  form,  the  proposition, 
dell^  n?  "^'  I"  ^  '""^^  proposition,'  aA  affirmation  (o; 
denial)  of  conjunction,  a  ^  synthetic '  or  *  ampliative  '  proposi- 
tion or  judgment,  a  declaration  of  the  '  order  of  nature  ' 
wi?b  r  «  propositions  that  assert  the  concurrence  of  a  name 
msL.  f  11  •^*''?  °^  resemblance,  there  is  seldom  any 
mistake,     fallacies  do  occur  in  the  more  difficult  and  subtle 

about '^'^r  VJ,,^^*^-'«  -"-g-tions  about  Conscience  and 
tw  f  i  *•  ^^^^.  P^^'°^"  ^  wen  to  be  very  ignorant  of  a 
subject  they  may  fall  into  the  mistake  of  supposing  the 
declaration  of  the  meaning  of  a  name  to  be  the  conjunctfon  of 
two  thmgs,  or  two  fa^^ts.  Such  ignorance  is  beyond  the  scope 
of  Logic,  which  can  only  give  warning  of  the  ambiguous  aid 
deceptive  character  of  the  prepositional  form. 

.nf V      ^^  ""f  ^  *^^  ^^^^''  '^  ^  ^^^^^^  predication.     We  know 
nothing  about  Homer  except  the  authorship  of  the  Iliad      We 
haje  not  a  meaning  to  attach  to  the  subject  of  the  proposition 
Homer,'  apart  from  the  predicate,  ^  wrote  the  iLd.'     The 

Il'^ltRollr^^^  ""'  '"'^  ''^*  *'^  '""''^'^  ^^*^^  ^^-^ 

iJnow'^'"''^ '"  i^ntaught  ability'  is  a  verbal  proposition.     If  it 
unparts  information  beyond  the  use  of  the  word  instinct,  the 


68 


CLASSES,  NOTIONS,   OR  CONCEPXa 


CLASSES  WITH  PLURALITY  OF  ATTIlIBUTEa 


69 


information  consists  in  substituting  a  precise  statement  of  the 
nature  of  instinct,  for  a  vague  and  confused  one.  All  improve- 
ments in  the  defining  of  words  have  the  same  eflPect ;  and  may, 
therefore,  djo  more  than  communicate  a  lesson  in  naminor. 
This  follows  from  the  high  function  of  a  general  name,  which 
assimilates  and  brings  together  widely  distributed  particulars. 

'Instinct  is  hereditary  experience*  (Darwin  and  Spencer),  ia 
a  real  proposition ;  the  predicate  is  an  entirely  new  fact, 
nowise  comprised  under  the  subject. 

'  Conscience  possesses  authority  over  men's  actions,*  is  a 
verbal  proposition.  When  we  enquire  into  the  meaning, 
connotation,  or  definition  of  Conscience,  we  find  that  authority 
is  its  essential  fact ;  take  away  authority,  and  conscience  would 
no  longer  be  present.  There  may  be  many  real  affirmations 
respecting  Conscience.  We  may  declare  it  to  be — a  simple 
faculty  of  the  mind,  a  compound  or  derived  faculty,  the  vice- 
gerent of  the  Deity  in  the  human  mind,  present  in  all  men, 
absent  in  some  men,  absent  in  the  animals,  essential  to  human 
society,  the  highest  dignity  of  man. 

*  Matter  is  inert  *  is  a  verbal  proposition ;  it  only  repeats  the 
essential  quality  of  material  bodies.  Real  propositions  respect- 
ing matter  would  be  such  as  these — Matter  is,  or  is  not,  eter- 
nal ;  is  indestructible ;  is  never  at  rest ;  is  of  many  different 
species ;  gravitates ;  is  endowed  with  numerous  attractions 
and  repulsions. 

*  Governments  are  not  made,  but  grow  *  is  real. 

*  Justice  is  honourable,'  '  virtue  is  lovely,'  are  real  proposi- 
tions, on  the  supposition  that  we  do  not  include  approving 
sentiment  in  our  ideas  of  those  qualities. 

*  Uninteresting  sensations  are  never,  for  their  own  sakes,  an 
object  of  attention,'  is  a  verbal  proposition.  The  predicate 
*  being  an  object  of  attention'  means  the  same  thing  as  the 
subject  *  uninteresting  sensations.*  To  interest  us  and  to  ex- 
cite our  attention  have  scarcely  an  assignable  shade  of  differ- 
ence ;  although  it  may  happen  that  the  use  of  the  designation 
in  the  predicate  may  assist  a  person  little  informed  to  see  the 
full  force  of  the  designation  in  the  subject. 

*  Sovereignty  is  the  authority  of  one  or  more  men  over 
others '  may  be  given  as  the  meaning  of  the  word,  and  is  there- 
fore a  verbal  predication.  All  hypotheses  as  to  the  actual,  or 
the  legitimate,  origin  of  the  sovereign  power,  are  real  predica- 
tions. 

8.  When  a  class  has  several  attributes  in  comraon,  there 


may  be  the  semblance  of  real  predication,  yet  witliout  the 
reality. 

*  A  house  is  made  to  dwell  in'  is  not  a  real  proposition.  *  To 
dwell  in'  is  a  part,  although  not  the  whole,  of  the  meaning  of 
a  house.  Whoever  knows  what  a  house  is,  knows  the  fact 
asserted  in  the  proposition. 

*  Mind  is  intelligent '  is  a  verbal  proposition ;  the  predicate 
repeats  what  is  already  included  in  the  subject.  The  connota- 
fcion,  or  meaning  of  mind,  embraces  Intellect,  together  with 
two  other  functions— Feeling  and  Will.  On  the  other  hand, 
« Mmd  is  coupled  with  a  material  organization '  is  real ;  the 
predicate  is  no  part  of  the  meaning  of  the  subject.  We  do 
not  include  the  material  accompaniment  in  the  explanation  of 
the  word  *  Mind.*     Aristotle  did  include,  in  the  meaning  of 

*  soul '  ^vxq,  the  bodily  organization ;  to  him,  therefore,  *  Soul 
IS  coupled  with  body'  was  a  verbal  or  analytic  proposi- 
tion. ' 

*  Fire  burns  '  is  not  a  real  proposition ;  it  merely  repeats,  or 
unfolds,  the  chief  attribute  of  the  subject.  Our  earliest,  and 
most  persistent  notion  of  fire,  is  the  same  as  is  expressed  by 

*  burning.  *  ^ 

9.  In  the  Natural  Kinds,  verbal  predication  is  still  more 
apt  to  be  confounded  with  real 

A  natural  kind  is  distingished  by  containing  not  one,  two, 
three,  or  four  features  of  community,  but  a  very  large,  indefi- 
nite, and  perhaps  inexhaustible  number — twenty,  fifty,  or  a 
hundred.  Oxygen  has  a  great  many  properties ;  the  aggre- 
gate of  all  these  is  pix)perly  the  meaning  of  the  word.  Oxy- 
gen is  a  gas,  has  a  given  atomic  weight,  combines  with  hydro- 
gen, &c., — are  all  in  strictness,  verbal  or  analytic  propositions. 
Are  they  therefore  useless  or  incompetent  ?  Certainly  not> 
yet  their  form  is  somewhat  misleading. 

The  technically  correct  form  of  these  predications  would  be 
as  follows  .-—There  exists  in  nature  an  aggregate  of  the  follow- 
ing properties: — matter,  transparency,  the  gaseous  form,  a 
certain  specific  gravity,  active  combining  power,  and  so  on  ; — 
to  which  aggregation  is  applied  the  name  *  oxygen.*  After 
the  information  thus  given  is  fully  imbibed  by  the  hearer,  the 
propositions  *  oxygen  is  a  gas,*  *  is  an  active  combining  agent,* 
&c.,  are  verbal,  identical,  or  tautological  propositions ;  the  pre- 
dicates, being  suggested  to  the  mind  when  the  name  ia  pro- 
nounced, are  a  superfluity. 


w 


70 


CLASSES,  NOTIONS,  OR  CONCEPia 


THE  DEFINITION. 


There  are,  however,  certain  circumstances  and  occasions 
when  such  predications  are  not  identical  or  taatological,  but 
real ;  the  predicate  adding  something  to  the  subject  as  under- 
stood by  the  hearer. 

(1.)  A  person  may  be  insufficiently  informed  as  to  the  pro- 
perties of  a  certain  complex  class,  but  yet  may  know  enough 
to  distinguish  the  class.  Most  people  know  that  an  elephant 
is  a  huge  animal,  with  thick  skin,  a  trunk,  and  ivory  tusks. 
In  such  a  state  of  knowledge,  the  affirmation  of  any  one  of 
these  facts  would  be  a  verbal  or  identical  proposition;  it 
would  merely  repeat  one  of  the  facts  already  entering  into 
the  meaning  of  the  word.  But  the  elephant  has  a  great  many 
peculiarities  besides  ;  and  the  communication  of  any  of  these 
would  be  real  knowledge;  they  would  be  *  synthetic*  affirma- 
tive—statements added  to  what  is  already  implied  by  the 
word.  Yet  after  being  communicated,  understood,  and  im- 
pressed in  the  memory,  they  would  cease  to  be  real  predica- 
tions; they  would  henceforth  be  verbal  or  analytic  state- 
ments ;  repeating  what  the  name  now  suggests  or  connotes  to 
the  person  whose  information  has  been  enlarged. 

All  newly  discovered  properties  are  real  predications  on 
their  first  announcement ;  althongh  immediately  on  being 
communicated,  they  become  verbal.  When  Faraday  discovered 
that  oxygen  is  magnetic,  the  intimation  of  the  fact  was  for 
the  moment  a  real  proposition  respecting  'oxygen*.  After 
being  once  communicated,  it  was  no  more  real  than  the 
affirmation  of  any  other  property  of  oxygen. 

(2.)  There  may  be  an  i^iducHve  operation  required  to  ascer- 
tam  the  fact  that  the  properties  of  a  complex  class  or  notion 
do  actaally  go  together  in  nature.  Thus,  Mind  is  defined  by 
the  three  facts— Feeling,  Will,  and  Thought ;— but  this  sup- 
poses a  foregone  induction,  to  show  that  these  three  properties 
always  concur— that  where  there  is  Feeling,  there  is  also  Will, 
and  where  there  is  Will,  there  is  also  Thought.  To  affirm 
that  Feehng,  Will,  and  Thought  are  associated,  is  a  real  pro- 
position. The  definition  of  Mind  tacitly  assumes  that  this 
conjunction  is  established;  hence  Mind  feels.  Mind  wills, 
Mind  thinks,  are  verbal  propositions.  Yet,  since  they  imply, 
when  taken  together,  that  the  three  distinct  facts  are  united  in 
nature,  they  may  be  considered  as  haviog  the  reality  of 
predication  underneath. 

In  like  manner,  the  affirmations—*  Chemical  affinity  is  in 
definite  proportions,  produces  heat,  is  followed  by  change  of 
properties  -are   a   series  of  verbal   or    analytic   affirmations 


71 


ye^  there  is  a  reality  at  bottom;  namely,  that  < union  in 
detinite  proportions  is  conjoined  with  evolution  of  heat  and 
change  of  properties.*  The  name  *  chemical  affinity '  covers  all 
three  facts ;  and  when  used  as  a  subject,  with  any  of  them  as 
predicates,  the  affirmation  is  strictly  verbal  or  identical :  the 
word  already  means  what  is  affirmed.* 

The  cases  now  quoted  diffigr  essentially  from  the  aggregates 
called     kinds  *— mineral,    vegetable,   and    animal    bodies,    for 
reasons  to  be  afterwards  given. 

(3)  The  verbal  proposition  may  be  not  improperly  used  as 
^reminder,  or  by  way  of  referring  to,  or  reciting  a  known  fact. 
VVe  may  say  oxygen  is  the  supporter  of  combustion,*  intend- 
ing only  to  brmg  to  mind  or  to  indicate  that  special  property 
with  a  view  of  making  some  inference  from  it.  It  is  as  tf  wo 
were  to  say— *  inasmuch  as  among  the  aggregate  of  powers  and 
properties  named  oxygen,  one  is  the  support  of  combustion, 
therefore,  &c-*  ' 

10.  The  verbal  proposition  is,  to  a  great  extent,  identical 
with   the  Definition,  which  has  the  form  of  predication 
but  IS  in  substance  coincident  with  the  Class,  Notion  or 
Concept*  ' 

In  definiDg,  we  use  the  form  of  the  proposition  ;— *a  square 

18  a  straight-lined,  four-sided  figure,  with  its  sides  equal,  and 

Its    angles     right     angles;*    *  a   society    is     an     aggregate 

ot   Human    bemgs   under  a  common  government.*     But  the 

alliance  indicated  by  the  affirmation  is  not  between  two  things 

but  between  a  name  and  a  thing,  so  that  all  definitions  ^ 

verbal  propositions;  and  aU  verbal  propositions,  relating  to 

general  words,  serve  the  ends  of  the  definition.    The  examples 

above  given  of  the  verbal  proposition  admit  of  being  expressed 

as  definitions,  in  whole  or  in  part.     *  Matter  is  inert '  may  be 

given  as  the  definition  of  matter.     *  Oxygen  is  a  gas,*  is  part 

ot  the  defimtion  of  oxygen. 

11.  The  Definition,  in  its  full  import,  is  the  sum  of  all 
the  properties  connoted  by  the  name.  It  exhausts  the 
meaning  of  a  word. 

♦Many  words,  from  the  circumstance  of  naming  complex  notiona. 
covertly  affirm  propositions ;    they  cause  it  to  be  supposed  Ihat  the  con- 

r^r'^V^  'T'^  P.^^P^^^^«  ^««  ^^^"  already  ^^erified;  wh^h  may 
or  may  not  have  been  the  case.  The  name  •  substance '  means  a  self- 
hpW  f°?  J'^'  underlying  and  supporting  the  attributes  of  things .  it 
being  taken  for  granted  that  there  is  in  nature  such  a  conjunctio^ 
tlentham  described  certam  names  as  •question-begging  appeUativea/ 
because  they  could  not  be  used  without  assuming  the  tfSth  of  prCsiS. 


S' 


%, 


72 


CLASSES,  NOTIONS,  OE  CONCEPTS. 


The  definition  of  *  Wealth  *  is  a  statement  of  everything  in- 
volved in  the  meaning  of  the  word.  The  definition  of  '  Mind  ' 
exhausts  the  properties  requisite  to  whatever  we  call  a  mind. 

12.  When  a  thing  has  numerous  properties,  as  in  the 
case  of  a  natural  Kind,  certain  purposes  may  be  served  by 
an  unexhaustive  definition. 

(1.)  Instead  of  our  enumerating  all  the  properties  essential 
to  a  kind,  we  may  mention  only  those  that  are  sufficient  for 
discriminating  it  from  other  kinds.  Thus  gold  could  be  defined 
as  yellow,  incorrosible,  and  having  the  specific  gravity  19'34  ; 
there  being  no  other  substance  possessing  the  same  combina- 
tion of  qualities.  Mercury  is  the  metal  that  is  liquid  at 
common  temperatures.  The  banyan  tree  sends  down  numerous 
shoots  which  take  root  and  prop  up  its  branches.  The  ele- 
phant could  be  defined  by  his  trunk  alone ;  this  would  be 
qaite  enough  to  prevent  his  being  confounded  with  any  other 
animal.  Man  could  be  defined  by  the  number  of  his  muscles, 
the  structure  of  his  hand,  or  his  mental  faculties,  all  which  are 
peculiar  to  humanity. 

These  are  the  definitions  that  serve  for  discrimination, 
testing,  or  diagnosis.  Weight  and  colour  together  are  suffi- 
cient to  detect  a  bad  sovereign.  In  chemical  testing,  two  or 
three  properties  are  sufficient  to  identify  a  substance.  There 
are  diseases  known  by  a  single  symptom ;  the  deposition  of 
urate  of  soda  happens  only  in  gout. 

The  sufficiency  of  such  definitions  is  owing  to  the  absence 
of  other  things  possessing  the  same  features.  New  discoveries 
may  take  away  this  advantage.  The  high  specific  gravity  and 
the  colour  of  platinum  failed  as  decisive  tests  when  the  allied 
metals,  osmium  and  iridium,  were  brought  to  light.  If  there 
were  quadrupeds  possessing  the  mental  faculties  of  man,  these 
faculties  would  no  longer  suffice  to  identify  a  human  being. 

(2.)  Such  definitions,  although  unexhaustive  or  incomplete, 
are  yet  essentials  of  the  thing  defined ;  they  are  included 
among  the  marks  or  characters  believed  to  be  inherent  in  the 
thing.  There  may  be  other  characters,  serving  the  purpose 
of  discrimination,  that  are  accidents  and  not  essentials.  Thus, 
it  is  an  accident  of  the  diamond  to  be,  quantity  for  quantity, 
the  most  precious  substance  in  nature.  It  is  the  accident  of 
man  to  be  *  the  paragon  of  animals ;  *  what  we  regard  as  the 
essential  features  of  humanity  would  still  remain,  although  a 
higher  creature  were  to  appear  on  the  earth.  Now,  so  long  as 
these  accidents  are  distinctive,  they  serve  for  a  definition,  in 


GENUS,   SPECIES,   AND  DIFFERENCE. 


73 


tiie  sense  of  a  test ;  they  prevent  the  thing  from  being  con- 
lounded  with  any  other  thing  known  at  the  time. 

If  we  know  a  thing  only  by  such  discnminative  tests,  the 
other  properties,  when  predicated  of  it,  make,  not  verbal  but. 
real  affirmations.  Yet,  aa  soon  as  we  learn  these  additional 
properties,  we  must  regard  them  as  falling  under  the  connota. 
tion  of  the  word.  When  we  are  told  that  diamond,  which  we 
knew  to  be  a  transparent,  glittering,  hard,  and  high-priced 
substance,  is  composed  of  carbon  and  is  combustible,  we  must 
put  these  additional  properties  on  the  same  level  as  the  rest  • 
to  UB  they  are  henceforth  connoted  bj  the  name. 

THE  FIVE  PREDICABLES. 

13.  The  Five  Predicables  relate  to  the  distinction  be- 
tween verbal  and  real  predication.  They  are  Genus, 
(7«/o9),  Species,  (66^09), Di fife rence,  (S^a^opa), Property  (r6^„) 
Accident  or  Concomitant  {aufi^e^rjKo^),  ^     *  ^        ^ 

The  three  last--DiFFERENOE,  Propertt,  and  Concomitant— 
are  the  predicates  strictly  so  called,  as  illustrating  the  distinc- 
tion above  mentioned  The  two  first-^e^.^.^  |nd  species-^ 
have  nothing  to  do  with  predication  in  the  sense  of  the  others. 

Cxenus,  Species,  and  Difference  are  mutually  correlated ; 
each  involves  the  two  others.  We  have  already  given  the 
meanings  of  Genus  and  Species ;  we  have  now  to  add  the 
meaning  of  difference,  which  is  involved  in  these.  The  Dif- 
ference expresses  the  characters  possessed  by  any  species,  over 
and  above  the  characters  of  the  genus.  If  we  suppose  *  wolf  to 
be  ot  the  genus  cani^,  the  characters  belonging  to  the  wolf,  in 
addition  to  those  of  the  genus,  are  the  Diflerence,  Differentia, 
or  specific  difference  of  the  wolf.  In  short,  the  surplus  of  con- 
notation  ot  the  species,  as  compared  with  the  genus,  is  the 
Uinerence.  ° 

•Science'  being  called  a  genns  and  ' chemistry  '  a  species 
under  it,  the  differentm  of  chemistry  is  what  distinguishes  it 
from  other  science,  what  it  has  pecnliar  to  itself,  besides  the 
generic  features  of  a  science. 

inf?r  t^f  It-^  focts-genus,  species,  difference-given  two  we 

\frJ^  •     ^""e""  ^^^  S^°"«  *°<i  *'^^  species,  we  can  tell 

the  difference ;  we  have  only  to  subtract  the  essential  attri. 
bntes  of  the  genus  from  the  essential  attributes  of  the  species. 
^.V.Z  ^^^  «Pf' «?.^°d  the  difference,  we  can  find  the  genus  by 
subtracting  the  difference  from  the  attributes  of  the  specie/ 


u 


CI^SSES,  NOTIONS,  OR  CONCEPTa 


PEOPJUUM. 


76 


Given  the  genus  and  the  difference  we  can  fix  the  species,  by 
adding  the  generic  marks  to  the  difference.  Fine  Art  being  a 
genus,  and  Painting  a  species,  the  difference  is  the  medium  or 
instrumentality  of  colour. 

14.  A  short,  and  yet  complete,  form  of  Definition  is  to 
state  some  higher  genus  of  the  thing  defined,  together 
with  the  specific  difference.  In  popular  language,  defining 
often  assumes  this  form,  and  it  has  been  improperly  re- 
garded by  logicians  as  the  regular  and  only  form. 

Physiology  is  defined  the  Science  (genus)  that  treats  of 
living  or  organized  bodies  (difference).  Poetry  is  a  Fine  Art 
(genus)  having  language  for  its  instrument  (difference). 

Ordinary  speech  being  addressed  to  persons  already  partially 
informed^  it  is  usually  sufficient  to  define  in  this  way.  The  per- 
son wishing  a  definition  of  Physiology  is  supposed  to  be  already 
familiar  with  the  generic  idea  of  science.  If  this  is  not  the 
case,  the  definition  fails.  Science  itself  would  require  defini- 
tion by  reference  to  a  higher  genus  as  *  knowledge,*  and  so  on. 

15.  All  the  attributes  of  the  genus,  and  the  additional 
attributes  of  the  species  (that  is,  the  difference)  are  con- 
sidered to  be  ESSENTIAL  attributes.  They  are  all  included 
in  the  meaning  or  connotation  of  the  nanie.  Hence  the 
affirmation  of  these  makes  a  verbal  (or  essential)  predica- 
tion. 

The  generic  characters  of  *  cams'  and  the  additional  or 
specific  characters  of  the  wolf  are,  by  the  very  nature  of  the 
case,  the  characters  connoted  by  the  terms  *  canis  '  and  *  wolf.* 
To  say  otherwise  would  apparently  be  a  contradiction  in 
terms.  But  the  force  of  the  remark  is  not  brought  out  until 
we  advert  to  the  two  remaining  heads  of  predication, — Pro- 
perty and  Concomitant. 

16.  Property,  or  Proprium,  belongs  to  real  predicatioa 
It  means  an  attribute  flowing  out  of,  deduced  from,  or  de- 
pendent on,  an  essential  character. 

The  meaning,  connotation,  essence,  or  definition  of  a  triangle 
is  a  right-lined  plane  figure  with  three  sides.  There  follow 
from  this  definition,  by  geometrical  deduction,  a  great  many 
propositions  relating  to  the  triangle  ;— as  *  any  two  sides  are 
greater  than  the  third,'  *  the  three  angles  are  equal  to  two  right 
angles.'     These  fall  under  the  head  of  predication  called  *  pro- 


perty or  propmum ;  they  are  not  essential  characters,  although 
derived  from  essential  characters.  They  typify  one  lai-cre 
department  of  real  predication— the  propositions  obtained  bv 
mathematical  inference.  ^ 

Again  •  oxygen  supports  combustion '  is  not  an  essential 
quality  of  oxygen ;  it  is  a  proprium.  It  is  clearly  deducible 
Irom  the  more  general  quality  of  oxygen  expressed  by  its  com- 
binmg  powers  :  it  is  more  immediately  derived  from  the  fact 
that  oxygen  combines  with  carbon. 

From  the  specific  gravities  of  a  number  of  substances  (an 
essential  quality),  we  can  deduce  a  great  many  propria.  Com- 
paring on  the  point  of  specific  gravity,  mercury  with  platinum 
and  gold,  we  infer  that  platinum  and  gold  will  sink  in  mercurv  • 
a  similar  comparison  would  show  that  iron,  tin,  copper,  lead! 
silver,  &c.,  will  float.  These  are  deduced  propositions  or  prol 
pria,  and  not  essences;  they  are  not  generic,  specificf  or 
differential  characters.  »     r  > 

'Fluids  press  equally  in  all  directions'  is  a  proprium;  it 
follows  from  the  definition  of  fluidity. 

The  power  of  speech  is  not  an  essential  or  defining  character 
ot  man  ;  it  proceeds  from  his  other  endowments  of  body  and 
oi  mmd  ;  it  is  b,  proprium. 

We  see,  therefore,  that  to  keep  up  the  distinction  of  essence 
and  property,  it  is  requisite  that  the  essential  or  defining  marks 
of  a  thing  should  be  ultimate  and  distinct,  and  not  resolvable 
into  one  another.  If  a  quality  could  be  shown  to  flow  from 
some  other  quality,  it  would  cease  to  be  an  essential  ordefininc^ 
mark  it  would  be  an  inference  or  proprium.  The  distinctioS 
IS  lost  when  we  mix  up  indiscriminately  ultimate  characters 
with  derived  characters,  as  is  not  unfrequently  done  in  the 
sciences  as  well  as  in  popular  usage.  The  enumeration  of 
the  attributes  of  oxygen,  of  gold,  of  man,  should  be  an  enume- 
ration  of  the  final  (so  far  as  can  be  made  out),  the  underivable 
powers  or  functions  of  each.  ^  ^rivaoie 

The  proposition  *  Man  is  rational'is  a  proprium.  The  ultimate 
analysis  of  man  s  mental  nature,  to  which  *  mtionalitv '  is 
referable,  shows  that  reason  is  not  a  fundamental  operation, 
but  derived  from  the  foundations  of  the  intelligence ;  whence 
this  should  not  be  given  as  part  of  a  scientific  definition  of 
man. 

The  same  may  be  said  of  *  Man  walks  upright ' ;  which  is 
an  easy  inference  from  his  anatomical  structure.  So  also  *  man 
18  a  cooking  animal, '  would  be  an  application  of  a  more 
general  fact— man  is  a  tool-using  animal ;  which   is  itself  » 


.ji^aafe^ 


n  '■ 


76 


•|| 


CLASSES,  NOTIONS,  OR  CONCEPTS. 


derivative  from  his  muscular  endowment  combined  with  hia 
intelligence. 

The  proposition  *  man  is  mortal  *  is  expressly  given  by  Mr. 
Mill  to  exemplify  real,  as  opposed  to  verbal,  predication.  If 
so,  it  is  a  proprium.  To  decide  the  question,  however,  we 
should  have  to  go  back  to  the  mode  of  stating  the  peculiar 
feature  of  organized  beings  that  refers  to  their  germination, 
growth,  and  decay.  Should  the  cycle  of  existence  signified 
by  these  words  be  reckoned  an  ultimate,  or  unanalyzable  attri- 
bute of  living  beings,  mortality  would  be  of  the  essence  of 
men,  as  of  all  animals,  and  all  plants  ;  and  therefore  to  affirm 
it  would  be  a  verbal  or  essential  predication. 

17.  The  Accident  or  Concomitant,  in  Predication,  ex- 
presses something  neither  belonging  to  the  essence  or  con- 
notation of  the  subject,  nor  deducible  from  it.  *  Gold  is 
the  most  valuable  of  the  metals,'  '  is  used  for  the  coin  of 
the  realm ' — are  propositions  where,  the  predicate  would  be 
called  an  Accident  or  Concomitant 

The  real  proposition,  as  opposed  to  the  verbal,  essential,  or 
identical  (Kant's  analytic  judgment),  reaches  its  highest  point, 
in  this  species  of  predication.  It  gives  us  the  full  meaning  of 
Kant's  *  synthetic  judgment,'  where  the  predicate  is  a  positive 
addition  to  the  subject,  and  neither  directly  nor  indirectly  con- 
tained under  it. 

These  affirmations  of  concomitance  are  exceedingly  abund- 
ant in  everyday  practice.  We  are  constantly  finding  about  us 
things  joined  together,  without  mutual  implication.  All  the 
affirmations  respecting  material  bodies  that  deal  with  their 
local  distribution,  their  quantity,  their  uses, — are  affirmations  of 
concomitance ;  we  do  not  include  these  points  in  the  defini- 
tion or  essence.  It  is  the  essence  of  gold  to  be  incorrosible 
(unless  it  were  to  be  found  to  be  derivative,  or  a  proprium)  ;  it 
is  not  the  essence  to  be  used  for  coin,  or  for  ornament ;  still 
less  is  its  occurring  in  California  and  in  Australia.  We  should 
not  think  of  including  these  facts  in  the  definition  of  gold. 
The  specific  gravity  is  an  essential  quality  (to  all  appearance^  ; 
and  doubtless  the  position  in  the  older  and  deeper  rocks  is  a 
consequence  of  this,  and  might  be  called  a  proprium  of  gold. 

The  putting  forth  of  energies  into  actual  display  is  the  occa- 
sion of  propositions  of  concomitance  Socrates  sits,  walks, 
converses,  are  real  predications.  All  the  shifting  usages,  habits, 
and  positions  of  things,  are  in  like  manner  real : — he  is  in  good 


ACCIDENT  OR  CONCOMITANT. 


77 


health  ;  the  mountain  is  covered  with  snow ;  the  crops  are 
ripe. 

Among  the  highest  propositions  of  science,  as  will  be  seen 
afterwards,  there  are  few  predications  of  concomitance. 

18.  A  distinction  is  made  between  separable  and  insepar- 
able  Concomitants.  The  inseparable  Concomitant  is  scarcely 
distinguishable  from  the  Essenca 

The  separable  concomitant  is  what  we  commonly  mean  by 
Accident ;  as  '  gold  is  found  in  California.*  We  see  plainly 
that  this  depends  upon  arrangements  where  other  matters 
besides  gold  are  concerned ;  and  which  might  have  been 
different  without  any  alteration  in  the  qualities  of  gold  itselfl 
That  geese  were  kept  in  the  capitol  of  Home,  was  an  accident, 
a  separable  concomitant,  of  the  goose. 

The  standing  example  of  this  distinction  in  the  old  logical 
books  was  *  Virgil  resides  in  Rome '  (separable),  *  Virgil  was 
born  in  Mantua  '  (inseparable) ;  a  distinction  sufficiently  real, 
but  practically  worthless. 

The  inseparable  concomitant  is  exemplified  in  the  colour  of 
those  animals  whose  colour  has  never  varied  ;  as  was  so  sup- 
posed to  be  the  case  with  the  whiteness  of  the  swan  and  the 
blackness  of  the  crow.  If  we  were  to  ask  why  an  attribute 
always  present  in  a  species,  and  not  known  to  be  a  proprium, 
was  not  adopted  into  the  Essence,  we  should  probably  be  told 
in  reply,  that  the  colour  of  animals  is  an  unstable  property  ; 
it  often  varies  when  everything  else  seems  to  remain  the  same ; 
hence  it  is  usually  left  open  in  assigning  the  marks  of  species. 
The  cases  quoted  justify  the  practice.  Neither  the  whiteness 
of  the  swan,  nor  the  blackness  of  the  crow  is  universal  in  those 
species. 

These  remarks  on  the  Predicables  will  serve  to  bring  out 
into  farther  prominence,  the  distinction  between  Verbal  and 
Eeal  predication. 


Mfl 


GENEKAUTY    OF  PK0P0S1TI0N& 


79 


-I 


Mi 


CHAPTER  m. 
PROPOSITIONa 

1.  The  Proposition  has  been  already  viewed  as  made  up 
of  Subject,  Predicate,  and  Copula. 

In  common  with  names,  and  with  notions;  Propositions 
may  be  classified  (I.)  according  to  Generality,  and  (II.)  ac- 
cording to  Relativity, 

We  now  enter  upon  the  full  consideration  of  the  Real  Pro- 
position,  where  there  is  both  the  appearance  and  the  reality  of 
predication. 

It  is  of  importance  to  view  propositions,  as  we  have  viewed 
names  and  concepts,  with  reference  to  the  two  fundamental 
attributes  of  knowledge — Agreement  and  Difference,  or  Gener- 
ality and  Relativity. 

I.  Propositions  follow  concepts  in  being  of  different  grades 
of  Generality.  *  The  St.  Lawrence  falls  at  Niagara ; '  'all  water 
descends;*  all  terrestrial  bodies  gravitate  towards  the  earth's 
centre ; '  '  the  bodies  of  the  solar  system  gravitate  towards  each 
other  *;  *  all  matter  gravitates  ;* — are  propositions  of  successive 
degrees  of  generality  ;  each  takes  a  wider  sweep  than  the  pre- 
vious, till  we  reach  the  widest  of  all.  *  People  should  be  taught 
not  to  take  cold' — 'to  take  care  of  health,'  'to  he  prudent^'  'to  he 
virtuous,' — are  four  propositions  rising  in  generality. 

It  is  obvious  that  the  generality  of  the  Proposition  follows 
the  generality  of  the  concept  or  notion.  Any  proposition  re- 
specting the  Earth,  is  merged  in  a  proposition  respecting  the 
planets  ;  a  proposition  respecting  the  Planets  is  less  general 
than  one  respecting  Heavenly  Bodies.  The  more  general  the 
concept  forming  the  subject  of  a  proposition,  the  more  general 
the  proposition  :  *  men,  animals,  organized  beings, — are  liable 
to  disease.* 

The  law  of  inverse  relationship  of  Extension  and  Compre- 
hension— Denotation  and  Connotation,  applying  to  the  notion, 
applies  also  to  the  proposition.  The  most  highly  generalized 
propositions  are  those  that  have  the  smallest  predication ;  the 
extent  is  gradually  lessened  as  predication  is  increased.     We 


Bay    all  maVer  is  indestructible  ;*  but  when  to  the  property  of 

indestructibility  we  add  the  property-unchangeable  in  state 

(as  regards  solid,  liquid,  gas)— we  have  to  limit  the  subject  to 

a  tew  bodies,  as  to  the  (hitherto)  uncondensihle  gases  and  to 
carbon*  *' 

II.  Propositions  come  under  Relativity,  in  this  respect, 
namely,  that  to  every  proposition  there  exists  a  correlative 
jDropo8ition,  something  denied  when  it  is  affirmed.  '  Europe 
lies  north  of  the  Equator  *— *  Europe  does  not  lie  south  of  the 
i^quator ;  *  friendship  is  pleasure '— *  friendship  is  not  painful 
nor  indifferent.' 

•  ."^f— Vi*^""*  *^®  proposition  follows  the  notion.  To  every 
intelligible  notion,  there  is  an  intelligible  opposite-something 
that  remams  when  the  notion  is  subtracted  from  the  universe : 
south  is  opposed  by  north  (universe  '  north  and  south ') ;  plea- 

..f  VJm^  circumscription  of  general  maxims,  with  reference  to  actual  cases 
of  practice,  is  thus  effected  by  adding  the  circumstances  of  the  given  case, 

limited  set  ot  hypothetical  data,  and  the  more  limited  they  are  the  more 
abstract  18  the  theorem  The  intensity  varies  inversely  with  the  extent  of  its 
B3gni6cation.  Nov  a  theoretical  proposition,  when  converted  into  InUe  of 
conduct,  may  be  conceived  as  taken  in  connexion  with  an  indefinite  number 
ot  sets  of  concomitant  circumstances,  which  may  modify  its  operation.  J£ 
theielore,  we  add  a  definite  number  of  circumstances  to  the  proposition,  we 
exc  ude  all  uncertainty  as  to  the  possible  combinations,  and  we  in  fact 
riinftT^*  ^""^^-f  P^i>?^l  «i*?"»^  *n/lntti.  We  substitute  a  real  and 
definite  lor  an  ideal  and  indefinite  compound.  The  addition  of  a  hmited 
number  of  terms  operates  as  the  exclusion  of  an  unlimited  number. 

Thus,  let  It  be  supposed  that  our  general  theorem  is  as  to  the  operation 
of  legal  punishment.    Legal  punishment,  if  left  to  itself,  may  be  expeS 

Ip^h^fH  -^^'^  w- ""  fr«°^«"°»«J  but  it  may  be  accompanied  as^ 
were,  held  in  solution  by  a  vast  variety  of  collateral  circumstances  wWch 
may  influence  its  operation.     Thus,  it  may  be  combined  with  an  inefficient 

Setectfon    i^'^r'  '  ^'°^^'  ''  *"'^^  administration  of  justicerdiSy  of 
detection,  unwilhngness  to  prosecute  or  to  give  evidence   or  a  fanatical 
contempt  of  suffering.      Various  other  circumstances  mfghtJike^^^^ 
mentioned  which  diminish  the  deterring  force  of  the  fear  of  legal  Zlh! 
ments  on  the  minds  of  given  individuals.     Now,  all  that  can  b!  saTwi^ 
reference  to  such  a  general  theorem,  so  long  as  it  remains  Tnab^raction 

fie?t^t'""r"-rr^"^"^  ^"^^°^^>  ^^^^^«  to  S^  i^sisteV^^^^^^^ 

Hed  by  an  unlimited  number  of  counter-influences  wif).  «,^-t  i  i 
punishment  may  be  combined.  But  when  In  actuXa  J  !^  -h^'"?  ^^^^ 
we  can  perceive  whether  any  is,  and  wkTcrof  those  othi  n'^  ^^^T  '''' 
are  present.  Of  such  as  are  wanting  we  take  no  ^1  .  circumstances 
which  are  discernible,  and  we  then  fo^  a  d.ffn^t«  °>  V  "^v*f  ^^""^ 
this  shape:  'How  will  the  denuLiSn  oMegal  S^^^^^^^^ 
taken  in  connexion  with  a  reluctance  of  wTtneesesL  i^^v«'  "S'"^  ""^'"^^ 
a  willingness  of  judges  to  take  bribes  (arthe  case  mfHr?'  'f^V^^'.^^^^^ 
be  the  effect  of  legal  punishment,  combined  ^UaToL.f  '  ^-^^  ""^ 
disregard  of  pain,  of  some  special  ascertained  nat^o?-      iT  Le^^iS'  ' 


80 


PROPOSITIONS 


Bure  is   opposed  by  the  two   states— pam   and   indifference 

(universe  *  feeling*).  ^  ,.    1 1      i-i     j.    j.u 

These  two  fundamental  distinctions,  applicable  alike  to  the 
Notion  and  to  the  Proposition,  being  presupposed,  we  proceed 
to  the  various  classes  of  Real  Propositions  that  have  a  bearing 
on  Logic.  The  primary  division  is  according  to  External 
Form, 'and  according  to  Import,  or  Meaning,  in  the  final 
analysis. 

The  term  *  Judgment '  is  used  in  most  logical  treatises  to  desig- 
nate the  proposition.  A  proposition  is  stated  to  be  *  a  judgment 
expressed  in  words  ;'  and  Judgment  is  termed  the  mental  operation 
whereby  we  pronounce  two  things  to  agree  or  disagree.  When  we 
affirm  a  mountain  to  be  four  thousand  feet  high,  we  pronounce  the 
aoreement  of  the  height  of  the  mountain  with  the  lineal  quantity 
denominated  four  thousand  feet ;  we  of  course  imply  the  disagree- 
ment with  any  other  quantity  more  or  less. 

It  may  be  remarked  on  this  employment  of  the  word  Judgment, 
in  connexion  with  the  proposition,  that,  in  the  view  of  Aristotle,  it 
had  a  real  significance.  Aristotle  took  account  of  the  aubjedtve 
element  of  affirmation,  the  implication  of  the  individual  mmd  of 
the  affirmer  in  the  process.  When  I  say,  *  the  earth  is  round,  the 
full  import  is  that,  according  to  my  behef ,  conviction,  or  judgment, 
the  earth  is  round  ;  or  I  believe  that  the  earth  is  round.  I  speak 
only  for  myself.  I  cannot  undertake  to  say  what  other  people 
believe,  unless  they  tell  me ;  and,  apart  from  all  behef,  the  propo- 
sition has  no  meaning,  no  existence. 

For  almost  all  practical  purposes,  this  indispensable  correlate 
may  be  left  in  a  tacit  condition.  Being  always  presumed,  it  need 
not  be  mentioned.  In  many  other  cases,  we  suppress  the  mention  of 
what  we  can  always  count  upon,  as  for  example,  gravity.  We  do 
not  say  that  a  certain  weight  will  maintain  the  movement  of  a 
clock,  provided  gravity  continue  to  operate ;  we  take  this  for  granted 
without  specifying  it.  But  there  are  occasions  when  the  correlated 
subject  in  affirmation  needs  to  be  brought  into  view ;  as  when 
metaphysicians  declare  that  there  can  be  objective  truth  without  a 
subject ;  and  when  certain  opinions  are  sought  to  be  imposed  by 
force,  as  absolute  and  infalUble.  '. 

Apart  from  this  circumstance,  the  term  Judgment  is  not  the 
most  apposite  word  for  expressing  the  formation  of  propositions. 
The  function  of  a  judge  may  require  propositions  to  be  stated ;  but 
more  usually  it  consists  in  discerning  the  agreement  or  disagree- 
ment of  a  proposition  with  a  given  case  ;  as  in  the  interpretation  of 
the  law.  The  faculties  needed  for  arriving  at  propositions  are  much 
more  extensive  than  is  meant  by  judgment ;  the  processes  of  obser- 
vation,  classification,  induction  and  deduction,  bring  mto  play 
the  senses  and  the  intellectual  powers  in  their  widest  scope. 

It  is  incorrect  and  misleading  to  describe  a  proposition  as 
<  judging  two  notions  to  be  congruent,*  *  conceiving  them  as  one  * 


QITA.NTITY   OF  PROPOSITIONa 


81 


(Hamilton).  All  that  a  proposition  can  do  is  to  link  together  two 
facts  (as  *  fluid '  and  *  level '),  it  does  not  in  any  sense  make  them 
one  fact,  or  bring  the  one  under  the  other. 

EXTERNAL  FORM  OF  PROPOSITIONS. 

2.  Propositions  aie  either  Total  or  Partial,  which  dis- 
tinction is  expressed  by  the  word  Quantity. 

Universal  and  Particular  are  the  names  most  used, 
although  not  the  aptest,  for  signifying  this  division. 

When  the  predicate  is  true  of  the  subject,  in  its  whole 
extent,  or  in  every  instance,  the  proposition  is  total  or  universal 
in  quantity  ; — *  all  the  planets  are  round  ';  *  all  the  virtues  are 
useful ';  *  all  coal  is  the  product  of  ancient  vegetation*. 

When  the  predicate  is  true  of  the  subject,  only  in  part  of  its 
extent,  or  in  an  indefinite  number  of  instances,  it  is  partial  or 
particular  in  quantity : — '  Some  planets  are  larger  than  the 
earth  ;'  *  some  of  the  virtues  are  painful  in  the  performance ;' 

*  some  coal  is  useful  for  making  coal  gas  * ;  *  some  men  are 
wise' ;  *  some  metals  are  incorrosible* ;  *  some  crystals  are 
transparent* ;  *  some  diseases  are  incurable.* 

The  usual  designations  for  total  or  universal  quantity  are 
*A11'  and  *  Every.*      *  All  earths  are  oxides  of  the  metals*; 

*  every  man  is  expected  to  do  his  duty.*  There  is  a  rhetorical, 
but  no  logical  distinction,  between  the  two ;  *  every  *  has  the 
emphasis  of  greater  individuality.  *  All '  is  sometimes  ambigu- 
ous ;  it  may  be  used  in  a  collective,  as  well  as  in  a  distributive 
sense ;  *  all  England  *  may  mean  the  whole  nation  in  a  col- 
lective capacity,  and  not  *  every  Englishman.*  ' 

Universal  quantity  is  sometimes  given  in  less  explicit  forms  : 
— '  The  earths  are  oxides,*   *  evil-doers  need  to  be  punished,* 

*  man  is  frail,*  'pleasure  tempts,*  'alcohol  is  a  stimulant,* — are 
understood  to  be  universal,  although  they  have  neither  the  de- 
cisiveness nor  the  emphasis  of  the  other  forms. 

The  term  of  Partial  or  Particular  quantity  is  *  some,* — mean- 
ing an  indefinite  number,  one  or  more,  and  possibly  all.  It 
negatives   *  none,*   without   saying  how  many.      The   logical 

*  some'  is  expressed  by  the  phrase  '  some  at  least.'  The  '  some  ' 
of  common  speech  is  difierent ;  *  some  men  are  wise,'  *  some 
fever  patients  recover,*  are  interpreted  as  implying  that  there 
are  some  men  that  are  not  wise,  and  some  fever  patients  that 
will  not  recover.  When  we  assert  a  quality  of  a  subject  that 
we  are  acquainted  with,  we  are  usually  aware  that  while  some 
instances  possess  the  quality,  others  do  not ;  the  use  of  *  some  ' 


82 


EXTERNAL  FOKM  OF  PROPOSITIONS. 


does  not  express  our  ignorance  of  the  others,  bat  rather  our 
knowledge  that  these  are  deficient  in  the  quality.  This  is  fully 
stated  by  *  some  at  most,*  a  small  or  limited  number,  in  com- 
parison with  the  whole.  The  logician's  view  of  *  some'  would 
correspond  to  a  case  of  first  contact  or  encounter  with  a  new 
class  of  things;  Thus,  a  voyager  in  landing  on  a  newly  dis- 
covered coast,  and  meeting  a  few  of  the  inhabitants,  while  as 
yet  ignorant  of  the  general  mass,  would  say  *  some  are  lank- 
haired  ;'  he  would  speak  of  those  he  saw,  and  of  no  more. 

The  logician's  *  some'  is  rarely  found  in  common  use.  The 
word  itself  is  frequent  enough  ;  but  in  using  it,  we  are  aware 
that  there  is  an  actual  limitation  of  the  subject.  The  logical 
importance  of  the  word  comes  out  in  the  conversion  of  proposi- 
tions, with  a  view  to  the  syllogism.  As,  in  nearly  every 
affirmative  proposition,  the  predicate  is  larger  than  the  subject, 
includes  the  subject  and  something  more,  we  can  never  trans- 
pose the  terms  (in  conversion)  without  a  qualification  ;  '  all 
men  are  mortal,'  if  transposed,  must  be  ^  some  mortals  are 

men.* 

In  what  is  called  the  *  minor  term  *  of  the  syllogism,  *  some  * 
can  be  replaced  by  any  other  word  of  quantity,  as  one,  ten, 
few,  a  small  number,  many,  Ac. ;  the  same  word  being  trans- 
ferred to  the  conclusion  keeps  the  syllogism  correct.  But  in 
the  really  important  case — the  expression  of  a  universal  affir- 
mative, m  transposed  terms,  we  are  restricted  to  *8ome*  op 

*  part.' 

The  reason  why  *  TJnivei-sal '  and  *  Particular '  are  not  suitable 
names,  for  the  two  modes  of  quantity,  is  that  these  names  desig- 
nate also  the  inductive  contrast  between  a  general  proposition  and 
the  particulars  or  individuals  that  we  derive  it  from.  The  distinc- 
tion of  General  and  Individual  belongs  to  the  substance  and  not  to 
the  form  of  propositions ;  it  is  their  inductive  and  not  their  deduc- 
tive, or  formal  aspect. 

Mr.  De  Morgan  (Syllabus,  p.  60)  proposes  the  terms  *  full '  and 

*  vague'  as  other  synonymes  for  the  objectionable  couple — Universal 
and  Particular.  *  All  Men '  is  full  extent ;  *  some  men '  is  vagv^ 
extent. 

Another  term  for  quantity  less  than  total,  is  *  Most ;  *  which 
has  been  introduced  into  the  syllogism  by  Mr.  De  Morgan ; 

*  most  gases  are  odorous  : '  *  most  of  the  cerebral  nerves  spring 
from  the  medulla  oblongata;'  *  most  plants  are  hermaphrodites.* 

Certain  forms  of  the  proposition  have  been  called  Indefinite 
in  quantity  ;  the  expression  leaving  it  uncertain  whether  they 
are  universal  or  particular.  They  are,  in  point  of  fact,  arw- 
higuous.     The  chief  examples  occur  with  names  of  material| 


QUALITY  OF  PROPOSITIONS. 


83 


which  are  the  subjects,  sometimes  of  universal,  and  at  other 
times  of  particular,  predication.  *  Food  is  chemically  consti- 
tuted by  carbon,  oxygen,  &c.*  is  a  proposition  of  universal 
quantity;  the  meaning  is  all  food,  all  kinds  of  food.  *  Food 
is  necessary  to  animal  life'  is  a  case  of  particular  quantity  ; 
the  meaning  is  some  sort  of  food,  not  necessarily  all  sorts. 
•  Metal  is  requisite  in  order  to  strength '  does  not  mean  all 
kinds  of  metal  collectively.  *  Gold  will  make  a  way*  means  a 
portion  of  gold. 

The  term  *  Distribution  *  or  *  Distributed  *  is  a  technical, 
but  not  very  suggestive,  term  for  universal  quantity.  With 
the  universal  designations  *  all,*  *  every,*  or  their  equivalents, 
a  subject  or  predicate  is  said  to  be  distributed ;  a  particular 
form  '  some '  is  said  to  be  undistributed. 

3.  Propositions  are  either  Affirmative  or  Negative ;  a  dis- 
tinction according  to  Quality. 

A  proposition  either  affirms  or  denies  a  predicate  of  a  sub- 
ject; *Wine  is  good,*  *  wine  is  not  good.'  Two  properties 
either  co-exist  or  do  not  co-exist ;  and  to  be  informed  of  non-co- 
existence is  as  important  as  to  be  informed  of  existence.  *  The 
moon  is  up,*  *  the  moon  is  not  up,'  are  propositions  equally  valu- 
able as  knowledge  ;  we  are  guided  by  the  one  no  less  than  by  the 
other.  *  He  is  guilty,'  *  he  is  not  guilty,*  are  fundamentally 
different  assertions  ;  each  drawing  its  own  consequences  with  it. 

Affirmative  and  Negative  propositions  are  not  merely  differ- 
ent, they  are  ojjposed  ;  which  signifies  that  by  interpreting  the 
opposition,  we  can  make  out  all  the  consequences  of  the  one 
from  the  consequences  of  the  other.  With  the  same  subject 
and  the  same  predicate,  affirmation  and  denial  are  so  implicated 
together,  that  if  we  know  what  the  affirmation  means,  we  also 
know  what  the  denial  means.  One  effort  of  understanding 
serves  for  both.  If  we  are  told  that  *  the  accused  is  guilty/ 
involves  a  fine  of  five  pounds ;  we  know  also  that  the  negative, 
*  the  accused  is  not  guilty '  involves  exemption  from  the  fine. 
This  is  merely  an  aspect  of  the  Law  of  Relativity  ;  according 
to  which  the  knowledge  of  opposites  is  one. 

Some  logicians  have  proposed  to  do  away  with  the  distinction 
between  affirmative  and  negative  by  transferring  the  sign  of 
negation  from  the  copula  to  the  predicate ;  '  A  is  not  B,'  '  A  is 
not-B ;  '  'penury  is  not  agreeable,'  'penury  is  disagreeable.* 
There  is  then  the  appearance,  but  only  the  appearance,  of  making 
all  propositions  affirmative.  The  attempt  is  illusory.  Affirmation 
and  Denial  belong  to  the  very  nature  of  things  ;  and  the  distinc- 
tion, instead  of  being  concealed  or  disguised  to  make  an  imaginary 


84 


EXTERNAL  FORM  OF  PROPOSITIONS. 


unity,  should  receive  the  utmost  prominence  that  the  forms  of 
language  can  bestow. 

Thus,  besides  being  either  universal  or  partial  in  quantity, 
a  proposition  is  either  affirmative  or  negative.  And,  by  the 
Law  of  Relativity,  to  every  affirmative  form  there  corresponds 
a  negative  form,  both  understood  if  one  is. 

Negation  is  complicated  by  the  quantity  of  the  propositions 
opposed.  The  simplest  form  is  seen  in  the  opposition  of  a  uni- 
versal  to  a  universal-^*  all  diamonds  are  precious/  *  no  dia- 
monds are  precious,'  or  when  the  subject  is  a  definite  indi- 
vidual, as  *  Francis  was  (or  was  not)  the  author  of  Junius.* 
When  a  particular  is  opposed  either  to  a  universal,  or  to 
another  particular,  there  arise  distinct  forms  of  negation  or 
contrariety,  which  will  be  described  presently. 

4  The  negative  words  '  not/  '  no,'  and  their  equivalent 
prefixes  and  suffixes,  are  the  explicit  forms  of  negation. 
There  are  other  forms  of  a  less  direct  kind, 

For   the   negative  of  a  definite   particular   proposition,  as 

*  John  is  here,'  *  the  day  is  fine,'  we  prefix  tiot  to  the  predicate, 

*  John  is  not  here.'  For  universal  propositions,  this  mode  is 
insufficient ;  *  all  planets  are  round,'  is  not  negatived  by  |  all 
the  planets  are  not  round ;'  the  meaning  of  such  an  expression, 
according  to  the  idiom  of  our  language,  is,  that  some  planets 
may  be  (and  probably  are)  round,  but  a  reservation  is  made  of 
the  rest.  We  arrive  at  a  thorough  negation,  to  the  complete 
denial  of  the  universal  affirmation,  by  prefixing  the  negative 
adjective  *no'  to  the  subject — *  no  planets  are  round.* 

*  No  useless  coffin  enclosed  his  breast ;' 

Another  form,  adopted  for  rhetorical  emphasis,  is  seen  in  *  not 
a  man  escaped,' 

*  Not  a  drum  was  heard,  not  a  funeral  note/ 

The  prefixes  *  in,'  *  un',  and  the  suffix  *  less,'  are  equally 
emphatic.  *  All  his  actions  were  just  (unjust),  wise  (unwise), 
prudent  (imprudent).'  *  The  country  in  stony  Arabia  is  water- 
less and  treeless.' 

Negation  may  be  conveyed  by  such  phrases  as  *  far  from, 
•the  reverse  of,'  *on  the  contrary,'  *  wanting  or  deficient  in,' 

*  devoid  of,'  &c.  Certain  words,  as  *  few,'  *  hardly,'  *  scarce,* 
have  a  positive  or  negative    effect  according  to  the   context 

*  Few '  admits  a  small  number,  and  denies  all  beyond  ;  occa- 
sionally it  is  a  polite  form  of  total  denial.  In  some  cases,  the 
meaning   is   positive,  the   stress   being   laid    upon  the  small 


SIMPLE  AND  COMPLEX  PK0P0SITI0N3. 


85 


amount  of  admission ;  in  other  cases,  the  force  is  meant  to  be 
negative,  *  few  will  see  that  day.' 

5.  Propositions  are  either  simple  or  complex,  a  distinc- 
tion only  partially  belonging  to  Logic. 

In  a  simple  proposition,  there  is  but  one  subject  and  one 
predicate  :  *the  sun  is  up,'  *  justice  is  excellent,'  *  Britain  has 
numerous  colonies.'  In  a  complex  proposition  there  are  more 
than  one  predicate  or  more  than  one  subject,  or  both. 
*  Britain,  France,  and  Prussia  are  maritime  powers  ;'  *  Britain 
has  often  been  at  war,  and  has  acquired  foreign  possessions.' 
In  the  first  example,  three  propositions  are  combined  in  one 
common  predicate ;  and  should  they  require  to  be  logically 
canvassed,  they  must  be  taken  separately:  *  Britain  is  a 
maritime  power,'  &c.  In  the  second  example,  two  propositions 
are  affirmed,  and  one  implied,  although  there  is  but  one  subject 
'Britain.'  It  is  affirmed  (1)  that  Britain  has  often  been  at 
war,  (2)  that  Britain  has  acquired  possessions  abroad;  and 
the  close  connexion  of  the  two  statements,  is  meant  to  convey 
an  additional  circumstance,  namely,  that  the  second  fact  was 
the  consequence  of  the  first.  As  before,  these  allegations  would 
be  taken  in  their  separate  and  simple  form,  in  any  question 
as  to  their  truth  or  falsehood,  or  as  to  the  evidence  in  their 

favour.  . 

The  whole  of  this  class  might  be  called  Compound,  instead 

of  complex,  Propositions. 

6.  The  Complex  Propositions  more  especially  entering 
into  Lof'ic  are  of  two  kinds,  named  Conditioned  and  Dis- 
jimctive!  In  these,  the  separate  propositions  are  conjoined 
in  one  meaning. 

The  Conditional  Proposition  is  extremely  common ;  it  is  a 
statement  with  a  qualification  ;  *  if  ignorance  is  bliss,  *  tis 
folly  to  be  wise* ;  '  if  every  one  speaks  together,  the  busmess 
cannot  be  done ;  *  *  unless  rain  come,  the  crops  will  fail.' 

This  form  is  also  expressed  by  saying  that  one  statement  is 
the  consequence  of  another ;  or  that  there  is  an  affirmation  of 
the  consequence  or  connexion  of  two  facts ;  that  where  one 
fact  is  present  the  other  fact  will  follow,  these  facts  being  ex- 
pressed in  propositions.  Thus,  *  the  consequence  of  ignorance 
being  bliss  is,  that  it  is  folly  to  be  wise  ; '  *  the  consequence  of 
every  one  speaking  together,  is  that  no  business  is  done  ;  the 
consequence  of  a  want  of  rain  will  be  a  deficiency  of  the  crops. 


!^ 


86 


EXTERNAL  FORM  OF  PEOPOSITIOKS. 


I!; 

'i  u 


In  all  sncli  cases,  it  is  only  a  matter  of  course,  that  supposing 
the  antecedent  present,  the  consequent  is  also  present. 

The  Disjunctive  Proposition  expresses  an  alternative  :  *  John 
is  either  in  the  house  or  in  the  office'  ;  *  granite  is  either  a 
sedimentary  deposit  or  a  product  of  igneous  action  ;'  *  to  be  or 
not  to  be,  that  is  the  question.' 

These  propositions  may  be  viewed  as  condensing  alternative 
conditions ;  '  If  John  is  not  in  the  house,  he  is  in  the  office  ; 
and  if  he  is  not  in  the  office,  he  is  in  the  house.* 

Each  class  is  the  basis  of  a  distinct  species  of  logical  trans- 
formations, constituting  a  supposed  variety  of  the  Syllogism. 
The  name  *  hypothetical'  expresses  both  the  conditional  and  the 
disjunctive  forms,  and  is  opposed  by  *  categorical'  which  desig- 
nates all  other  propositions. 

7.  The  combination  of  difference  in  Quantity  with 
difference  in  Quality,  gives  rise  to  four  classes  of  Proposi- 
tions : — 

(1)  Universal  Affirmative  (A) 

(2)  Particular  Affirmative  (I) 

(3)  Universal  Negative  (E) 

(4)  Particular  Negative  (O). 

These  propositions  are  expressed  symbolically  by  the  letters 
A,  I,  E,  O.  The  first  and  second  forms,  the  affirmative,  derive 
their  symbols  from  the  vowels  of  the  word  Aff'Irm :  A  being 
the  universal,  I,  the  particular  affirmitive.  The  third  and 
fourth  forms,  the  negative,  derive  their  symbols  from  the  vowels 
of  nEgO;  E  being  the  universal,  and  O  the  particular  negative. 

A — All  men  are  fallible  :  all  X  is  Y. 

I — Some  men  are  wise  :  some  X  is  Y. 

E — No  men  are  gods  :  no  X  is  Y". 

O — Some  men  are  not  wise  :  some  X  is  not  Y, 

HamiltorCs  Quantification  of  the  Predicate, 

ft  These  are  all  the  forms  admitted  into  the  usual 
syllogism,  being  sufficient  for  ordinary  purposes.  We 
may  notice,  however,  in  all  of  them,  that  the  quantity 
spoken  of  has  reference  to  the  subject ;  and  nothing  is  said 
explicitly  of  the  quantity  of  the  preclicate.  By  supplying 
this  omission,  Hamilton  has  indicated  four  additional  forms. 

Thus,  to  take  All  X  is  Y  :  all  men  are  fallible.  Y  may 
mean  some  Y  or  all  Y;  some  fallible  beings  or  all  fallible 
beings.     There  are  then  two  forms  : — 


HAMILTON'S   QUANTIFICATION. 


87 


(1)  All  the  Xs  are  some  (a  part)  of  the  Ys;  all  men  are 
some  (a  part  of)  fallible  beings.  This  is  what  is  presumed  to 
be  the  meaning  of  the  common  form,  where  the  quantity  of  the 
predicate  is  not  stated.  As  there  is  no  assurance  given  that 
the  Xs  are  all  the  Ys — that  men  are  the  whole  of  the  beings 
that  are  fallible — we  must  leave  it  to  be  understood  that  there 
are  other  Ys,  other  fallible  beings,  and  therefore  take  for 
gi*anted  only  that  men  are  among  the  fallible  beings,  whether 
there  be  others  or  not.  Usually,  we  do  not  concern  ourselves 
with  this  farther  enquiry ;  it  is  enough  for  us  to  know,  on  a 
particular  occasion,  that  a  certain  man,  or  a  number  of  men, 
are  fallible,  or  that  a  certain  substance  is  poisonous,  without 
determining  whether  others  besides  those  in  hand  have  the 
same  quality.  This  last  is  a  distinct  and  superadded  enquiry, 
useful  in  particular  situations,  but  not  in  all,  nor  even  in  the 
majority  of  instances.      The   fact  is  valuable  to  know   that 

*  wines  are  stimulating  or  intoxicating,'  whether  or  not  they 
include  the  whole  of  the  stimulants.  It  is  a  farther  discovery, 
having  a  separate  utility,  to  find  that  there  are  stimulants 
besides  wines.  The  common  form  is  suited  to  the  first  case  ; 
the  quantified  form — all  wines  are  some  stimulants,  there  are 
other  stimulants  besides  wine — is  suited  to  the  second  case. 

On  the  strict  Logical  sense  of  *  some,' — some  at  least,  and 
it  may  be  all, — the  quantified  form  *  all  X  is  some  Y '  is  the 
same  as  the  unquantitied  form  *all  X  is  Y.'  There  is  merely 
this  difierence  that  in  the  quantified  form,  attention  is  called 
to  the  circumstance  whether  there  be  more  Ys  than  are  Xs ; 
in  the  common  form,  no  question  is  raised  or  even  suggested 
as  to  additional  Ys  beyond  the  Xs.  If  *  some '  were  inter- 
preted in  the  more  familiar  meaning  *  some  at  most,'  which  it 
is  apt  to  be,  the  particular  quantification  would  not  give  the 
meaning  of  the  unquantified  form. 

It  will  be  seen,  in  the  account  to  be  afterwards  given  of 
Boole's  Logic,  that  he  finds  it  necessary  to  express,  by  a  sym- 
bol, that  the  predicate  of  affirmative  propositions  is  taken 
only  in  part  of  its  extent. 

(2.)  With  the  predicate  made  universal,  the  form  A  becomes 

*  All  X  is  all  Y;'  there  are  no  Ys  but  the  Xs.     Such  is  not 

a  usual  form  of  predication.     In  the  great  mass  of  positive 

affirmations  the  predicate  is  larger  than  the  subject,  includes 

it  and  other  things  besides :  *  the  coin  of  the  realm  is  metallic ;' 

there  are  many  things  made  of  metal  besides  coin.     *  The  stars 

are  heavenly  bodies,'  but  not  exclusively  so. 

To  exemplify  this  kind  of  proposition,  there  are  offered  such 
6 


tl 


88 


EXTERNAL  FORM  OF  PROPOSITIONS. 


instances  as  these; — *  Chloride  of  sodinm  is  common  salt,* 
which  means,  there  is  no  chloride  of  sodium  but  what  is 
common  salt.  But  these  terms  are  co-extensive  only  because 
they  are  synonymous ;  they  are  two  names  for  the  same  thing. 
Defining  propositions  must  be  co-extensive. 

As  an  example  taken  from  real  propositions,  we  may  have 
this — *  All  equilateral  triangles  are  all  equiangular  triangles  ;* 
for  there  are  none  equilateral  but  are  also  equiangular.  Such 
cases  are  not  frequent  even  in  the  deductions  of  Geometry, 
where  the  propositions  afiirm  propria^  and  not  concomitance. 

There  are  a  few  cases  of  unique  properties  furnishing  propo- 
sitions where  the  subject  is  as  large  as  the  predicate.  *  Mercury 
is  a  liquid  metal '  is  known  to  be  *  all  mercury  is  all  liquid 
metal.'  In  such  instances,  it  is  usual  to  note  the  fact,  that 
subject  and  predicate  are  co-extensive  in  the  language  used  ; 
as  by  saying,  mercury  is  the  only  liquid  metal ;  there  is  no 
metal  liquid  at  common  temperatures  but  mercury.  Being  an 
exceptional  predication,  it  receives  exceptional  notice.  Of  a 
similar  nature  is  Hamilton's  example,  '  All  rational  is  all 
risible  ;*  we  should  say,  *  only  rational  beings  are  able  to  laugh,' 

In  the  more  general  conjunctions,  or  concomitance  of  dis- 
tinct qualities,  it  is  exceedingly  rare  to  find  a  proposition  where 
subject  and  predicate  are  co-extensive.  Only  one  unequivocal 
instance  can  be  suggested  at  the  present  time,  namely,  the 
proposition,  *  all  matter  gravitates  ;*  the  meaning  of  which  is 
that  the  defining  property  of  matter — Inertness — is  always 
accompanied  with  the  attraction  of  gravitation.  Now,  these 
two  attributes  are  co-extensive,  and  yet  distinct ;  all  matter  is 
all  gravitating  things ;  there  is  nothing  devoid  of  inertia,  and 
yet  possessing  gravity.  Even  here  it  may  be  said,  that  although 
we  can  easily  suppose  inertia  without  gravity,  wo  cannot  easily 
enppose  gravity  without  inex'tja. 

Folarizatiojj  and  Ponble  Befraction  are  co-extensive  pro- 
perties. 

Mr.  De  Morgan,  as  will  be  afterwards  seen,  calls  the  form  a 
complex  proposition^  being  tantamount  to  two  propositions — 
All  X  is  y,  and  all  Y  is  X. 

Mr.  Mill  makes  substantially  the  same  criticism  on  Hamil- 
ton's Quantified  forms.  Whatever  can  be  proved  from  "  all 
A  is  all  B,"  can  be  proved  in  the  old  form  from  o^ie  or  both  of 
its  elements^  All  As  are  Bs,  and  all  Bs  are  As,  *  Whatever  can 
be  proved  from  **  Some,  and  only  some,  A  is  some  (or  all)  B," 
can  be  proved  in  the  old  form  from  its  elements,  Some  As  are 
Bs,  some  As  are  poib  Bs,  and  (in  the  case  last  mentioned)  all 


HAMILTON'S   QUANTIFICATION. 


89 


Bs  are  As.'  (Mill's  Hamilton,  chap.  XXII).  To  say  *A11 
Philosophy  is  all  Poetry'  is  to  affirm  these  two  propositions, 
Poetry  is  Philosophy,  and  Philosophy  is  Poetry. 

The  Particular  Affirmative,  I,  has  two  forms,  when  the 
quantity  of  the  predicate  is  supplied : — Some  X  is  some  Y,  (the 
understood  form),  some  X  is  aZZ  Y  :  *  Some  planets  are  sonie 
celestial  bodies;'  *some  mortals  are  all  men.'  The  second  is 
the  new  or  additional  form.  Its  best  justification  is  the  cir- 
cumstance that,  under  the  common  form,  we  lose  predication 
in  converting  a  universal  affirmative  :  thus,  All  X  is  Y,  all  men 
are  mortal,  become,  some  Y  is  X,  some  mortal  beings  are  men, 
meaning  some  X,  some  men,  whereas  we  are  entitled  to  say  all 

X,  all  men. 

These  two  additional  affirmative  forms  have  been  admitted 
by  some  logicians,  as  Thomson  (Laws  of  Thought)  and  Spald- 
ing ;  and  have  been  made  the  basis  of  an  extension  of  the 
syllogism.  The  universal  affirmative— All  X  is  all  Y— is  sym- 
bolized by  U  (Thomson)  and  by  A^  (Spalding).  The  par- 
ticular affirmative  with  universal  predicate  is  Y  (Thomson), 
P  (Spalding). 

The  additions  made  by  Hamilton  to  the  negative  forms, 
E,  and  O,  have  not  been  received  by  any  other  logician.  In 
E,  '  no  X  is  Y,  *  no  men  are  gods,'  both  subject  and  predicate 
are  universal ;  there  is  total  and  mutual  exclusion ;  no  one 
of  the  class  men  is  identical  with  any  one  of  the  class  god ;  the 
coincidence  of  a  man  with  a  god  is  denied  seriatim.  The  pre- 
dicate here  is  quantified  universally.  We  may,  however,  state  a 
form  where  the  predicate  is  particular ;  *  no  X  is  some  Y,'  *  no 
men  are  some  animals,'  no  men  are  to  be  found  in  a  certain 
class  or  species  of  animals ;  there  are  classes  of  animals  that 
entirely  exclude  men.  If  the  *  some  animals '  could  be  speci- 
fically defined,  as  quadrupeds,  fishes,  &c.,  the  proposition  would 
revert  to  the  common  form; 

In  the  Particular  Negative,  0,  *  some  X  is  not  Y,'  the  sub- 
ject is  particular,  and  the  predicate  universal  *  Some  Xs  are 
not  to  be  found  among  the  Ys ;'  *  some  men  are  not  any 
Europeans,  are  not  to  be  found  among  Europeans ;'  *  some 
heavenly  bodies  do  not  shine  by  their  own  light.' 

Now,  particular  quantity  may  be  assigned  to  the  predicate ; 
which  would  then  be,  some  X  is  not  some  Y  ;  some  of  the  Xs 
do  not  occur  among  some  of  the  Ys.  Some  men  are  not  to  be 
found  among  some  of  the  mammals.  If  *  some  of  the  mam- 
mals,' could  be  rendered  specific,  as  the  *  carnivorous  quadru- 
peds, *  the  thick-skinned  quadrupeds,*  we  should  have  the  old 


!i 


\i 


I 


90 


EXTERNAL  FORM  OF  PROPOSITIONS. 


form  of  O.  In  answer  to  the  objection  against  the  new  form, 
that  it  is  never  practically  realized,  Hamilton  contends  that  it 
is  the  form  wherein,  exclusively,  we  declare  a  whole  of  any  kind 
to  be  divisible.  Thus,  in  dividing  the  genus  *  soldier,'  we 
should  say  to  ourselves — "  some  soldier  is  not  some  soldier  ; 
for  some  Soldier  is  (all)  Infantry,  some  Soldier  is  (all)  Cavalry, 
&G. ;  and  (any)  Infantry  is  not  (any)  Cavalry." 

De  Morgan's  Enumeration  of  Propositions. 

9.  With  a  view  to  exhaust  all  the  possible  modes  of  pre- 
dication, there  needs  to  be  a  thorough-going  expression  of 
contraries. 

According  to  the  true  view  of  contrariety,  as  given  by  De 
Morgan,  the  negative  is  a  remainder,  gained  by  the  subtraction 
of  the  positive  from  the  universe  ;  the  negative  of  X  is  U — X, 
and  may  be  symbolized  by  a  distinct  mark  x  ;  whence  X  and 
X  are  the  opposites  under  a  given  universe  ;  not-X  is  x,  and 
not-x  is  X.  For,  Some  Xs  are  not  Ys,  we  may  substitute, 
Some  Xs  are  ys  ;  and  so  on. 

We  have  now,  instead  of  the  two  terms  X,  Y,  the  four 
terms  X,  Y,  x,  Y.  Hence,  in  room  of  the  one  couple,  X,  Y,  to 
be  given  under  the  four  fonns  of  predication — A,  E.  I,  O — we 
have  no  less  than  four  difierent  couples — X,  Y  ;  X,  Y  ;  x  Y  ; 
X,  Y.  Every  one  of  these  may  be  stated,  as  A,  as  E,  as  I,  or 
as  O.  Consequently  there  are  sixteen  possible  arrangements. 
On  examination,  however,  eight  turn  out  to  be  repetitions  of 
the  other  eight. 

We  may  exhibit  the  sifting  operation  thus : — Take  A,  or 
universal  affirmation,  and  express  all  the  four  couples  accord- 
ingly. 

(1)  All  X  is  Y  (the  usual  form) 

(2)  All  X  is  Y  (not-Y) 

(3)  All  X  (not-X)  is  Y 

(4)  All  X  (not-X)  is  y  (not-Y) 

The  second — All  X  is  Y  (not-Y) — is  identical  with  E,  in  the 
old  scheme — No  X  is  Y. 

The  third — All  x  (not-X)  is  Y,  is  the  same  as  no  not-X  is 
not-Y  ;  nothing  is  both  not-X  and  not-Y  ;  everything  is  either 
X  or  Y.  No  not-mind  is  a  not-matter ;  everything  is  either 
mind  or  matter.  This  is  a  new  form.  It  means  that  every- 
thing is  either  in  X  or  in  Y  (or  in  both). 

The  fourth— All  x  (not-X)  is  Y  (not-Y),  (all  not-mortals  are 
not-raen),  is  the  same  as  All  Y  is  X,  a  new  form,  so  far,  that 
the  symbols  are  transposed. 


DE  morgan's  propositions. 


91 


Again,  putting  the  four  couples  through  particular  affirma- 
tion (1)  ; — 

Some  X  is  Y 

Some  X  is  Y  (not-Y) 

Some  X  (not-X)  is  Y 

Some  X  (not-X)  is  Y  (not-Y) 
The  first  being  the  common  form ;  the  second  is  the  common 
particular  negative.  The  third,  *  Some  not-X  is  Y,'  may  bo 
transformed  into  *  Some  Ys  are  not  Xs,'  or  *  All  Xs  are  not  Some 
Ys,'  in  which  shape  it  is  received  among  the  additional  forms. 
The  last  *  Some  not-X  is  not  Y  ;'  *  some  things  are  neither  Xs 
nor  Ys  ;*  all  the  opposites  of  X  are  opposites  of  Y.  Infantry- 
is  neither  cavalry  nor  artillery  ;  the  negative  of  X  (cavalry)  is 
the  negative  of  Y  (artillery),  that  is,  infantry. 

The  same  method  pursued  with  universal,  and  with  particu- 
lar negation,  completes  the  survey,  and  also  yields  a  new- 
form,  already  quoted, 

Some  Y  is  not  X 
which,  like  the  form — All  Y  is  X — is  merely  the  transposition 
of  the   letters   in   0.       The   author   has   special  reasons  for 
including  these  two  varieties  among  prepositional  forms. 

Thus,  then,  in  addition  to  the  old  fundamental  forms,  A,  I, 
E,  0,  we  have  these  four  : — 

(1)  Every  Y  is  X 

(2)  Some  Y  is  not  X 
which  are  A  and  O,  reversing  the  terms. 

(3)  Everything  is  either  X  or  Y 

(4)  Some  things  are  neither  X  nor  Y 

These  last  are  a  contrary  couple  of  Disjunctives,  added  to  the 
four  regular  forms,  which  are  all  Categorical. 

The  author  next  adverts  to  the  compatibility  or  incompati- 
bility of  these  various  forms.  There  are  three  alternatives.  (1) 
The  separate  individuals  may  be  such  as  cannot  exist  together, 
(2)  They  may  be  such  as  mtist  exist  togetJier.  (3)  They  may 
exist  either  with  or  without  each  other,  in  neutral  concomitance. 
It  is  evident,  for  example,  with  regard  to  the  old  forms  that  A 
cannot  co-exist  with  E,  or  with  O ;  if  every  X  is  Y,  it  cannot 
be  true,  either  that  no  X  is  Y,  or  that  some  X  is  not  Y. 
Again,  if  A  exists,  I  must  exist :  and  so  with  E,  and  O ;  the 
particular  is  involved  in  the  universal.  Lastly,  the  particulars 
I  and  O,  may  or  may  not  exist  together :  they  are  neutral 
concomitants ;  *  some  men  are  wise,'  and  *  some  men  are  not 
wise.'  [Substantially  the  statement  of  the  Opposition  of  Pro- 
positions.] 


!l 


l\     ■% 


I'-  1 


92 


EXTERNAL  FOUM  OF  PROPOSITIONS. 


From  this,  the  author  proceeds  to  define  what  he  terms  a 
coviplez  proposition;  *  one  involving  within  itself  the  assertion 
or  denial  of  each  and  all  of  the  eight  simple  propositions. 
Thus  supposing  X  and  Y  to  be  such  that  none  of  the  four 
universals  are  true  ;  then  all  the  four  particulars  are  true. 
This  is  one  case,  called  a  complex  particular.  Another  case  is 
to  suppose  one  of  the  universals  true  ;  then  five  others  are 
settled,  either  by  affirmation  or  by  denial :  and  there  are  two 
concomitants,  which  however,  are  contradictions,  so  that  only 
one  is  true.  Of  this  generic  character,  there  are  six  modes  or 
forms  ;  one  of  which  has  an  especial  interest.  ^ 

The  case  is  this,  Let  A  (the  old  form),  ^Eveiy  X  is  Y  be 
trae.  Then  E  and  O,  are  denied,  and  I,  is  included  (of  the 
old  forms).  Of  the  four  new  forms,  the  neutral  concomitant 
is  *  Every  Y  is  X ' :  these  may  co-exist,  and  when  taken  to- 
gether make  the  complex  proposition— Every  X  is  Y,  and 
every  Y  is  X :  in  other  words,  X  and  Y  are  co-existent,  or 
identical.  Now  this  is  Hamilton's  Universal  Affirmative,  with 
universal  quantity  in  the  predicate.  All  Xs  are  all  Ys.  So 
that,  in  De  Morgan's  view,  that  form  has  no  claim  to  be  a 
simple  or  fundamental  prepositional  form  ;  it  is  a  compound 
or  complex  proposition,  derived  from  the  simple  fonns,  by  the 
process  now  described.  He  supports  this  view,  by  the  farther 
alleo'ation,  that  the  proposition  in  question  does  not  admit  of  a 
simple  denial,  as  every  proposition  of  a  fundamental  kmd 
should  :  it  is  contradicted  either  by  '  Some  Xs  are  not  Ys 
and  by  '  some  Ys  are  not  Xs ' ;  that  is,  by  the  disjunction 
*  either  some  Xs  are  not  Ys,  or  some  Ys  are  not  Xs' ;  and  it 
is  not  necessary  to  determine  which,  so  that  the  contradictory 
is  ambiguous  or  undecided. 

Opposition  of  Propositions, 

10.  Negation  in  the  full  sense  is  exhibited  by  opposing  a 
Universal  Affirmative  to  a  Universal  Negative— A  to  E, 
as  '  all  men  are  wise,  no  men  are  wise.'  This  is  called,  in 
Logic,  the  opposition  of  Cokteakies. 

Contrariety,  in  this  sense,  is  the  setting  up  of  a  Universal 
Negative,  agkinst  a  Universal  Affirmative,  or  a  Universal  Affir- 
mative against  a  Universal  Negatiye  :  All  X  is  Y,  no  A  is  Y  ; 
*all  the  ship's  crew  perished,'  *  all  the  ship's  crew  survived 
In  point  of  extent,  this  is  the  largest,  the  most  sweeping  and 
thorough  negation,  that  can  be  advanced.  The  amount  ot 
knowledge  required  for  such  a  denial,  is  at  its  maximum.     It 


1     X 


OPPOSITION  OP  CONTRARIES. 


93 


is  not  often  that,  in  dissenting  from  a  Universal  Proposition, 
we  are  able  to  substitute  the  opposite  uni  -ersal.  We  may 
doubt  the  truth  of  the  affirmation  ^all  stars  t«  inkle  ; '  but  we 
cannot  carry  our  denial  to  the  length  of  Universal  Negation — 

*  no  stars  twinkle.'  Rarely  does  any  informed  person,  in  ad- 
vancing a  universal  proposition,  go  so  far  wrong,  that  the 
truth  consists  in  the  opposite  universal. 

There  is  the  appearance  of  complete  contrariety  in  the  op- 
posing views  of  the  Immortality  of  the  Soul.     Christians  say 

*  the  souls  of  all  men  are  immortal ; '  Buddhists  and  others  say, 

*  no  men's  souls  are  immortaL'  This,  however,  is  one  of  the 
instances,  where  a  universal  is  alike  proved  or  disproved  upon 
an  individual  case. 

In  small  matters,  total  contrariety  is  frequent  enough.  The 
assertion  may  be  made — *  All  the  voters  were  bribed,'  and 
may  be  met  with  the  universal  denial — *  no  voters  were  bribed  ;* 
which  is  felt  to  be  the  strongest  denial  that  can  be  given. 

Of  this  opposition,  it  is  i*emarked,  that  both  cannot  be  true, 
but  both  may  be  false.  *  All  men  are  wise '  and  *  no  men  are 
wise,'  cannot  be  both  true  ;  the  intention  of  the  one  is  to  de- 
clare the  other  to  be  false ;  between  the  two,  there  is  a  con- 
tradiction in  terms.  Yet  it  is  possible  that  neither  may  be 
true,  that  hoth  may  be  false.  The  truth  may  be  neither  the 
one,  nor  the  other,  but  something  betwixt  the  two  sweeping 
universals ;  as,  that  some  men  are  wise,  and  some  not  wise. 
Total  contrariety,  or  complete  negation,  thus  leaves  room  for 
a  middle  assertion. 

It  is  farther  pointed  out  in  regard  to  this  opposition,  that 
the  opposed  propositions  differ  only  in  quality ;  the  one  affirms, 
and  the  other  denies,  of  the  same  quantity,  that  is  to  say,  the 
universal, 

11.  A  Negation  may  consist  in  opposing  a  Universal  Affir- 
mative to  a  Particular  Negative — A  to  O,  or  a  Universal 
Negative  to  a  Particular  Affirmative — ^E  to  I.     This  called 

the  opposition  of  Contradictories. 

Instead  of  *  All  men  are  wise,'  *  no  men  are  wise,'  we  may 
have  the  opposing  couple,  '  All  men  are  wise,*  *  some  men  are 
not  wise ;  A  and  O.  So,  *  No  voters  were  bribed '  (E),  is 
opposed  by  *  Some  voters  were  bribed '  (I).  Such  is  contra- 
dictory opposition. 

Of  this  opposition  (as  with  contraries)  both  cannot  be  true  ; 
but  farther,  hoth  cannot  be  false,  or  if  the  one  be  false  the  other 
must  be  true,  and  if  the  one  be  true,  the  other  must  be  false. 


F^l 


'A 

■■y 


94 


EXTEKNAL  FORM   OF  PllOPOSITIONS. 


I 


There  is  not,  as  with  contraries,  an  intermediate  supposition  ; 
there  is  no  middle  ground.  Either  *  all  men  are  wise,' or 
'  some  men  are  not  wise  ;'  either  *  no  voters  were  bribed  ;*  or 

•  some  voters  were  bribed/  The  two  opposites  are  so  related 
that  we  must  choose  one  or  other.  Hence  to  this  kind  of 
opposition  belongs  that  principle  lirst  signalized  by  Aristotle, 
and  ever  since  regarded  as  a  primary  Law  of  Thought — the 
Law  op  Excluded  Middle. 

It  is  farther  noticed,  that  in  contradictory  opposition,  there 
is  change  both  in  the  quality,  and  in  the  quantity  of  the  opposed 
assertions ;  while  one  is  affirmative  and  the  other  negative 
the  one  has  universal,  and  the  other  particular  quantity.  This 
circumstance,  however,  instead  of  increasing,  diminishes  the 
contrariety.  The  change  from  universal  to  particular  quantity 
abates  the  force  of  the  opposition  of  quality. 

The  application  of  perhaps  the  strongest  negative  word  in 
the  language, — contradiction — to  this  kind  of  opposition  calls 
for  some  comment.  In  common  speech,  the  person  that  could, 
in  reply  to  the  charge — *  All  the  voters  were  bribed,'  maintain 

•  No  voters  were  bribed,'  would  be  held  to  have  contradicted 
that  charge  in  the  most  thorough-going  way.  While  the  de- 
claration *  some  voters  were  not  bribed'  would  be  regarded  as 
a  contradiction,  the  declaration — *  no  voters  were  bribed ' 
would  be  held  as  a  contradiction  in  a  still  higher  degree.  The 
word  *  contrary '  would  be  thought  too  feeble  for  universal  denial. 

It  is  apparent,  that  the  logical  contradictory,  as  now  defined, 
denies  much  less  than  the  logical  contrary ;  indeed,  denies  so 
little,  that  it  excludes  the  possibility  of  a  smaller  denial ;  it  is 
the  minimum  of  denial.  For,  whereas  the  affirmer  boldly  com- 
mits himself,  for  example,  to  the  broad  universal  *  all  men  are 
wise,'  the  denier,  timid  and  shrinking,  ventures  only  upon  an 
exception  to  the  sweep  of  .the  rule  ;  he  will  not  sa}^  *  no  men 
are  wise,'  which  would  be  in  common  speech  the  fiat  contra- 
diction, the  thorough  negation  ;  he  merely  says  some  men  are 
'iiot  wise ;  he  denies  so  little,  as  to  leave  no  room  for  any  one  to 
deny  less.  He  takes  ground  so  limited,  so  humble,  as  to  ex- 
clude any  more  limited,  more  humble  opponent.  His  *  some  * 
commits  him  only  to  the  fact  of  taking  an  exception.  It 
may  mean  only  one  ;  which  of  course  would  be  an  *  excluded 
middle,'  for  who  that  challenged  the  assertion  *  all  men  are  wise  * 
could  say  less  than  '  one  man  is  not  wise  ?  '  It  is  shaving  the 
universal  affirmative  by  the  breadth  of  a  hair  that  cannot  be  split. 

The  employment  of  the  stronger  term  for  the  smaller  oppos- 
tion,  is  explicable  thus.     Aristotle,  in  dividing   propositions 


OPPOSITION  OF  CONTRADICTORIES. 


95 


accoifling  to  quantity — as  universal  and  partial, — ^put  great 
stress  upon  the  difficulty  in  establishing,  and  the  facility  in 
subverting,  a  universal,  whether  affirmative  or  negative.  The 
task  of  the  affirmer  is  hard,  he  has  to  secure  every  individual 
instance  ;  the  task  of  the  denier  is  easy,  he  has  but  to  destroy 
one.  If  it  were  necessary,  with  a  view  to  impugn  a  universal 
proposition,  to  establish  an  opposite  universal,  the  difficulty  of 
disproving  an  unsound  generalization  would  be  often  insuper- 
able. This,  however,  is  not  required.  A  single  opposing  fact 
is  enough.  A  hole  in  a  ship's  bottom  sinks  her  as  surely  as  if 
she  were  torn  plank  from  plank.  It  is  this  sufficiency  for 
disproof  that  makes  the  importance  of  the  limited  contradictory 
affirjnation.  It  can  be  more  easily  procured  than  the  full 
contrary,  and  yet  it  is  equally  effective.  It  possesses  the 
imposing  circumstance  of  securing  great  ends  by  small  means. 

There  are  certain  cases  where  the  contrary  and  the  contra- 
dictory are  the  same  thing.  The  first  is  when  the  proposition 
is  singular  or  individual :  *  John  is  here ' — *  is  not  here,'  *  The 
world  was  created  in  time,'  *  The  world  is  eternal,'  There  is 
no  middle  ground  in  such  assertions  as  these. 

Another  case  is  where  a  generality  stands  or  falls  by  an 
individual  case,  as  in  Laws  of  Causation.  A  single  unambigu- 
ous observation  (under  what  is  called  the  Method  of  Difference) 
will  prove  Cause  and  Effect.  If  a  new  metal  is  discovered, 
and  fused  on  one  single  occasion  at  1100  deg.  Fah.,  we  may 
affirm  generally  that  the  same  temperature  will  always  fuse  the 
metal.  Here  contrariety  and  contradiction  are  the  same. 
The  metal  either  is  or  is  not  fused  at  that  temperature.  The 
Uniformity  of  Nature  prohibits  the  middle  supposition,  that 
some  portions  of  the  metal  may  be  fused  and  some  not. 

These  remarks  serve  to  explain  the  use  of  the  Law  of  Excluded 
Middle,  by  Sir  W.  Hamilton,  in  regard  to  certain  questions,  such 
as  the  Infinite  Divisibility  of  Matter,  Free- Will,  the  Eternity  of 
the  "World.  *  Matter  is  divisible,'  'matter  is  not  divisible' — are 
contraries  not  contradictories ;  there  may  be  a  middle  position — 
*  some  matter  is  divisible  * — making  them  both  false.  But  Hamilton 
must  be  understood  to  assume  that  Matter,  either  is  a  singular 
subject,  or  is  homogeneous  to  such  an  extent  that  what  is  true  of 
one  portion  must  be  true  of  all,  and  consequently  that  the  opposi- 
tion above  specified  comes  under  contradictory  opposition,  which 
is  governed  by  the  Law  of  Excluded  Middle.  Accordingly,  he 
niaiuiains  that  of  the  opposite  alternatives — matter  is  divisible, 
matter  is  indivisible ;  the  will  is  free,  the  will  is  necessitated— 
one  must  be  true  and  the  other  false. 

A  farther  logical  convenience  supposed  to  attach  to  the  con- 
tradictoi*y  form  is  the  substitution,  tor  the  denial  of  a  universal, 


\l 


« 


1^^ 
■  i 

I  i 

If  i 


M 

I'    i 

I  ■ 


If  ]  . 


96 


EXTERNAL  FORM  OF  PROPOSITIONS. 


of  the  equivalent,  and  corresponding  affirmation.  Wheif  A  is 
denied,  then,  in  that  very  act,  0  is  affirmed.  It  being  untrue  that 
*  All  men  are  wise,'  it  must  be  true  that  *  Some  men  are  not  wise.' 

The  Contrary  and  the  Contradictory  are  the  only  important 
forms  of  opposition.  It  is  usual  to  add  another  variety,  that 
between  a  Particular  Affirmative  and  a  Particular  Negative — 
I  and  0 — *  Some  men  are  wise,*  *  some  men  are  not  wise.' 
So  imperfect  is  this  opposition,  that  there  need  not  be  any 
contrariety  between  the  two  forms.  They  are  compatible,  and 
are  often  both  true.  All  that  can  be  said  of  them  is,  that  they 
cannot  he  both  false;  if  it  is  false  that  some  men  are  wise,  it 
cannot  also  be  false  that  some  men  are  not  wise.  But  as  the 
one  predicate  may  relate  to  one  set  of  men,  and  the  other  predi- 
cate to  a  different  set,  there  is  no  real  contrariety  ;  frequently 
the  two  propositions  together  give  the  exact  state  of  the  case. 

The  name  *  sub-contraries  *  has  been  given  to  these  opposites. 
According  to  Hamilton,  they  were  brought  forward  merely  as 
completing  the  logical  diagram,  called  the  *  Square  of  Opposition.' 

For  the  explanation  of  the  diagram,  it  is  farther  to  be  re- 
marked that  the  relation  (which  cannot  be  called  opposition  in 
the  strict  sense)  between  Universal  and  Particular—A  and 
I,  E  and  O,  is  called  suhaltemate,  or  subaltern,  the  relationship 
of  subordination.  There  is  a  sufficiently  obvious  propriety  ia 
BO  designating  it. 

Common  Square. 
A  Contraries.  B 


Sub- Contraries. 


SQUARE  OF  OPPOSITION. 


97 


Mr.  Da  Morgan  departs  from  this  square  on  certain  points. 
Regarding  the  words  *  contrary  *  and  *  contradictory '  as  the 
same  in  meaning,  he  drops  *  contradictory/  and  applies  *  con- 
trary '  to  the  old  meaning  of  contradictory,  that  is  to  the 
diagonal  opposition,  A — O,  E — I.  The  opposition  of  the 
Universals,  A — E,  he  proposes  to  style  sub-contrary;  and  the 
opposition  of  the  Particulars,  I — O,  which  he  retains,  he  calls 
sv^er-contrary. 

If  we  were  to  introduce  any  innovation  of  this  nature,  founded 
on  the  identity  of  contrary  and  contradictory  in  common  speech, 
there  would  be  a  greater  seeming  propriety  in  the  inveting  of 
Mr.  De  Morgan's  designations.  The  opposition  of  the  Uni- 
versals A  and  B — is  fall  contrariety ;  the  opposition  of  the  Uni- 
versal to  the  Particular  of  opposite  quaUty  (however  effective 
as  a  logical  instrument)  is  still  but  partial  contrariety,  or 
subaltern  contrariety,  and  would  better  suit  the  name  '  sub- 
contrary.'  A — O,  E — L  The  opposition  of  the  particulars  I 
and  O  does  not,  so  far  as  can  be  seen,  need  any  descriptive 
name.     If  it  did,  'super- contrary '  might  be  taken. 

The  supposed  square  would  stand  thus  : — 

A  Contraries.  E 


This  form  is  the  following  out  of  the  view  already  taken  of 
the  imperfect  negation  of  the  so-called  contradictories.  It 
is  also  so  far  in  harmony  with  the  scheme  of  the  diagram 
(borrowed  from  the  Paralleligram  of  Forces),  a  superficial 
harmony  founded  on  a  deeper  propriety.    Thus,  A  E,  being  one 


§ 


«li 


J'  r 


■     f 

i    ^ 

I  if 


93 


EXTERNAL  FOKxM  OF  PROPOSITIONa 


side  of  the  square,  and  the  line  of  the  sabalterns,  A  I,  being 
the  side  adjoining ;  the  composition  of  these  two,  into  the 
diagonals,  A— O,  or  E— I,  yields  mhaltern  contraries,  contracted 
into  suh'Contraries.  This  is  not  a  mere  accidental  coincidence 
of  laneniao-e  ;  it  is  the  expression  of  the  fact  that  subaltern  or 
subordinate  contrariety,  is  a  subordinated,  narrowed,  or  partial 
form  of  contrariety  ;  a  whole  is  opposed,  not  by  a  whole,  but  a 
part  •  a  aniversal  met,  not  by  a  universal,  but  by  a  particular  ; 
giving  a  diagonal  or  oblique  contrariety,  instead  of  a  full  or 
total  contrariety. 

This  is  different  from  the  common  square,  as  well  trom  the 
two  others  given  above.  Aristotle  uses  the  diagonal  for  the 
full  contrary  opposition  of  the  two  universals  A  and  E.  The 
contradictories,  or  sub- contraries,  A-0,  E-I,  are  the  sides  (be- 
tween right  and  left).  There  is  no  opposition  indicated  between 
A  and  I,  E  and  0  ;  and  the  second  diagonal  is  left  blank,  in- 
asmuch as  I  and  O,  are  not  proper  contraries.  This  square 
has  the  diagrammatic  property  of  representing  the  strongest 
contrariety  by  the  longest  line,  the  line  also  that  bisects  the 
figure  •  from"  which  arrangement  arose  the  emphatic  phrase 
diametrical  opposition,  to  signify  the  thorough  opposition  of 
the  universals. 

Aristotle's  Square, 

A  Contradictory.  O 


Contradictory. 


KECESSARY  AND  CONTINGENT. 


99 


Modal  p7'opositions, 

12.  Since,  in  common  speech.  Propositions  often  occur 
in  a  qualified  or  modified  form,  a  class  was  constituted  by 
Aristotle  for  such  cases,  under  the  name  of  Modal  Pro- 
positions ;  the  unqualified  forms  being  called  the  Pure 
forms. 

If  we  were  to  say  that,  in  Geometry,  *  the  conclusion  neces- 
sarily follows  from  the  premises,'  the  affirmation  would  be 
called  Modal ;  it  lays  down  a  truth  and  farther  designates  it 
as  a  necessary  truth.  The  contrast  of  necessary  is  contingent^ 
which  is  also  a  modal ;  the  propositions  of  physical  science  are 
looked  upon  as  not  necessary,  bat  contingent ;  the  facts  might 
have  been  arranged  otherwise.  So  that  besides  affirming  that 
oxygen  combines  with  hydrogen,  we  might  call  it  a  *  contin- 
gent' doctrine  or  statement.  Other  generic  forms  of  modal- 
ity, included  by  Aristotle,  are  the  possible,  and  impossible  ;  both 
which  may  qualify  propositions.  He  reduces  these  four  forms 
to  two, — necessary  and  contingent.  He  was  supposed  also  to 
have  taken  in  true  and  false  among  the  kinds  of  modality. 
Although  this  is  doubted  by  some,  there  would  be  no  reason 
why  they  should  not  be  included.  So,  probability  and  impro- 
bability  might  be  likewise  admitted.  Subsequent  logicians 
extended  the  species  of  modality  to  qualifying  adjectives  or 
adverbs,  as  *  the  white  man  runs,'  *  he  runs  quickly,*  Again, 
the  qualification  of  time  is  an  important  fact  entering  into 
many  propositions  ;  he  ran  yesterday  ;  he  continues  running. 

That  such  propositions  are  frequently  to  be  found  is  obvious. 
By  Hamilton  and  the  stricter  of  the  formal  logicians  they  are 
excluded  from  Logic.  They  clearly  do  not  belong  to  the  narrow 
Formal  or  Syllogistic  Logic.  They  have  reference  to  the  matter 
and  not  the  form  of  predication.  They  are  included  in  the  more 
comprehensive  Logic  sketched  in  this  work ;  and  we  can 
easily  assign  their  proper  position  in  the  enlarged  scheme 
Propositions  qualified  as  Necessary,  first  give  an  affirmation, 
and  secondly,  declare  that  such  affirmation  belongs  to  the  class 
of  necessary  truths,  whatever  these  may  be  ;  whether  this 
be  true  or  false  depends  on  a  comparison  of  the  marks  of  the 
class  *  necessary  truths,*  or  the  connotation  of  the  word  'neces- 
sary,' with  the '  affirmation  in  question.  The  case  falls  under 
Deductive  Evidence,  not  formal,  but  material,  like  the  inter- 
pretation of  Law.  The  same  remarks  apply  to  Contingent, 
Possible,  and  Impossible  propositions.    With  regard  to  Froba- 


,1 


100 


IMPORT  OR  MEANING  OF  PROPOSITIONS. 


t,  1  . 


hilityf  as  a  modal,  a  reference  would  be  made  to  the  branch  of 
Induction  treating  of  Probable  evidence. 

Propositions  qualified  by  present,  past,  or  future  time,  or  in 
any  of  the  tenses  of  the  verb  besides  the  present  viewed  as  the 
universal  tense,  may  be  treated  as  compound  propositions ; 
asserting  first  a  fact,  and  then  the  time  of  its  happening. 
Another  view  of  these,  suggested  by  Mr.  Mill,  is  to  associate 
the  tense  with  the  copula. 

In  the  Appendix  (Explanation  of  Terms,  Modah)  will  be  given 
the  usual  statement  of  the  Opposition  of  Propositions,  as  applied 
to  Necessary,  Impossible,  and  Contingent  matter.  It  is  withheld 
from  the  Text,  as  being  an  irrelevant  and  useless  complication, 

IMPORT   OR  MEANING  OP   PROPOSITIONS. 

is.  For  laying  out  the  divisions  of  the  Inductive  Logic, 
it  is  requisite  to  classify  propositioDS  according  to  their 
Import  or  Meaning. 

Although  the  special  meanings  of  propositions  are  as  various 
as  human  knowledge,  there  ai-e  certain  highly  generalized 
meanings,  pointing  to  difiierence  of  Logical  Method. 

14.  To  the  question,  what  is,  iu  matter  or  mhstance  (as 
contrasted  with  form),  the  meaning  of  a  Proposition,  Hobbes 
answered  that,  in  a  proposition,  the  predicate  is  a  name  for 
tJte  same  thing  as  the  subject  is  a  name  for. 

Thus,  *  Aristides  is  just '  is  a  true  proposition  if  'just*  be 
the  name  of  Aristides.       *  Men  are  gods  *  is  false,  because 

*  god '  is  not  a  name  ior  man. 

This  is  true,  but  not  the  whole  truth.  The  theory  is  correct 
so  far  as  it  goes,  but  it  does  not  reach  to  the  final  import  of 
predication.  Hobbes  did  not  advert  to  the  real  meaning,  which 
is  found  in  the  connotation  of  class  names.      When  we  say, 

*  Aristides  is  just,*  the  preliminary  question  arises,  how  came 
the  name  *just'  to  be  applied  to  Aristides?  When  the 
word  was  first  determined  on,  people  knew  nothing  of  Aris- 
tides. What  they  knew  was  the  agreement  of  a  certain 
number  of  persons  in  a  peculiar  feature  of  conduct ;  to  that 
agreement  was  given  the  name  *  just.'  Any  one  in  after  times 
found  to  have  the  agreeing  feature,  succeeded  to  the  name ; 
and  the  meaning  of  the  proposition  as  regards  Aristides  is 
that  he  resembled  a  number  of  persons  that  went  before  him, 
in  a  certain  point  where  they  resembled  one  another ;  and  on 


THEORY  OF  PREDICATION. 


101 


account  of  which,  they  were  named  *just.*  In  one  view, 
therefore,  the  proposition  in  question  is  an  affirmation  of  like' 
ness  ;  but  that  fact  must  enter  into  every  proposition  asserting 
participation  in  a  community  of  attributes.  More  characteristic 
of  the  case  is  the  feature  of  co-existence;  the  co-existence  of  the 
man  Aristides  with  the  quality  named  *  just.'  Two  things  are 
mentioned ;  and  these  two  things  are  united  in  predication, 
by  declaring  their  co-existence  in  one  subject.  Whether  this  is 
a  typical  or  representative  instance,  will  be  seen,  after  a  fuller 
examination  of  particulars. 

15.  A  second  theory,  sharing  in  the  same  defect  as  the^ 
foregoing,  is  that  Predication  consists  in  referri^  somet/iing 
to  a  class, — placing  an  individual  under  a  class,  or  one 
class  under  another  class. 

When  we  say  *  the  planets  are  round,'  on  this  hypothesis 
the  meaning  would  be,  *  the  class  planet  falls  under,  or  is 
enrolled  in,  the  class  round ;'  *  Neptune  is  a  planet,'  Neptune 
is  in  the  register  of  bodies  named  planets.  Or,  negatively, 
*  men  are  not  gods,'  men  are  not  to  be  found  in  the  list  of  the 
gods.  This  is  both  inadequate  and  incorrect.  It  confounds 
the  connotation  of  a  name  with  its  denotation ;  the  class 
attribute,  which  is  elastic  and  indefinite,  with  the  class  as 
supposed  to  be  an  aggregate  of  definite  individuals.  The 
meaning  of  a  general  name  is  as  extensive  as  the  things  that 
possess  the  attribute ;  although  a  certain  number  of  known 
individuals  may  be  recognised  as  a  group,  or  class,  correspond- 
ing to  the  name,  the  class  must  ever  remain  open  to  new 
individuals.  We  have  a  general  name  *  sea,'  which  is  also  a 
class  name,  in  the  narrow  sense.  The  individual  seas  of  the 
globe  are  enumerated  in  geography  ;  but  these  are  not  exclu- 
sive. We  could  not  refuse  the  name  *  sea '  to  a  newly  discovered 
individual,  because  it  is  not  in  the  old  list ;  if  it  possessed  the 
common  features,  we  should  give  it  the  name  at  once,  and 
write  it  down  in  the  Hst  afterwards.  Most  general  names 
have  no  lists  or  registers  of  individuals  ;  we  have  no  exhaustive 
tables  of  round  things,  of  stars,  of  coal  strata,  of  whales,  or  of 
human  beings.  We  have  merely  points  of  agreement,  defining 
marks;  in  other  words,  a  meaning  or  connotation  to  each 
term ;  the  correspondence  with  this  rules  the  application  of 
the  word,  or  the  truth  or  falsehood  of  the  proposition  asserting 
that  any  individual  is  round,  is  a  star,  and  so  on. 

In  forming  a  class,  we  do  not,  as  in  forming  a  society, 
enroll  certain    definite   individuals,   and    decide  each  one's 


I'  ! 


102 


IMPORT  OK  MKANING  OF  PEOPOSlTIONa 


pretensions  by  referring  to  the  roll.  We  indicate  an  attribute 
or  attributes,  and  test  tbe  individual  by  the  presence  or  the 
absence  of  the  attributes. 

16.  There  are  two  ways  of  arriving  at  the  highest  gener- 
alities of  Predication.  One  is  a  sufficiently  wide  examina- 
tion of  actual  propositions  in  the  detail.  The  other  is  to 
refer  to  the  classification  of  '  Nameable  Things.'  The  two 
modes  should  confirm  each  other. 

By  an  examination  of  propositions  in  detail,  we  should  soon 
find  many  of  the  kind  already  noted  as  affirming  Co-existence; 
the  co-existence  of  two   things,  or  facts,  or  two   properties. 

*  Man  is  mortal,'  is  the  co-existence  of  humanity  and  mortality. 

*  The  fall  of  the  barometer  is  a  sign  of  rain,'  is  tbe  concurrence 
of  the  two  facts,  the  fall  of  the  barometer  and  rain. 

We  might  then  turn  from  co-existence,  to  its  contrasting 
property,  *  Succession,'  and  enquire  whether  any  propositions 
are  made  up  of  two  or  more  things  affirmed  to  happen  in 
succession.  We  should  find  many  such.  *The  wind  raises 
the  sea,'  *  the  sun  is  the  cause  of  vegetation,'  *  Cajsar  subverted 
the  Roman  Republic,'  might  all  be  interpreted  as  affirmations 
of  succession.  Speaking  generally,  wherever  there  is  produc- 
tion, causation,  or  change,  there  must  be  succession  ;  one  state 
of  things  is  followed  b}--  another  state  of  things.  In  cause 
and  effect,  which  is  a  very  wide  department  of  human  enquiry, 
there  is  understood  to  be  succession  ;  something  called  a  cause 
is  followed  by  some  other  thing,  called  an  effect. 

We  have  seen,  farther,  that  in  predication,  there  is  involved 
the  declaration  of  Likeness  and  Unlikeness.  This  contrast, 
however,  is  a  universal  fact  inseparable  from  predication  ;  the 
very  basis  of  cognition  is  laid  in  Difference  and  in  Agreement. 
But  there  are  certain  cases  where  the  specializing  point  of  a 
proposition  lies  in  likeness  or  unlikeness  ;  as  in  propositions  of 
Number.  *  Twice  two  is  four'  is  an  affirmation  of  Equality  ; 
the  test  of  its  truth  would  be  a  test  suited  to  ascertain  equality 
or  inequality.  Ife  could  not  be  brought  under  either  co-exist- 
ence or  succession  in  an  easy  or  natural  way  ;  it  falls  readily 
and  fitly  under  agreement  or  disagreement  in  respect  of 
Quantity. 

17.  A  reference  to  the  classification  of  Nameable  Things 
shows  the  wide  compass  of  these  three  affirmations  — 
Co-existence,  Successiou,  and  Equality  or  Inequality. 

Under  Nameable  Things  (Appendix  C),  we  find  attributes 


PRKDICATE  OF  EQUALITY. 


103 


special  to  the  Object,  attributes  special  to  the  Subject,  and 
attributes  common  to  both.  The  attributes  common  to  both 
are  Quantity,  Co-existence,  and  Succession.  We  might,  on  the 
strength  of  this  enumeration,  give,  as  universal  forms  of  Predica- 
tion ;  attributes  of  the  Object,  and  attributes  of  the  Subject, 
declared  as  agreeing  or  disagreeing  in  Quantitij,  as  Co-existing^ 
or  as  Successive. 

18.  I.  Propositions  of  Quantity  include  the  whole  of 
the  Mathematical  sciences,  and  all  the  applications  of 
number  to  quantity  in  every  science  and  art.  The  predi- 
cation is  equality  or  inequality. 

Thus,  in  Arithmetic,  the  addition  and  subtraction  of  num- 
bers, the  multiplication  table,  and  the  rule  of  three, — which 
are  the  fundamental  processes — are  affirmations  of  agreement 
or  disagreement  in  quantity.  Three  and  four  is  seven  ;  five 
from  nine  leaves  four ;  six  times  eight  is  forty-eight ;  as  two 
is  to  ten,  so  is  six  to  thirty, — are  affirmations  of  equality  or 
agreement  in  numerical  quantity. 

The  propositions  of  geometry  may  all  be  resolved  in  like 
manner.  The  angle  in  a  semi-circle  is  equal  to  a  right  angle. 
A  sphere  is  equal  in  balk  to  two  thirds  of  the  circumscribed 
cylinder.  Two  sides  of  a  triangle  taken  together  are  greater 
than  the  third  (Inequality). 

In  Algebra,  we  need  allude  only  to  the  extensive  process  of 
manipulating  by  Equations,  * 

la  every  art  and  in  every  emergency  of  life,  occasion  arises 
for  measuring  quantity,  that  is  for  declaring  equality  and  in- 
equality, greater  or  less.  Even  when  the  quantity  does  not 
admit  of  numerical  statement,  as  in  shades  of  feeling  and  of 
human  character,  we  still  express  and  compare  quantity ;  we 
call  one  man  more  energetic,  more  far-seeing  than  another. 

19.  It  is  the  characteristic  of  the  Sciences  of  Quantity 
to  be  purely  Deductive  Sciences.  They  have  Inductive 
foundations  like  all  the  rest,  but  the  chief  labour  attending 
them  consists  in  purely  deductive  operations. 

This  determines  the  Logical  Method  and  the  Logical  Depart- 
ment of  Mathematics.  All  that  is  peculiar  in  the  science 
belongs  to  the  branch  of  Logic  named  Deduction. 

20.  II.  Propositions  of  Co-existencr  are  of  two  kinds. 
In  the  one  kind,  account  is  taken  of  Place  ;  they  may  be 
described  as  propositions  of  Order  in  Place.  They  refer 
purely  to  the  Object,  or  Extended  World. 


\n\ 


i  '• 


i»  I 


t 


104 


IMPORT   OK  MEANING  OF  PEOPOSITIONa 


The  Object,  or  Extended  Universe  is  a  vast  array  of  things 
distributed  in  space  ;  they  are  said  to  have  place,  or  a  mutual 
relationship  as  to  extension.  Thus,  the  stars  are  arranged  in 
the  celestial  vault  at  definite  distances.  Geography  is  a  body 
of  propositions  of  order  in  place  ;  an  ocean,  a  mountain  chain, 
a  river — are  described  geographically  as  having  local  situa- 
tion with  reference  to  other  things ;  to  these  are  applied  the 
more  purely  mathematical  or  quantitative  propositions  of  mag- 
nitude. 

Some  propositions  of  Place  affirm  nothing  beyond  containing 
and  contained ;  they  declare  one  thing  to  be  either  in  or  out 
of  another  thing ; — John  is  in  the  room ;  the  constellation 
Orion  is  in  the  northern  hemisphere ;  St.  Helena  is  in  the 
South  Atlantic;  The  British  Museum  contains  the  Portland 
vase.  These  may  be  called  the  more  vague  and  indetermin- 
ate propositions  of  quantity.  The  degree  of  precision,  in  this 
case,  depends  upon  the  relative  magnitudes  of  the  container 
and  of  the  contained.  A  thing  affirmed  to  be  in  a  house  is 
better  defined  than  a  thing  in  a  town,  and  not  so  well  as  a 
^hing  in  a  drawer. 

Another  mode  of  giving  order  in  place  is  to  affirm  close 
proximity.  One  thing  outside  another,  but  in  contact  with  it, 
has  a  definite  position,  expressed  by  such  forms  as  *  by,*  *  by 
the  side  of,'  *  close  to,'  *  above,*  *  beneath.*  If  there  be  an 
interval,  a  measured  distance  must  be  assigned. 

The  more  precise  propositions  of  Order  in  Place  are  those 
th^t  declare  mutual  position  by  numerical  stat-ements  of  dis- 
tance or  extension  ;  to  which  form  every  fact  of  order  in  place 
might  be  reduced,  if  we  had  sufficient  knowledge,  and  if  we 
thought  it  necessary  or  desirable.  Thus,  the  mutual  position 
of  the  stars,  in  the  sphere  of  the  sky,  is  stated  in  terms  of 
angular  measui'ement ;  the  position  of  places  in  the  earth  is 
given  by  latitude  and  longitude,  and  also,  if  need  be  in  linear 
distances.  The  determination  and  the  expression  of  this  rela- 
tionship, therefore,  may  be  wholly  referred  to  Arithmetic  and 
Geometry.  The  precise  statement  of  relative  position  is  the 
peculiar  province  of  Analytic  or  Co-ordinate  Geometry. 

The  description  of  all  objects  of  the  external  world  having 
parts,  or  a  defined  structure,  demands  propositions  of  Order  in 
Place,  according  to  some  one  of  the  foregoing  methods ;  as 
buildings,  machinery,  plants,  animals,  aggregates  and  collec- 
tions of  objects. 

21.  The  second  form  of  Co-existence  may  be  designated 
Co-inherence  of  Attributes. 


CO-INHERENCE  OF  ATTRIBUTES. 


105 


This  is  a  distinct  variety  of  Propositions  of  Co-existence. 
Instead  of  an  arrangement  in  place,  with  numerical  intervals, 
we  have  the  concurrence  of  two  or  more  attributes  or  powers 
in  the  same  part  or  locality.  A  mass  of  gold  contains,  in  every 
atom,  the  concurring  attributes  that  mark  the  substance — 
weight,  hardness,  colour,  lustre,  incorrosibility,  &c.  An  animal, 
besides  having  parts  situated  in  place,  has  co-inhering  func- 
tions in  the  'same  parts,  exerted  by  the  very  same  masses  and 
molecules  of  its  substance.  Every  blood  corpuscle  has  a 
plurality  of  relations,  indivisible  and  inseparable. 

The  Mind,  which  affi>rds  no  propositions  of  Order  in  Place, 
has  co-inhering  functions.  We  affirm  mind  to  contain  Feeling, 
Will,  and  Thought,  not  in  local  separation,  but  in  commingling 
exercise.  Every  pleasurable  feeling  has  its  power  of  acting 
on  the  will  and  of  impressing  the  memory  ;  all  the  attributes 
are  joined  in  the  unity  of  the  mental  being. 

A  wide  range  of  Scientific  knowledge  is  comprised  under  the 
present  head.  The  concurring  properties  of  minerals,  of  plants, 
and  ol  the  bodily  and  the  mental  structure  of  animals,  are 
united  in  affirmations  of  co-inherence.  The  investigation  of 
these  concurrences,  whether  special  or  general,  is  a  branch  of 
scientific  method,  or  of  Logic,  coming  under  Inddciion,  al- 
though not  the  largest  portion  of  the  Inductive  department. 

22.  III.  Under  Succession,  there  are  also  two  kinds  of 
Propositions.     By  the  first  is  predicated  Order  in  Time, 

This  is  Parallel  to  Order  in  Place,  under  Co-existence.  Many 
propositions  consist  in  assigning  the  order  and  sequence  of 
events,  without  intimating  any  closer  relationship.  The  world 
being  constituted  on  the  principle  of  change,  there  is  a  serial 
order  in  its  phenomena,  which  may  be  given  in  narration. 
Spring  is  preceded  by  winter,  and  succeeded  by  summer; 
infancy  is  followed  by  youth.  The  treaty  of  1815  followed 
Waterloo. 

The  position  of  events  may  be  defined  by  their  close  succes- 
sion. First  the  seed,  then  the  ear,  then  the  full  corn  in  the  ear. 
Henry  VIII,  succeeded  Henry  VH,  and  preceded  Edward  VI. 
A  serial  order  being  given,  the  position  in  the  order  is  fixed 
either  by  contiguous  events,  or  by  a  numerical  position,  as  the 
sixth  Earl. 

Here,  too,  as  in  order  in  place,  the  precise  method  consists 
in  the  use  of  numbers.  The  flow  of  time  being  divided  into 
years,  months,  days,  hours,  &c.,  the  position  of  any  occurrence 
is  given  by  numbers  and  by  fractions  of  numbers.  This  is 
merely  another  application  of  Arithmetic.     In  the  com  plica- 


f 


106 


iMPOr.T  on  MEANING  OF  PROPOSITIONS 


i    t 


It 
1 1 


;1 


H 


;  * 


i 


tions  of  Astronomy,  the  element  of  time  may  require  difficult 
algebraical  formulae.  There  is,  however,  no  new  and  distinct 
department  of  scientific  enquiry  involved  in  propositions  of 
mere  sequence  in  time,  however  accurately  they  may  be  inves- 
tigated and  recorded. 

23.  The  second  mode  of  Succession,  is  that  denominated 
Cause  and  Effect.  The  largest  part  of  Induction  is  occupied 
with  this  department. 

Cause  and  Effect  appears  under  the  guise  of  Succession,  but 
contains  something  beyond  the  sequences  above  considered. 
There  is  supposed  to  be  a  certain  bond  or  7iexus,  a  determining 
power  or  agency,  whereby  the  one  gives  birth  to  the  other. 
Propositions  of  Cause  and  Effect  are  such  as  these  : — the  ex- 
plosion of  gunpowder  propels  a  cannon  ball ;  the  combustion 
of  coal  converts  water  into  steam  ;  light  is  an  agent  of  decom- 
position ;  anxiety  wears  the  constitution  ;  a  good  hai'vest 
makes  prices  fall ;  Demosthenes  incited  the  Athenians  against 
Philip. 

The  Logic  of  Induction  is  occupied  first  with  propositions 
of  Co-inhering  Attributes  ;  secondly,  and  mainly,  with  pro- 
positions of  Causation.  Although  the  foundations  of  the 
science  of  Qiicmtitij  are  also  inductive,  yet  so  limited  and  simple 
is  the  induction,  that  it  may  be  sufficiently  noticed  in  the  ac- 
count given  of  this  department  under  Deduction  and  the 
Deductive  Sciences. 

The  foregoing  is  a  modification  of  Mr.  Mill's  scheme  of  the 
Import  of  Propositions  in  the  final  analysis,  conceived  with  the 
view  of  ascertaining  the  divisions  of  Logic 

Mr.  Mill  enumerates  five  ultimate  predicates,  or  classes  of 
predications — Existence,  Co-existence  (including  Order  in 
Place),  Succession,  Causation,  Resemblance. 

Apart  from  Existence,  these  are  substantially  the  classes 
here  adopted.  Co-existence,  as  explained  by  Mr.  Mill,  com- 
prises Order  in  Place,  and  also  the  Properties  of  Kinds  (Book 
III.  Chap.  XXII),  which  are  given  above  under  *  co-inhering 
attributes,'  By  Succession,  is  meant  the  looser  successions 
included  under  Order  in  Time.  The  successions  of  Cause  and 
Effect  are  given  in  a  distinct  and  co-ordinate  predicate — Causa- 
tion. Under  Resemblance,  Mr.  Mill  indicates  propositions  ex- 
pressing the  identity  of  the  things  discovered  to  be  identical, 
as,  for  example,  in  classification  ;  but  this  underlies  all  pro- 
positions where  there  is  generality,  and  does  not  mark  off  a 
scientific  department.     In  the  end,  however,  he  gives  as  the 


EXISTENCE  NOT  A  PREDICATE. 


107 


special  science  of  Resemblance,  propositions  of  Quantity,  or 
Mathematics. 

With  regard  to  the  predicate  Existence,  occurring  in  certain 
propositions,  we  may  remark  that  no  science,  or  department,  of 
logical  method,  springs  out  of  it-  Indeed,  all  such  propositions 
are  more  or  less  abbreviated,  or  elliptical ;  when  fully  expressed 
they  fall  under  either  co-existence  or  succession.  When  we  say 
there  exists  a  conspiracy  for  a  particular  purpose,  we  mean  that, 
at  the  present  time,  a  body  of  men  have  formed  themselves  into 
a  society  for  a  particular  object ;  which  is  a  complex  affirmation 
resolvable  into  propositions  of  co-existence  and  of  succession 
(as  causation).  The  assertion  that  the  dodo  does  not  exists 
points  to  the  fact  that  this  animal  once  known  in  a  certain 
place,  has  disappeared  or  become  extinct ;  is  no  longer  associated 
with  the  locality  :  all  which  may  be  better  stated  without  the 
use  of  the  verb  *  exist.'  There  is  a  debated  question — Does 
an  Ether  exist  ?  but  the  correcter  form  would  be  this — *  Are 
heat  and  light  and  other  radiant  influences  propagated  by  an 
etherial  medium  diffused  in  space  ;  *  which  is  a  proposition  of 
causation.  In  like  manner  the  question  of  the  Existence  of  a 
Deity  cannot  be  discussed  in  that  form.  It  is  properly  a  ques- 
tion as  to  the  First  Cause  of  the  Universe,  and  as  to  the  con- 
tinued exertion  of  that  Cause  in  providential  superintendence. 


EQUIVALENT  PROPOSITIONAL  FORMS — IMMEDIATE,  OR 

APPARENT   INFERENCE. 

24.  Great  importance  often  attaches  to  the  equivalent 
modes  of  expressing  the  same  fact,  assertion  or  proposition. 
The  transforming  of  one  expression  to  another  is  so  far  aa 
aid  to  reasoning  as  to  be  sometimes  termed  *  Inferenca' 

The  enumeration  of  Equivalent  Forms  is  as  follows  : — 
I.  Universal  and  Particulars. 
II.  Greater  and  less  in  Connotation. 

III.  Ob  version. 

IV.  Conversion. 

V.  Hypothetical  Inference. 

VI.  Synonymous  Propositions. 

The  first  to  the  fifth,  inclusive,  are  each  conducted  on  a  de- 
finite plan,  admitting  of  precise  rules.  They  are,  therefore, 
the  properly  logical  jjaodes.  The  sixth, — Synonymous  expres- 
sion— is  indefinite  and  various  ;  so  that,  although  deserving  of 
notice,  it  is  not  reducible  to  rule. 


M 


i*f 


If 


m 

i**i 


108 


EQUIVALENT  PEOPOSITIONAL   FORMS. 


It  will  appear,  in  the  course  of  the  exposition,  that  in  none 
of  these  cases  is  there  Inference  properly  so  called,  that  is  to 
say,  the  transition  from  a  fact  to  some  different  fact ;  there  is 
merely  the  transition  from  one  wording  to  another  wording  of 
the  same  fact.  Hence,  the  designations  *  Immediate  Inference,' 
and  ^  Apparent  Inference,'  to  distinguish  the  process  from 
Mediate  or  Beal  Inference. 

Universal  and  Particulars — Greater  and  Less  in  Denotation. 

25.  A  Universal  Proposition  and  its  constituent  particu- 
lars being  the  same,  there  is  no  real  inference,  but  a  repetition, 
in  saying  All  A  is  B,  therefore  Some  A  is  B  ;  all  men  suffer, 
therefore  some  men  suffer. 

A  Universal  Proposition  is  the  summed  up  equivalent  of 
many  particular  propositions,  air^  has  no  force  beyond,  or  apart 
from  the  particulars.  Hence,  when  we  state  a  particular  case, 
we  do  but  resolve  the  universal  into  its  elements,  and  take  these 
individually  as  they  were  before  the  universal  was  fonned.  *  All 
the  honses  of  the  street  are  newly  built*  is  a  mere  summary  or 
abbreviation  of  the  separate  enumeration— No.  1  is  new.  No.  2 
is  new,  and  so  on.  To  say  *  all  the  houses  are  new,*  therefore 
*  No.  6  is  new,'  is  not  to  make  an  advance  in  knowledge,  but  to 
fall  back  upon  one  of  the  constituents  of  the  general  proposition. 
The  law  of  Consistency  requires  that  whoever  asserts  a  fact 
universally  must  be  prepared  to  abide  by  it  in  each  particular 
instance.  A  shopman  advertises  a  number  of  articles  at  a 
shilling  each  ;  the  buyer,  taking  him  at  his  word,  chooses  some 
one  article,  and  puts  down  a  shilling. 

Greater  and  Less  in  Connotation, 

26.  In  regard  to  the  Connotation  or  Comprehension  of  a 
term,  it  is  no  inference  to  affirm  the  less  alter  assuming  the 
greater. 

When  we  say  *  John  is  a  man,'  we  say  that  he  has  each  and 
all  of  the  properties  connoted  by,  or  comprehended  under 
I  man.*  It  is  no  new  affirmation,  therefore,  but  merely  unfold- 
ing in  the  detail  what  is  already  summed  up  in  the  aggiegate, 
to  say  John  is  a  living  creature,  an  animal,  a  compound  of  body 
and  mind.  Whoever  is  not  prepared  to  admit  these  affirma- 
tions, should  not  declare  John  to  be  a  man. 

In  maintaining  that  *  quadrupeds  are  endowed  with  mind,* 
we  hold  that  they  possess   Feeling,  Will,  and  Thought.     It 


GREATER  AND  LESS  IN  CONNOTATION. 


109 


is,  therefore,  not  a  real  inference  but  a  mere  iteration,  to  add 

*  quadrupeds  feel,  *  *  quadrupeds  will.* 

When  we  affirm  that  a  certain  substance  is  arsenic,  we  affirm 
of  it  all  the  known  properties  of  arsenic.  It  is  an  equivalent 
or  identical  proposition  to  say,  *.the  substance  is  poisonous.* 

These  affirmations  of  the  properties  of  things  in  the  detail 
have  already  come  under  our  notice,  as  verbal  essential,  or 
identical  propositions. 

We  must  consider  ourselves  at  liberty  to  join  or  disjoin  the 
attributes  of  a  thing,  without  real  inference.  We  may  say 
either  *  Socrates  was  wise,  virtuous,  and  a  martyr,*  or  *  Socrates 
was  wise,*  *  Socrates  was  virtuous,*  *  Socrates  was  a  martyr/ 
Given  an  aggregate  or  compound  proposition,  we  may  reduce 
it  to  its  elements  ;  given  a  number  of  elementary  propositions, 
we  may  compound  them  into  one.  The  operation  lies  more  in 
the  grammar  than  in  the  sense. 

*  Socrates  was  virtuous,*  *  there  was  one  man  virtuous,' — 
may  be  held  to  be  a  purely  equivalent  form.  If  we  enquire 
into  the  meaning  of  the  word  Socrates,  we  find  *  among  other 
things  *  that  it  means  *  a  man,*  *  one  man,*  and  to  say  *  one 
man  was  virtuous  *  is  no  new  meaning,  but  a  part  of  the  ori- 
ginal meaning.     So,  after  saying,  *  Socrates  was  virtuous  *  and 

*  Socrates  was  poor,*  there  is  no  inference  in  saying  *  one  man 
was  virtuous  and  poor,'  or  *  one  poor  man  was  virtuous.*  This 
example  has  some  importance  in  the  theory  of  the  Syllogism. 

Under  the  designation — Immediate  Inference  by  Added  De- 
terminants, the  following  case  is  given  (Thomson*s  Laws  of 
Thought)  ; — *  A  negro  is  a  fellow-creature  ;  therefore  a  negro 
in  sufiering  is  a  fellow-creature  in  suffering.*  This  seems 
self-evident,  but  it  is  somewhat  different  from  the  other  cases. 
It  resembles  the  following  mathematical  inference  :  A  =  B, 
whence  A  -f-  C  =  B  -|-  C  ;  which  is  not  an  immediate  judg- 
ment, but  deductively  inferred  from  the  axiom — *  The  sums  of 
equals  are  equal.* 

Even  allowing  the  axiom  of  addition  of  equals  for  such  a 
case,  we  must  be  cautious  in  applying  it  without  regard  to  the 
matter,  seeing  that  the  same  addition  may  not  have  the  same 
effect  upon  both  sides.  *  Beauty  is  pleasure  ;  hence  beauty  in 
excess  is  pleasure  in  excess,'  is  not  a  safe  inference ;  the  quali- 
fication does  not  operate  precisely  alike  upon  both  subjects. 

Ohversion. 

27.  In  affirming  one  thing,  we  must  be  prepared  to  deny 
the  opposite  :  '  the  road  is  level,'  *  it  is  not  inclined,*  are 


110 


EQUIVALENT  PROPOSITIONAL  FOUMS. 


OBVERSION. 


Ill 


not  two  facts,  but  the  same  fact  from  its  other  side.     Thia 
process  is  named  Obvehsion. 

On  the  principle  of  Rclati\ity,  every  statement  has  two 
sides,  as  a  part  of  its  nature  :  there  is  alwa3^s  something  to  be 
denied  when  any  one  thing  is  affirmed-  Whoever  is  *  wise'  is 
*  not  foolish  ; '  we  must  grant  both  propositions  or  neither.  In 
this  we  make  no  march,  no  addition  to  our  knowledge ;  the 
utmost  that  we  do  is  to  give  completeness  to  the  statement, 
there  being  usually  an  ellipsis  or  omission  of  the  co-related 
fact.  *  This  end  of  the  magnet  is  not  the  north  end  ;  therefore 
it  is  the  south  end,'  is  no  inference ;  if  is  is  not  north,  it  is, 
by  necessary  implication,  south.  *  I  don't  like  a  curving  road, 
because  I  like  a  straight  one,'  is  a  childish  reason,  being  no 
reason  at  all,  but  the  same  fact  in  obverse. 

To  each  of  the  four  Prepositional  Forms,  A,  I,  E,  0,  there 
is  an  obverse  form : — 

Thus,  in  A, 

Every  X  is  Y;  every  man  is  mortal, 

We  first  ohvert  the  predicate, 

Every  X  is  not  Y ;  every  man  is  immortal. 

And  next  prefix  the  sign  of  negation. 

No  X  is  not  Y ;  no  man  is  immortal. 

So,  all  inert  matter  gravitates,  no  inert  matter  (not-gravitates) 
fails  to  gravitate.  All  gold  is  precious,  no  gold  is  (not-precious) 
worthless.  All  virtue  is  profitable,  no  virtue  is  (not-profitable) 
useless,  devoid  of  utility.  Freedom  of  Trade  tends  to  peace  ; 
freedom  of  Trade  averts  war.  All  knowledge  is  useful ;  no 
knowledge  is  useless. 

To  obvert  I, 

Some  X  is  Y  ;  some  men  are  wise, 

Ohvert  the  predicate,  and  prefix  the  sign  of  negation 

Some  X  is  not  not-Y  ;  some  men  are  not  (not-wise)  foolish. 

Some  stones  are  precious  ;  some  stones  are  not  (not-precious) 
worthless.  Some  virtues  are  burdensome ;  some  virtues  are 
not  (not-burdensome)  easy. 

For  E, 

No  X  is  Y,  no  men  are  gods. 

The  obverse  is, 

All  X  is  not-Y ;  all  men  are  no-gods  (excluded  from  the  gods). 

No  crows  are  white  ;  all  crows  are  excluded  from  white 
things,  are  of  some  other  colour  than  white  ;  or,  if  the  universe 
of  the  predicate  *  white/  be  not  colours,  but  white  and  black, 
'all  crows  are  black.' 


The  mle  here  is  the  opposite  of  the  rule  for  A  :  ohvert  the 
predicate,  and  remove  the  negative  sign. 

The  obverse  of  O, 

Some  X  is  not  Y ;  some  men  are  not  is — wise 

Some  X  is  not-Y ;  some  men  are  (not-wise)  foolish. 

Some  of  the  crew  were  not  saved  ;  some  were  (not  saved)  lost 

The  rule  still  is  ohvert  tJie  predicate,  and  remove  the  neaative 
sign,  which  is  to  change  the  quality  of  the  proposition,      " 

The  Universal  affirmative  with  universal  quantity  in  the  pre- 
dicate,— 

All  X  is  all  Y ;  all  inert  things  are  all  gravitating  things,  is 
obverted  to  the  same  form  as  the  obverse  of  A. 

No  X  is  not-Y ;  no  inert  things  are  found  among  things  that 
do  not  gravitate. 

All  equilateral  triangles  are  all  equiangular  triancrles ;  no 
equilateral  triangles  are  to  be  found  among  triangles  with  un- 
equal angles.  All  double-refracting  bodies  are  all  bodies  that 
polarize  light ;  no  double-refracting  bodies  are  to  bo  found 
among  bodies  that  do  not  polarize  light. 

The  Particular  Affirmative  with  a  universal  predicate,  Y  has 
the  same  obverse  as  I.  Some  X  is  all  Y  :  some  mortals  are 
all  men.  Some  X  is  no  not-Y ;  some  X  is  not  to  be  found 
among  not-Ys.  Some  mortals  are  not  to  be  found  amonff 
objects  that  are  not  men.  There  is  a  class  or  group  of  mortals 
that  you  will  not  discover  among  the  brutes  (Universe  Ani- 
mals), among  the  plants  (Universe  organized  bodies). 

Material  Ohversion. 

28.  There  are  Obverse  Inferences  justified  only  on  an 
examination  of  the  matter  of  the  proposition. 

From  'warmth  is  agreeable'  we  can  affirm,  by  formal  ob- 
version,  *  warmth  is  not  disagreeable,  and  not  indifferent.'  Wo 
cannot  affirm,  without  an  examination  of  the  subject-matter, 
'  cold  IS  disagreeable. 

There  is  a  mode  of  inference,  included  by  some  logicians 
among  Immediate  Inferences,  whereby  we  might  say,  'the 
absence  of  warmth  is  the  absence  of  an  agreeable  thinff'.'  This 
granted,  we  are  still  a  good  way  from  *  cold  is  disagreeable.' 
We  must  be  able  to  say  farther-*  the  absence  of  warmth  is 
the  same  as  cold  and  the  absence  of  the  agreeable  is  the  same 
as  the  disagreeable.'  But  we  are  not  entitled  to  say  this  ex- 
cept  on  a  reference  to  the  fact;  and  such  a  reference  teaches 
us  that  the  absence  of  warmth  may  not  be  the  same  as  cold. 


'  I 


\  i 

If' 


112 


EQUIVALENT  PROPOSITIONAX  FORMS. 


and  the  absence  of  the  aonreeablo  not  the  same  as  the  disagrree- 
able ;  there  is  a  possible  neatral  state  in  both  cases.  Bat  the 
same  experience  teaches  us  that  in  an  actual  state  of  pleasare- 
able  warmth,  the  sudden  change  to  cold  is  also  a  change  to  the 
disagreeable.  Whenever  an  agent  is  giving  us  pleasure  in 
act,  the  abrupt  withdrawal  of  that  agent  is  a  positive  cause  of 
pain.  On  the  faith  of  this  induction,  we  can  obvert  ma- 
terially a  large  number  of  propositions  regarding  pleasure  and 
pain,  good  and  evil.  If  the  sight  of  happy  beings  gives 
pleasure,  we  may  infer,  not  by  formal  implication,  but  by 
material  or  real  inference,  that  the  sight  of  unhappy  beings 
gives  pain.  The  inference  is  a  consequence  of  the  laws  of  our 
sensibility.  While  the  sight  of  happy  beings  is  giving  us 
actual  pleasure,  any  sudden  withdrawal  or  disturbance  of  that 
eight  is  a  painful  shock  or  revulsion.  What  is  more,  the 
organization  formed  to  take  pleasure  in  happy  beings,  is  by 
that  very  circumstance  formed  to  take  pain  at  the  sight  of  the 
unhappy.  So  we  cannot  take  pleasure  in  opposing  facts — 
praise  and  blame ;  we  cannot  become  indifferent  to  the  one 
without  becoming  indifferent  to  the  other. 

From  '  War  is  productive  of  evil,'  we  cannot  say  by  formal 
ob version,  '  Peace  is  productive  of  good/  As  before,  *  the 
cessation  of  war  is  the  cessation  of  an  evil,*  and  is  therefore 
good,  in  accordance  with  the  law  of  our  sensibility  that  the 
remission  of  a  felt  pain  is  a  pleasure. 

It  is  a  true  inference,  but  not  a  formal  implication,  that  if  an 
upright  minister  gives  public  confidence,  a  shufiling  minister 
causes  mistrust.  Provided  the  public  confidence  is  owing  to 
the  minister's  uprightness,  the  replacing  of  that  quality  by  its 
materia]  opposite  must  produce  the  opposite  of  confidence. 

The  remark  is  sometimes  made,  *  government  has  great 
power  for  evil,  and  but  little  power  for  good.*  Rigidly  ex- 
amined, this  is  a  contradiction.  He  that  is  able  to  do  us  a 
great  harm  is  able  to  refrain  from  that  harm,  and  to  make  all 
the  difference  in  our  lot  between  our  present  tolerable  condition 
and  a  condition  of  intolerable  misery.  The  saying  is  true  to 
this  extent,  that  government  interference,  exerted  for  bad,  could 
cause  more  misery  than  the  same  interference,  exerted  for  good, 
could  cause  happiness, 

*Cold  kills  animals,*  does  npt  necessitate  *heat  keeps  them 
alive.*  By  a  material  inference  from  the  law  of  causation,  we 
are  entitled  to  say,  keep  away  the  cold  that  kills,  and,  so  far  as 
that  agency  is  concerned,  the  animals  will  live.  This  is  not 
formal  implication  ;  it  is  a  certainty  grounded  on  caqsatioo. 


SIMPLE  CONVERSION. 


113 


« Force  compresses  bodies,'  does  not  justify  *  the  withholding 
of  force  expands  them.*  We  can  say  only,  '  the  absence  of 
force  leaves  bodies  in  their  uncompressed  state.  This,  m  hke 
manner,  is  a  material  inference  from  causation. 

If  *  knowledge  is  good,*  we  must  concede  the  obverse, 
*  ignorance  is  bad,*  but  not  by  formal  implication.  Whatever 
amount  of  good,  knowledge,  as  knowledge,  is  capable  of  domg, 
must  be  lost  according  as  knowledge  is  withheld. 

Aristotle  says,  *  the  beneficent  man  loves  those  he  has  done 
good  to.*  There  is  a  famiUar  saying  that  may  be  given  as  a 
material  obverse,  *  we  hate  those  we  have  injured.*  By  the 
laws  of  our  sensibility,  the  two  facts  are  mutually  mvolved ; 
although  there  are  limitations  that  we  learn  by  an  induction 

from  the  facts. 

Conversion. 

29  The  Logical  doctrine  of  the  Conversion  of  Proposi- 
tions is  a  case'^of  equivalence.  In  Conversion,  the  Subject 
and  the  Predicate  of  a  Proposition  exchange  places. 

The  Proposition  X  is  Y  converted,  becomes  Y  is  X ;  X  is 
not  Y,  Y  is  not  X ;  men  are  mortals,  mortals  are  men. 

The  simple  reversal  of  subject  and  predicate  does  not  always 
give  an  equivalent  form :  *  all  men  are  mortals  *  is  not  the 
same  as  *  all  mortals  are  men.*  This  arises  from  the  cu-cum- 
stance — taught  us  by  our  knowledge  of  things,  and  not 
discoverable  by  the  examination  of  forms — that  there  are  other 
mortals  besides  men.  In  all  such  propositions,  therefore,  a 
qualification  must  go  along  with  the  reversal  of  the  terms. 

(1)  In  the  forms  E  and  I,  the  reversal  of  the  order  of  the 
terms  needs  no  qualification.  Accordingly,  this  is  termed  un- 
qualified, or  Simple  Conversion.  *  No  X  is  Y,*  is  commutable 
into  *  no  Y  is  X,*  without  alteration  of  meaning.  If  '  no  men 
are  gods,*  *  no  gods  are  men ;  *  the  proposition  declares  mutual 
exclusion  or  incompatibility,  and  we  are  at  liberty  to  signify 
the  exclusion  from  either  side ;  X  excludes  Y,  and  Y  equally 
excludes  X.  No  crows  are  red ;  no  red  objects  are  crows.  No 
chemical  combinations  take  place  in  fluctuating  proportions ; 
no  combinations  in  fluctuating  proportions  are  chemical. 

In  I,  *  Some  X  is  Y,*  *  some  minerals  are  crystals,*  we  can 
say,  by  simple  reversal.  Some  Y  is  X,  some  crystals  are  mine- 
rals. Some  water  is  pure,  some  pure  material  is  water.  It  is 
as  when  two  areas  cover  one  another  partially ;  the  partial 
coincidence  is  expressed  from  either  side  without  change  of 
signification. 


I 


s^ 


114 


EQUIVALENT  PROPOSITIONAL   FORMa 


In  a  simple  conversion  of  this  nature,  *  some '  has  a  different  value 
in  the  two  propositions,  unless  the  predicate  and  the  subject  are 
co-extensive.     Thus,  in  the  couple, — '  Some  men  are  dark-haired,* 

*  some  dark-haired  beings  are  men,' — *  Some  men,*  as  compared  with 

*  all  men,'  is  a  larger  fraction  than  '  some  dark-haired  beings,*  as 
compared  with  '  all  dark-haired  beings.' 

(2)  In  converting  A,  the  universal  affirmative,  *  All  X  is 
T,'  *  all  fires  give  heat,'  we  have  to  qualify  or  limit  the  subject, 
Some  Y  is  X,  some  sources  of  heat  are  fires.  There  may  bo 
other  Ys  besides  the  Xs,  and  other  sources  of  heat  besides  fires  ; 
so  that  we  must  leave  the  possibility  open,  which  would  not  be 
done  in  simple  conversion — (all  Y  is  X,  all  sources  of  heat  are 
fires).  To  this  qualifying  conversion,  logicians  apply  the  de- 
signations Limitation^  and  per  accidens.  The  Greek  original  of 
Aristotle  was  more  descriptive, /cara  /nepo^,  'partitive*  conversion. 

One  of  the  recommendations  of  the  thorough-going  quanifica- 
tion  scheme  of  Hamilton,  is  that  it  anticipates  this  necessity  of 
qualifying  the  new  subject.  The  proposition  being  expressed, 
in  the  first  instance,  as  All  X  is  some  Y,  or  all  X  is  all  Y,  as 
the  case  may  be,  the  converse  is  Some  Y  is  all  X,  or  all  Y  is 
all  X.  *  All  men  are  some  frail  things ;  *  some  frail  things  are 
all  men. 

By  far  the  most  fertile  source  of  purely  syllogistic  fallacies 
is  the  tendency  of  the  mind  to  convert  universal  affirmatives 
without  limitation.  The  usual  form  of  the  language.  All  X 
is  Y,  unless  we  are  specially  put  on  our  guard,  is  apt  to  be 
interpreted,  as  if  X  and  Y  were  co-extensive  ;  in  other  words, 
^}  we  are  disposed  to  regard  it  as  justifying  the  simple  conver- 
\  sion,  all  Y  is  X.  The  errors  of  syllogism  to  be  afterwards 
pointed  out,  under  such  names  as  Undistributed  Middle,  and 
Illicit  Process,  mostly  grow  out  of  this  subtle  error  of  conver- 
sion. When  it  is  said,  *  All  powerful  minds  have  large  brains,* 
the  hearer  readily  slips  into  the  unlimited  converse,  *  All  large 
brains  indicate  powerful  minds/  This  fallacy  of  conversion 
is  of  frequent  occurrence  ;  and  there  is  no  more  useful  appli- 
cation of  Logical  forms  than  to  warn  against  it.  The  best 
warning,  however,  consists  in  multiplying  examples  to  show 
that,  in  universal  affirmative  propositions,  the  subject  and  the 
predicate  are  very  rarely  of  equal  extent ;  and  that,  when 
they  are  equal,  it  is  usual  to  make  known  the  fact  by  some 
form  of  language. 

A  few  instances  are  subjoined.  *  HI  doers  are  ill  dreaders,' 
does  not  suppose  that  *  111  dreaders  are  ill  doers  * ;  there  may 
be  many  causes  of  dreading  evil,  besides  having  done  evii 


r; 


CONVEKSlOli    BY  LIMITATION. 


115 


*  All  protestants  exercise  the  right  of  private  judgment ; '  so 
do  other  persons  besides  ;  hence  we  cannot  say  that  whoever 
exercises  private  judgment  is  a  protestant. 

*  All  beautiful  things  are  agreeable  ' ;  beautiful  things,  how-  , 
ever,  do  not  exhaust  all  that  is  agreeable ;  there  are  more  agree-  j 
able  things  than  there  are  beautiful  things.  / 

*  All  virtue  conduces  to  the  good  of  mankind  ;  *  it  does  not 
follow  that  whatever  conduces  to  the  good  of  mankind  is  vir- 
tuous. *  The  good  of  mankind '  is  a  much  wider  meaning  than 
virtae. 

*  All  the  pleasures  of  the  imagination,'  says  Addison,  *  arise 
from  the  great,  the  uncommon,  and  the  beautiful'  He  must 
be  supposed  to  mean  that  the  sources  of  these  pleasures  are 
found  among  things  that  are  great,  among  things  that  are  un- 
common, and  among  things  that  are  beautiful.    But  the  classes 

*  great  *  and  '  uncommon  *  must  contain  many  objects  besides 
those  yielding  imaginative  pleasure.  If  this  is  not  the  case 
with  the  *  beautiful,*  it  is  because  *  beauty  *  and  *  imaginative 
pleasure '  are  almost  synonymous. 

When  Sir  G.  C.  Lewis  remarks  that  *  Historical  evidence 
requires  contemporary  registration,*  he  does  not  mean  that  con- 
temporary registration  will  of  itself  make  historical  evidence. 
This  is  one  condition,  but  there  are  other  conditions  besides. 

The  universal  affirmative,  when  stated  in  Comprehension,  or 
Connotation, — '  the  property  A  is  accompanied  by  the  property  B,' 

*  the  attributes  of  man  are  accompanied  by  attributes  mortal,'  is  the 
form  least  favourable  to  suggest  a  limited  or  qualified  conversion. 
We  are  still  more  disposed  than  with  the  form  of  Extension,  to 
convert  simply ; — *  the  attribute  mortal  is  accompanied  by  the 
attributes  of  men.*  Hence,  for  all  the  purposes  of  the  Syllogism, 
the  proposition  in  Extension  is  alone  useful ;  the  fact  being  borne 
in  mind,  however,  that  the  Extension  is  determined  by  the  Connota- 
tion. 

(3)  In  converting  O,  the  Particular  Negative,  (Some  X  is  not 
Y,  Some  men  are  not  Englishmen)  a  complex  operation  is 
necessary.  Simple  conversion — Some  Y  is  not  X,  Some 
Englishmen  are  not  men — does  not  apply.  Two  steps  have  to 
be  gone  through,  first,  ohversion,  and  secondly,  simple  conver- 
sion. 

Thus,  by  ob version. 

Some  X  is  not-Y  (something  that  is  not  Y), 

Some  men  are  not-Englishmen  (out  of  the  class  Englishmen). 

These  obverted  forms  are  Particular  Affirmatives,  and  are 
therefore  converted  simply  : — 

Some  not-Y  (something  not  Y)  is  X. 


11 


116 


EQUIVAXENT  PEOPOSITIONAL  FOKMS, 


CONDITIONAL  INFERENCE. 


117 


Some  beings  that  are  Dot  Englishmen,  are  mezL 
*  Some  men  are  not  wise.*     By  obversion, 

Some  men  are  not-wise  (foolish). 
By  simple  conversion, 

Some  foolish  beings  are  men. 
The  names  given  to  this  compound   process  are  conversion 
by  Negation,  or  Coniraposition,     It  might  also  be  called  06- 
verted  Conversion. 

A  similar  operation  may  be  performed  upon  A,  the  Universal 
Affirmative,  so  as  to  yield  an  equivalent  negative  form  with 
transposed   terms.      The  reduction  of  the   syllogistic   mood 
named  Barokoj  requires  this  operation. 
Thus, 

All  X  is  Y, 
gives,  by  Obversion, 

No  X  is  not-Y. 
wliich,  by  simple  conversion  (of  E),  is 

No  not-Y  is  X. 
Or, 

All  men  are  mortal 
No  men  are  immortal 
No  immortals  are  men« 
In  the  same  way,  *  All  the  righteous  are  happy,'  is  con- 
verted into  *  No  unhappy  persons  are  righteous.* 

Hyjpotlutical  Inference, 

30.  Hypothetical  Propositions  are  of  two  kinds — Con- 
ditional and  Disjunctive.  They  have  been  treated  as  the 
basis  of  a  distinct  form  of  Syllogism,  called  the  Hypotheti- 
cal Syllogism. 

If  the  education  of  children  is  neglected,  they  will  grow  up 
ignorant,'  is  regarded  as  the  major  premise  of  a  syllogism; 
and  by  adding,  as  minor,  *  now  certain  children  have  been 
neglected,'  we  are  entitled  to  the  conclusion,  *  they  will  grow 
up  ignorant.*  This  has  been  called  a  Hypothetical  Syllogism 
(Conditional).  By  a  Disjunctive  Proposition  (A  is  either  B  or 
C),  coupled  with  a  proposition  givinor  one  alternative  (A  is 
not  B),  we  seem  to  infer  the  other  alternative  (A  is  C) ;  which 
would  be  a  Disjunctive  Syllogism. 

In  his  Lectures  on  Logic,  Sir  W.  Hamilton,  following  the  usual 
practice,  takes  up  hypothetical  reasoning  after  Syllogism ;  but  in 
the  notes  at  the  end,  published  after  his  death,  he  prefers  to  treat 
it  as  a  case  of  Immediate  Inference.    Mr.  Mansel.  also,  argues  that 


hypothetical  reasoning,  so  far  as  it  is  purely  logical,  is  purely  cate- 
gorical. The  obvious  differences  between  the  syllogism  and  hypo- 
thetical reasoning  are  (1)  the  absence  of  a  middle  term;  in  the 
hypothetical  syllogism  all  the  terms  are  introduced  in  the  so-called 
major;  (2)  the  minor  and  the  conclusion  indifferently  change 
places,  and  each  of  them  is  merely  one  of  the  two  members  con- 
stituting the  major;  (3)  the  major  (so-called)  consists  of  two 
propositions,  the  categorical  major  of  two  terms. 

The  Conditional  form  applies  in  the  first  instance  to  cause  and 
effect.  If  the  cause  is  present  the  effect  is,  and  if  the  effect  is 
absent  the  cause  is  absent.  But  the  same  form  holds  good  when 
one  thing  is  the  sign  of  another,  or  is  constantly  associated  with 
that  other. 

Boole  and  De  Morgan  are  of  opinion  that  the  hypothetical  in- 
ference is  not  different  from  immediate  inference.  Boole  observes 
in  his  *  Laws  of  Thought'  (p.  241)  that  the  hypothetical  syllogism  is 
no  syllogism  at  all,  as  it  need  contain  no  more  than  two  terms. 
De  Morgan  says — *  The  law  of  thought  connecting  hypothesis 
with  necessary  consequence  is  of  a  character  which  may  claim  to 
stand  before  syllogism,  and  to  be  employed  in  it,  rather  than  the 
converse.'      (Syllabus,  p.  66). 

31.  In  the  Conditional  Proposition — If  A  is  B,  C  is  D, 
the  equivalent  is — A  being  assumed  to  be  B,  it  follows 
that  C  is  D. 

There  is  no  inference  in  this  case.  Accepting  *  A  is  B,'  we 
accept  *  C  is  D  ;*  this  is  another  expression  for  the  same  fact. 

*  If  the  weather  continues  fine,  we  shall  go  to  the  country*, 
is  transformable  into  the  equivalent  form  *  The  weather 
continues  fine,  and  so  we  shall  go  to  the  country.\  Any 
person  affirming  the  one,  does  not,  in  aflB.rming  the  otfti^  de- 
clare a  new  fact,  but  the  same  fact.  No  new  matter  is  intro- 
duced into  the  assertion  ;  it  is  a  pure  instance  of  the  Law  of 
Consistency.  When  a  buyer  offers  a  seller  a  certain  price  for 
an  article,  and  the  seller  says, — Here,  then,  is  the  article — the 
buyer  is  only  consistent  with  himself  in  paying  the  price.  Yet 
this  is  all  that  is  done  in  a  supposed  conditional  inference. 

A  second  form  of  so-called  conditional  inference,  is  that  the 
denial  of   the  consequent  is   the  denial  of   the   antecedent; 

*  C  is  not  D,  therefore  A  is  not  B,*  If  the  weather  is  fine, 
we  go  to  the  country ;  *  *  we  are  not  going  to  the  country, 
therefore  the  weather  is  not  fine.*  This  is  still  mere  formal 
equivalence.  It  is  implied  in  what  has  already  been  stated. 
It  is  not  a  distinct  fact,  but  the  same  fact,  in  obverse.  *  X  is 
followed  by  Y*  implicates  one  of  two  statements;  X  has 
happened,  hence  Y  has  followed  j  or, — Y  has  not  hap|)ened. 


\( 


118 


EQUIVALENT  PEOPOSITIONAL  FORMS. 


DISJUNCTIVE  INFERENCE. 


119 


hence  X  has  not  happened  (if  it  did,  Y  would  follow).  Such 
is  the  two-fold  bearing  of  a  conditional  proposition. 

It  is  laid  down,  as  part  of  the  tlieory  of  Conditional  Proposi- 
tions, that  the  granting  of  the  consequent  does  not  prove  the 
antecedent ;  the  assertion  *  C  is  D,'  does  not  prove  that  *  A  is 
B.'  *  If  he  has  caught  the  infection,  he  will  die ;  *  his  death 
does  not  prove  he  has  caught  the  infection,  because  there  are 
many  causes  of  death,  besides  the  one  mentioned.  This  rule, 
or  precaution,  is  therefore  grounded  on  our  experience,  which 
informs  us  that  in  nature  there  frequently  occurs  a  plurality 
of  causes.  The  case  is  parallel  to  the  rule  for  the  conversion 
of  a  Universal  AffiiTnative,  which  depends  on  our  knowing  as 
a  fact  that  in  such  affirmations,  the  predicate  is  not  necessarily 
co-extensive  with  the  subject,  but  is  most  frequently  larger 
than  the  subject. 

If  the  condition  given  were  the  sole  condition  of  the  conse- 
quent, the  affirmation  of  the  consequent  would  be  the  affirma- 
tion of  the  antecedent.  *  If  force  is  expended,  an  equivalent 
force  will  be  generated '  is  a  statement  containing  the  one 
indispensable  condition  of  the  effect  (an  equivalent  force 
generated).  Under  all  possible  circumstances,  the  production 
of  force  supposes  a  prior  force  expended :  hence  the  affirma- 
tion of  the  consequent  (the  generation  of  force)  is  the  affirma- 
tion of  the  antecedent  (the  expenditure  of  force).  Such  condi- 
tionals, however,  being  the  exception,  and  not  the  rule,  logicians 
forbid  the  affirmation  of  the  antecedent  from  the  affirmation 
of  the  consequent. 

On  the  same  ground  it  is  forbidden  to  deny  the  consequent, 
because  the  antecedent  is  denied  ;  A  is  not  B,  therefore  C  is 
not  D  ;  *  the  man  has  not  caught  the  infection,  and  therefore 
he  will  not  die.' 

The  common  form  of  conditional  proposition  is  when  both  the 
members  are  affirmative.  But  either  member,  or  both,  may  be 
negative.    There  are  thus  four  forms  : — 

(1)  If  A  is  B,  C  is  D. 

(2)  If  A  is  not  B,  C  is  D.  *  If  the  rebellion  be  not  crushed,  the 
king  will  be  executed.'  It  is  equally  proper  to  say  that  the  rebel- 
lion having  been  successful,  the  king's  execution  is  certain,  or  that 
if  the  king  is  not  executed,  the  rebellion  has  been  crushed.  *  If  the 
jury  cannot  agree,  they  will  be  discharged.*  If  the  jury  be  not 
discharged,  they  have  agreed.  *  If  succour  be  not  speedily  sent, 
the  city  will  surrender.'  If  the  city  does  not  surrender,  succour 
has  been  sent. 

(3)  If  A  is  B,  C  is  not  D.  *  If  the  will  of  Henry  VIII.  was 
valid,  James  I.  had  no  legal  title  to  the  throne  of  England :  If 
Juiues  I.  had  a  legal  title,  then  the  will  of  Henry  was  not  valid.* 


*  If  the  harbour  is  frozen,  the  ships  cannot  come  in  :  If  the  ships 
can  come  in,  the  harbour  is  not  frozen.'  So  '  He  can't  be  wrong 
whose  life  is  in  the  right :  If  he  is  wrong,  his  life  is  not  in  the  right.' 

(4)  If  A  is  not  B,  C  is  not  D.  *  If  inspectors  be  not  appointed, 
no  regard  will  be  paid  to  the  act.'  This  implies  that  if  the  act  is 
observed,  inspectors  have  been  appointed.  *  No  Bishop,  no  King.* 
If  the  king  is,  the  bishops  are.  *  If  there  be  no  God,  no  future 
life  awaits  us :  If  a  future  life  does  await  us,  there  is  a  God.' 

These  forms  are  all  regulated  by  the  same  law  of  transposition. 
The  chief  interest  of  (2)  and  (3)  lies  in  this,  that  when  both  forms 
apply  to  two  propositions,  the  union  of  the  two  is  equivalent,  as 
we  shall  see,  to  a  disjunctive  proposition. 

32.  The  Disjunctive  Proposition  may  appear  in  the 
foUowiug  forms  : — 

I.  A  is  either  B  or  C. 
II.  Either  B  or  C  exists. 
III.  Either  A  is  B,  or  C  is  D. 

*  He  is  either  a  fool  or  a  rogue  *  means  *  If  not  a  fool,  he  is 
a  rogue,  and  if  not  a  rogue,  he  is  a  fool.'  Otherwise,  '  Not 
being  a  fool,  he  is  a  rogue,'  and  *Not  being  a  rogue,  he  is  a 
fool.'  These  are  all  equivalent  forms;  and  the  supposed  rea- 
soning consists  merely  in  electing  one  alternative,  according  to 
the  facts  of  the  case.  The  datum  being,  *  he  is  a  not  a  fool,* 
we  use  the  alternative  *  he  is  a  rogue,'  and  so  on. 

This  corresponds  to  the  working  out  of  a  Logical  Division. 
'  Feelings  are  either  pleasures,  pains,  or  neutral  excitement.* 
The  equivalent  propositions  are  such  as  these  : — a  feeling  not 
a  pleasure,  is  either  pain,  or  a  neutral  state ;  a  feeling  not  a 
pain,  and  not  neutral,  is  a  pleasure ;  a  feeling  not  neutral  is 
either  pleasure  or  pain,  and  so  forth.  There  is  no  real  infer- 
ence in  these  transmutations.  They  are  strict  equivalents  of 
the  original  Disjunctive  Division. 

Compared  with  the  Conditional  propositions,  this  form 
exhibits  a  greater  degree  of  complexity  in  the  relation  of 
dependence.  The  Conditional  form  expresses  a  simple  or 
one-sided  dependence ;  the  presence  of  the  first  gives  the 
presence  of  the  second,  and  the  absence  of  the  second  implies 
the  absence  of  the  first.  The  Disjunctive  proposition  indicates 
a  double  or  reciprocal  dependence  ;  the  presence  of  either  is 
the  absence  of  the  other,  and  the  absence  of  either  is  the 
presence  of  the  other.  This  is  the  ordinary  case,  but  the 
disjunctive  form  might  be  employed  when  the  presence  of 
either  implied  the  presence  of  the  other,  the  absence  of  either, 
the  absence  of  the  other.     Thus,  *  Everything  in   nature  is 


120 


EQUIVALENT  PROPOSITIONAL  FORMa 


either  inert  or  has  no  weight/  From  this  we  derive  the 
following : — 

(1)  It  is  inert,  and  so  it  has  not  no- weight  =  it  has  weight. 

(2)  It  is  not  inert,  and  so  it  has  no  weight. 

(3)  It  has  no  weight,  and  so  it  is  not  inert. 

(4)  It  has  not  no- weight,  i.e.  it  has  weight,  and  so  it  is  inert. 
Owing  to  the  double  negation,  this  form  is  very  awkward  ; 

but  it  shows  an  intermediate  stage  between  the  conditional 
and  the  ordinary  disjunctive  propositions. 

*  You  must  either  pay  a  fine  or  go  to  prison '  implicates 
four  facts : — 

(1)  If  you  pay  the  fine,  you  don't  go  to  prison, 

(2)  If  you  don't  pay  the  fine,  you  go  to  prison. 
(8)  If  you  go  to  prison,  you  don't  pay  the  fine. 
(4)  If  you  don't  go  to  prison,  you  pay  the  fine. 

A  disjunction  is  not  thoroughgoing  and  valid  unless  it  gives 
four  true  propositions  in  that  form,  and  the  only  sure  test  of 
its  validity  is  to  put  it  through  the  forms.     Thus  : — 

*  Either  the  witness  is  perjured,  or  the  prisoner  is  guilty,* 

(1)  If  the  witness  is  perjured,  the  prisoner  is  not  guilty. 

(2)  If  the  witness  is  not  perjured,  the  prisoner  is  guilty 

(3)  If  the  prisoner  is  guilty,  the  witness  is  not  perjured. 

(4)  If  the  prisoner  is  not  guilty,  the  witness  is  perjured. 
The  propositions  (2)  and  (4)  are  correct,  but  (1)  and  (3) 

coald  not  be  maintained.  This  reveals  a  weakness  in  the  form 
of  the  statement.  Put  thus—*  If  the  witness  tells  the  truth, 
the  prisoner  is  guilty  ' — the  assertion  is  perfectly  accurate,  for 
the  witness  may  be  perjured,  and  still  the  prisoner  may  be 
guilty ;  or  the  prisoner  may  be  guilty,  and  still  the  witness 
may  not  have  told  the  truth. 

*  Punishment  is  intended  either  to  repress  crime  or  reform 
the  criminal.' 

*  If  punishment  represses  crime,  it  does  not  reform  the  crimi- 
nal (1).'     Here  we  see  at  once  that  both  things  may  concur. 

'Either  the  ballot  must  be  given,  or  intimidation  will 
prevail.' 

If  intimidation  does  not  prevail,  the  ballot  exists  (4).  This 
would  not  be  affirmed,  and  therefore  the  disjunction  is  not 
thoroughgoing. 

*For  many  years  past,  this  country  has  been  governed 
either  by  the  Whigs  or  by  the  Tories'  leaves  open  a  third 
case,  namely,  by  a  coalition. 

*  He  either  cannot,  or  will  not,  do  it '  leaves  open  the  supposi- 
tion of  *  neither.' 


t 


r 


DILEMMA. 


121 


*  The  substance  held  in  solution  is  either  lime  or  magnesia ' 
is  an  example  from  chemistry,  and  deserves  to  be  put  through 
all  the  forms,  as  each  form  is  a  test. 

(1)  If  the  reaction  of  lime  is  given,  magnesia  is  not  present. 

(2)  If  the  reaction  of  lime  is  not  given,  magnesia  is  present. 

(3)  If  the  reaction  of  magnesia  is  given,  lime  is  absent. 

(4)  If  the  reaction  of  magnesia  is  not  given,  lime  is  present. 
A  chemist  would  not  be  satisfied  without  trying  two  of 

these  forms,  a  positive  and  a  negative. 

33.  The  Dilemma  combines  a  Conditional  and  a  Dis- 
junctive proposition. 

If  the  Antecedent  of  a  conditional  is  made  disjunctive,  there 
emerges  what  Whately  calls  a  simple  Constructive  Dilemma, 
If  either  A  or  B  is,  C  is. 
Now,  either  A  or  B  is. 
Therefore,  C  is. 
If  either  plants  or  animals  are  found,  there  must  have  been 
previous  germs. 

Now,  either  plants  or  animals  are  found. 

Whence,  there  have  been  previous  germs. 

The   Consequent   being   made  Disjunctive,   gives  the  more 

usual  type : — 

If  A  is,  either  B  or  C  is. 
If  the  barometer  falls,  there  will  be  either  wind  or  rain. 
Various  suppositions  may  be  made,  bringing  out  the  possible 
alternatives.     Thus — 

A  is  ;  then,  B  or  C  is. 

C  is  not ;  then,  If  A  is,  B  is. 

C  is  ;  then,  If  A  is,  B  is  not. 

B  is  ;  then,  if  A  is,  C  is  not. 

B  is  not ;  then  if  A  is,  C  is. 

B  is  not,  and  C  is  not ;  then,  A  is  not.* 

•  Another  form  of  simple  Dilemma  is 

If  B  is,  A  is  ;  and  if  C  is,  A  is. 
Now,  either  B  or  C  is. 
Whence,  A  is. 
This  form  is  illustrated  by  a  sentence  from  Macaulay : — 
Predestination  makes  men  immoral ;  for  if  a  man  be  an  heir  of  grace, 
his  exertions  must  be  useless ;  if  an  heir  of  wrath,  they  must  be  unavailing. 
If  a  man  be  an  heir  of  grace,  his  exertions  are  useless  ;  if  of  wrath, 
unavailing. 

But,  according  to  predestination,  a  man  is  an  heir  either  of  grace  or  of 
wrath;  therefore,  according  to  predestination,  his  exertions  must  be 
useless. 

But  he  who  believes  his  exertions  to  be  useless  must  be  immoral ; 
therefore,  predestination  makes  men  immoral. 


i 


/ 


122 


EQUIVALENT  PROPOSITION  AL   FORMS. 


EXAMPLES  OF  THE  DILEMMA, 


123 


This  last  is  the  true  dilemma,  which  is  Destructive,  The 
forms  preceding  are  equally  valid,  and  are  occasionally  appli- 
cable.    For  instance — 

If  the  orbit  of  a  comet  is  diminished,  either  the  comet  passes 
through  a  resisting  medium,  or  the  law  of  gravitation  is  partially 
suspended. 

But  the  second  alternative  is  inadmissible. 

Hence,  if  the  orbit  of  a  comet  is  diminished,  there  is  a 
resisting  medium. 

The  conclusion  is  a  simple  conditional  proposition,  the  com- 
plexity having  been  reduced. 

The  following  are  examples  of  the  common  Dilemma  : — 

If  a  classical  education  is  worth  the  cost,  either  it  must  be 
pre-eminently  fitted  to  develop  the  mental  powers,  or  it  must 
lurnish  exceedingly  valuable  information.  But  neither  alter- 
native can  be  maintained,  and  so  a  classical  education  is  not 
worth  the  cost. 

If  schoolmasters  can  claim  exemption  from  poor's  rates,  it 
must  be  either  by  statute  or  by  the  common  law.  Now,  no 
statute  exempts  tliem  ;  and  the  common  law  does  not  apply. 
Hence  they  can  claim  no  exemption  from  Poor's  Rates. 

Sometimes  the  antecedent  is  more  conveniently  put  in  the 
form  of  a  question. 

How  do  we  know  that  our  intuitive  beliefs  concerning  the 
world  are  invariably  true  ?  Either  it  must  be  from  e'cperience 
establishing  the  harmony,  or  an  intuitive  belief  must  certify  the 
correctness. 

Now,  experience  cannot  warrant  such  harmony  except  in  so 
far  as  it  has  been  perceived.  Still  more  futile  is  it  to  make  one 
instinctive  belief  the  guarantee  of  another.  Thus  we  cannot 
know  that  any  intuitive  belief  is  universally  valid. 

The  Dilemma,  although  occasionally  a  useful  form,  is  per- 
haps oftener  a  snare.  The  point  is  whether  the  disjunction  is 
valid  ;  and  there  is  always  supposed  the  rejection  of  many 
possible  cases.  We  begin  with — If  A  If,  B  or  C  or  D  or  E  is. 
One  after  another  of  the  suppositions  is  rejected,  until  at  last  only 
two  are  left,  and  these  being  removed,  the  antecedent  is  finally 
denied.  The  illusive  case  is  when  tlie  logician  trusts  to  the 
law  of  excluded  middle  as  a  guarantee  of  the  disjunction.  If 
A  is,  A  is  either  B  or  not-B.  We  may  easily  affirm  that  A  is 
not  13,  but  how  can  we  affirm  that  it  is  not  not-B,  ie.  it  is  neither 
B  nor  anything  else  than  B.  It  is  plain  that  if  we  were  able 
to  affirm  that  A  is  not  anything  else  than   B,  we  should  not 


require  a  dilemma  nor  yet  the  term  B  to  disprove  A's  existence. 
As  an  example  of  a  false  disjunction,  we  may  take  the  ancient 
fallacy  of  Motion. 

If  a  body  moves,  it  must  be  either  in  the  place  where  it  is, 
or  in  the  place  where  it  is  not. 

But  a  body  cannot  move  in  the  place  where  it  is,  nor  yet 
in  the  place  where  it  is  not.     Hence,  a  body  cannot  move  at  all. 

The  disjunction  to  conform  to  the  law  of  Excluded  Middle 
must  be  in  this  form  : — 

The  body  must  move  in  the  place  where  it  is,  or  it  must  not 
move  in  the  place  where  it  is.  We  then  admit  that  a  body 
does  not  move  in  the  place  where  it  is,  and  the  possibility  of 
motion  is  still  undestroyed. 

*  If  the  books  in  the  Alexandrine  Library  be  in  conformity 
with  the  doctrines  of  the  Koran,  there  is  no  need  of  them,  if 
they  are  adverse  to  the  doctrines  of  the  Koran,  they  should  be 
destroyed.'  This  is  not  exhaustive,  as  the  books  might  not 
treat  of  religion  ;  but  the  assertion  implies  that  no  knowledge 
is  desirable  except  religious  knowledge. 

*  A  Berkeleian  is  reduced,  in  truth,  to  this  dilemma :  if  he 
knows  what  external  things  are,  it  can  only  be  by  perceiving 
them  as  external, — which  contradicts  his  theory.  If,  on  the 
other  hand,  he  does  not  know  what  they  are,  he  is  incapable  of 
usino"  the  expression  external  with  any  meaning,  and  could,  in 
fact,  never  have  invented  or  thought  of  employing  it.*  This 
assumes  that  the  meaning  of  *  external  objects  '  is  not  in  dis- 
pute ;  it  is  a  summary  mode  of  stating  one  side ;  Berkeley 
could  say  that  the  meaning  of  external  objects  was  just  the 
point  in  dispute.  ^ 

Synonymous  Propositions, 

34  Every  language  contains  various  wordings  for  the 
same  matter  of  fact ;  and  there  is  occasionally  an  advan- 
tac^e  in  passing  from  one  of  these  to  the  other.  We  may 
call  these  variations  Synonymous  Propositions, 

There  being,  in  many  instances,  a  plurality  of  names  for 
che  same  object,  or  the  same  fact,  we  find  them  freely  inter- 
changed. The  essential  characteristic  of  all  material  substance 
is  expressed  as  Resistance,  Fo»ce,  Momentum,  Inertness,  all 
which  means  the  same  thing,  although  viewed  in  different 

aspects. 

*  Men  are  mortal,'  *  all  will  die,*  *  we  are  doomed  to  dissolu- 
tion,' *  decay  is  the  law  of  our  being  ' — are  mere  synonymoua 


i 


Ht^M-'rX, 


J 


124 


EQUIVALENT  PROPOSITIONAL  FORMS. 


variations  that  add  nothing  to  the  fact^  but  may  contribute  to 
the  force  of  it. 

*  This  weighs  that  down,  therefore,  it  is  heavier/  is  not  a 
real  inference  ;  the  two  expressions  signify  one  operation. 
There  is  no  other  criterion  of  the  comparative  heaviness  of 
two  things,  but  weighing  them.  This  block  of  marble  is  larger 
than  that,  therefore,  it  is  heavier,  is  a  real  inference.  The 
superior  size  is  given  as  the  evidence  of  superiority  in  another 
and  different  quality,  weight. 

*  What  has  been,  will  be ;  *  *  the  future  will  resemble  the 
past ;'  *  nature  is  uniform  ;*  *  the  laws  of  the  universe  are 
constant  ;* — these  are  all  synonymous  expressions  for  the  same 
fundamental  fact.  One  of  them  cannot  be  tendered  as  the 
reason  or  evidence  of  another.  The  multiplication  of  forms  may 
aid  in  expounding  the  great  truth  underlying  them  all.  One 
form  may  be  suggestive  of  one  class  of  examples,  a  different 
form  may  suggest  another  class.  The  variation  of  language  is 
often  a  great  intellectual  help.  It  is,  however,  a  source  of 
danger.  One  of  the  lures  and  snares  of  language  lies  in  the 
tendency  of  the  mind  to  suppose  that  two  different  forms  of 
expression  mean  two  different  things.  Hence,  it  is  a  common 
fallacy,  and  a  device  of  Rhetoric,  to  give  a  fact  as  the  reason 
for  itself ;  there  being  merely  a  change  in  the  expression. 

There  is  often  a  difficulty  in  finding  a  single  satisfactory  ex- 
pression for  notions  and  truths  of  great  generality.  Thegreatlaw 
of  the  Conservation  of  Force,  needs  the  aid  of  other  terms  to 
suggest  all  its  meaning — Persistence,  Exchangeability,  Equi- 
valence, Correlation.  The  grounds  of  the  Transcendental 
part  of  Algebra,  called  the  Differential  Calculus,  have  been 
viewed  in  a  great  variety  of  aspects,  expressed  by  different 
names — Exhaustions,  Limits,  Prime  and  Ultimate  Ratios, 
Evanescent  Quantities,  Fluxions,  Differential  Co-efficients. 

The  elements  of  the  mind  called  intuitive  by  the  a  priori 
school  of  philosophy,  are  stated  sometimes  under  the  guise  of 
the  Notion,  and  sometimes  under  the  guise  of  the  Proposition  ; 
the  subject  matter  being  identical.  We  may  say  either  *  Cause* 
is  an  innate  notion;  or  *  every  effect  must  have  a  cause '  is  an 
innate  proposition,  principle,  or  judgment. 

The  Dictionary  mode  of  defining  words  consists  in  giving 
tautologous  phrases,  which  shows  that  these  abound  in  lan- 
guage. If  there  were  only  one  name  for  one  thing,  an  Eng- 
lish Dictionary,  conceived  on  the  usual  plan,  could  not  exist. 


ASPECTS  OF  THE  PROPOSITION. 


126 


EXERCISES   ON  PROPOSITIONS,  INCLUDING  NOTIONS. 

The  following  are  examples  of  Propositions,  to  be  used 
as  exercises,  in  connexion  vith  the  Classification  of  Pro- 
positions, and  the  Equivalent  Forms.  As  every  real  pro- 
position has  two  notions,  while  even  verbal  propositions 
contain  at  least  one  notion,  the  examples  will  also  furnish 
exercises  on  the  Notion. 

As  regards  the  Class  or  Notion,  in  opposition  to  the  Real 
Proposition,  the  points  to  be  illustrated  are  comparatively  few. 
An  Individual  or  Singular  object  or  thing  may  be  exhibited  in 
contrast  to  classes  or  Generalities  ;  Homer  to  poets,  the  R»hine 
to  rivers ;  Britain  to  sovereign  states.  Of  generalized  things, 
we  have  the  Class  (concrete),  and  the  Attributes  (abstract). 
The  grades  of  generality  may  be  exemplified, — a  very  valuable 
exercise.  There  remains  only  the  illustration  of  Relativity, 
the  assigning  of  the  correlative  class  or  notion  in  a  definite 
universe. 

The  Notion  often  condenses  in  a  word  what  would  require 
one  or  more  propositions  to  express  in  full.  Refraction,  Elec- 
tricity, Crystallization,  Chemical  Affinity, — are  names  for  com- 
plex facts,  involving  many  propositions,  and  not  to  be  explained 
without  giving  these  propositions.  'Refraction'  is  the  sum- 
mary designation  of  the  principle  or  law  of  the  bending  of 
light  in  passing  from  one  transparent  medium  to  another  ;  and 
its  full  and  proper  expression  is  the  law  itself  given  as  a  real 
predication. 

The  various  aspects  of  the  Proposition,  exhibited  in  the 
foregoing  chapter,  may  be  summarized  as  follows  :— 

I.  As  Individual  or  General,  and  as  of  different  grades  of 
Generality,  under  which  is  brought  out  the  diminishing  Con- 
notation or  Comprehension  that  accompanies  increasing  Gene- 
rality or  Extension. 

The  principle  of  Relativity  applied  to  Propositions,  appears 
under  various  subsequent  heads — Negation,  Opposition,  and 
Obversion. 

II.  As  possessing  Quantity  and  Quality,  with  reference  to 
the  uses  of  Syllogism. 

III.  As  Complex  in  contrast  to  Simple;  the  important 
logical  example  of  Complexity  being  Hypothetical  proposi- 
tions (Conditional  and  Disjunctive). 

IV.  As  opposed  in  the  various  modes  named  Contbaeies, 
Coktbadictories,  &c. 


,.» 


f 


126  EXERCISES  ON   PROPOSITIONS,  INCLUDING  NOTIONS. 

Y.  As  in  their  final  Import,  affirming  Equality,  Co-exist- 
ence or  Succession  ;  the  two  last  containing  the  special  kinds 
named  respectively  Co-inhering  Attributes  and  Causation. 

In  this  connexion,  there  might  be  given  the  particular 
Science  that  the  proposition  belongs  to  : — as  Mathematics, 
Chemistry,  Psychology,  &c.  For  although  propositions  of 
Equality  make  up  the  one  science.  Mathematics  ;  those  under 
the  two  other  heads — Co-inhering  Attributes  and  Causation- 
are  distributed  among  several  sciences. 

VI.  As  having  numerous  Equivalent  Forms,  namely  General 
and  Particular,  Greater  and  Less  in  Connotation,  Obverse, 
Converse,  Hypothetical  Equivalents,  Synonyms. 

VII.  All  the  foregoing  classes  suppose  real  predication.  It 
is,  however,  important  to  taking  every  opportunity  of  contrast- 
ino"  Real  with  Vekbal  propositions.  A  farther  interest 
attaches  to  the  difference  between  predicating  a  Fropriitm  and 
predicating  a  Goncomitayit, 

Many  of  the  propositions  occurring  in  common  speech  are 
not  certain,  but  only  probable ;  the  affirmation  holds  not  in  all 
cases,  but  in  a  very  great  number,  as  *  Tempemte  persons  are 
lono-  lived.'  The  subject  of  Probability  belongs  to  the  Induc- 
tive Logic,  and  has  not  been  adverted  to  in  the  foregoing 
classification.  Still,  the  distinction  of  probable  and  certain  is 
so  easily  understood,  in  the  main  circumstance,  and  so  im- 
portant to  be  born  in  mind,  in  matters  of  truth  and  false- 
hood, that  it  should  be  impressed  on  every  suitable  oppor- 
tunity. 

At  the  present  stage,  consideration  is  given,  not  to  the  actual 
truth  and  falsehood  of  propositions,  but  only  to  what  they  pro- 
fess. The  proof  or  evidence  of  assertions  belongs  to  the  sub- 
sequent heads — Deduction  and  Induction. 

Of  the  following  examples,  promiscuously  chosen,  the  vari- 
ous forms  are  to  be  used  according  to  their  peculiar  suitability 
for  the  different  classes  of  propositions.  In  a  large  proportion 
of  them,  there  is  scope  for  translating  the  idioms  of  ordinary 
language  into  modes  of  expression  more  in  accordance  with 
the  logical  forms. 

*  Honesty  is  the  best  policy.' 

A  proposition  of  a  certain  grade  of  Generality ;  one  relating 
to  *  virtue '  would  be  more  general ;  one  relating  to  *  paying 
one's  debts'  would  be  less  general,  but  would  have  a  more 
comprehensive  predicate. 

As  regards  Quantity  and  Quality  (in  Form),  it  is  a  universal 


EXAMPLES   OF  PROPOSITIONS. 


127 


affirmative;    being  translateable  into  *  all  honest  actions  are 
more  politic  than  actions  not  honest.* 

We  read,  in  Otway,  *  Honesty  is  a  damned  starving  quality,' 
which  is  the  full  Contrary.  The  Contradictory  is,  'Some 
honest  actions  are  not  good  policy.' 

In  Import,  the  proposition  is  one  of  Causation — *  Honest 
actions  bring  good  consequences  to  the  agent.'  The  subject 
being  lilind,  it  belongs  to  the  science  of  Psychology. 

Many  Equivalent  Forms  could  be  given — *  Some  honest 
actions  are  politic'  Obversion  (Formal)  :— *  Honesty  is  not 
bad  policy ;'  '  No  honest  men  are  unsuccessful  men ;'  (Material) 
*  Dishonesty  is  bad  policy.'  Conversion  : — '  Some  politic 
actions  are  honest  actions." 

The  proposition  is  not  verbal  but  Real ;  good  policy  is  not, 
in  whole  or  in  part,  the  definition  of  honesty.  It  is  a  Pro- 
prium,  or  derivative  proposition,  and  not  an  ultimate  fact ;  it 
is  deducible  from  the  operation  of  honesty,  under  general  laws 
of  cause  and  effect  in  the  human  mind. 

It  is  a  proposition,  not  certain,  but  Probable.  It  is  true,  not 
universally,  but  in  a  large  and  preponderating  number  of 
cases. 

*A11  the  alkalies  and  alkaline  earths  are  oxides  of  the 
metals.'  A  complex  affirmation,  containing  two  in  one,  which 
must  be  taken  separately.  In  form  and  import,  they  are  so 
closely  allied,  that  one  may  represent  both. 

As  regards  External  Form,  each  is  an  example  of  A,  with  no 
peculiarities  requiring  attention. 

In  Import,  they  belong  to  the  class  of  affirmations  of  Co- 
inhering  Attributes,  and  fall  under  Chemistry. 

Strictly  analyzed,  each  is  a  verbal  proposition;  the  predicate-— 
oxides  of  the  metals  —is  now  given  as  one  of  the  essential 
characters  of  Alkalies,  and  of  Alkaline  Earths.  In  the  origi- 
nal connotation  of  these  words,  however,  the  composition  or 
derivation  of  the  substances  was  not  taken  into  account;  the 
main  fact  was  the  relation  to  acids,  and  to  neutral  salts.  At 
that  stage,  Davy's  discovery  was  an  additional  fact,  and  there- 
fore a  real  predication.  In  so  far  as  the  terms  still  suggest 
to  the  mind  only  the  primitive  meaning  of  an  Alkali,  the 
proposition  is  but  real,  not  essential  and  verbal. 

*  Fishes  breathe  by  gills.'  Equivalent  to  *  All  fishes.'  A 
verbal  or  essential  proposition  of  Kinds;  the  subject  *  fishes' 
connotes  all  the  essential  attributes  of  fishes,  of  which  the  pre- 


i 


128  EXERCISES  ON  PROPOSITIONS,  INCLUDING  NOTIONS. 


Bent  is  one.  As  the  structure  is  confined  to  fishes,  the  subject 
and  predicate  are  co-extensive.  It  is  a  proposition  in  Biology, 
or  Zoology. 

*  One  aid  to  health  is  exercise.*  An  inversion  for — *  Exercise 
aids  oV  promotes  health.*  *  All  persons  that  take  exercise  use 
one  of  the  aids  to  health.'  A  proposition  of  Cause  and  Efiect, 
in  Biology.     A  Real  proposition. 

*Pain  is  a  consequence  of  Sensibility.'  (Concrete)  All 
sensitive  being  are  beings  subject  to  pain ;  all  sensitive  beings, 
under  certain  circumstances,  are  pained  beings.  A  Verbal  or 
analytical  proposition ;  *  being  subject  to  pleasure,  to  pain  and 
to  neutral  excitement,*  is  the  definition  of  *  Sensitive.*  Might 
be  given  to  illustrate  the  Aristotelian  distinction  of  the  PoteU' 
tial  and  the  Actual. 

*  Whatever  is,  is  right.*  The  generality  of  the  subject  is  even 
beyond  the  two  summa  genera — Object  and  Subject.  Exist- 
ence is  a  fictitious  predicate,  and,  in  intelligible  propositions, 
means  something  more  definite  than  it  seems.  The  proposi- 
tion must  be  interpreted — '  all  the  arrangements  of  the  world 
are  righl^  or  are  good.*  In  Import,  this  is  Cause  and  Effect. 
The  obverse  is  *  nothing  that  is,  is  wrong,*  *  there  is  no  wrong/ 

*  The  Beautiful  and  the  Useful  are  partially  coincident ; '  a 
synonymous  form  for — Some  Beautiful  things  are  useful,  and 
conversely. 

*  The  wages  of  sin  is  death,*  or  Death  is  the  wages  of  sin. 
This  form  would  suggest  a  universal  co-existence  between 
Death  and  Sin — all  beings  that  die  are  all  beings  that  sin. 
Another  interpretation  is  *Adam*s  sin  was  the  cause  of 
death.* 

*  Self-confidence  is  not  inconsistent  with  great  weakness.* 
*  Self-confident  persons  may  be  weak  persons.*  This  is  a  con- 
tradictory to  *  AH  self-confident  persons  are  strong.* 

Of  a  similar  nature  is — *  A  proud  man  is  not  necessarily  a 
bad  man.' 

*  Man  is  the  only  animal  combining  sociability  and  solitude. 
A  form  equivalent  to  the  universal  Quantification  of  the  Predi- 


i^\ 


EXAMPLES  OF  PROPOSITIONS. 


129 


cate,  and  useful  to  test  De  Morgan's  criticism  as  to  the  denial 
of  such  propositions. 

Take  together  the  47th  and  the  48th  propositions  of  the 
First  Book  of  Euclid,  and  show  their  bearing  on  universal 
quantification. 

*  Adverbs  qualify  verbs  ; '  *  Adverbs  are  to  be  placed  near 
the  words  they  qualify.*     How  do  these  differ  logically  ? 

*The  greater  the  novelty,  the  greater  the  pleasure.'  A 
proprium  or  inference  from  *  Novelty  is  a  source  of  pleasure.* 
In  propositions  of  cause  and  effect,  we  are  entitled  to  infer 
the  proportionality  of  the  one  to  the  other. 

•Symmetry  is  the  general  law  of  creation ; '  a  greatly  distorted 
expression  of  what  is  meant.  *  Symmetry  *  is  a  word  condens- 
ing a  proposition ;  and  the  sounding  phrase  *  the  general  law 
of  creation  *  signifies  merely  that  a  fact  is  frequent  or  usual 
*Many  (or  some)  things  in  nature  are  symmetrically  con- 
structed.* 

The  angle  in  a  semicircle  is  a  right  angle. 
Ice  is  cold. 

The  diamond  is  surpassingly  brilliant. 
Extreme  heat  destroys  life. 
Motion  follows  the  line  of  least  resistance. 
Truth  is  more  easily  extricated  from  error  than  from  con- 
fusion. 

An  age  of  ignorance  is  an  age  of  ceremony. 

Power  corrupts  the  mind. 

Time  abates  grief. 

Custom  blunts  sensibility. 

Private  vices  are  public  benefits. 

Uneasy  lies  the  head  that  wears  a  crown. 

Tyranny  is  irresponsible  power. 

Benevolence  is  the  sum  of  virtue. 

Distance  lends  enchantment  to  the  view. 

Consumption  is  a  fatal  disease  in  this  country. 

International  law  has  no  written  statutes. 

Conception  is  involved  in  every  act  of  perception. 

None  but  the  brave  deserve  the  fair. 

Not  being  rich  is  not  always  an  evil. 

All  is  not  gold  that  glitters. 


130   EXEKCISES   ON  PROPOSITIONS,   INCLUDING  NOTIONS. 

The  causes  of  strength  are  not  pledges  for  its  continu- 
ance. 

Not  every  advice  is  a  safe  one. 

A  great  deal  need  not  be  attempted. 

He  is  no  fool. 

No  news  is  good  news. 

No  men  are  placed  in  exalted  situations  and  free  from  envi- 
ous regards. 

Good  orators  are  not  always  good  statesmen. 

There  are  studies  much  vaunted,  and  yet  of  little  utility. 

Few  even  of  our  best  aspirations  are  gratified. 

Hardly  any  virtue  is  quite  safe  from  passing  into  a  vice. 

The  two  following  extracts  are  from  Plato — 

*  All  men  who  have  gout,  or  fever,  or  ophthalmia,  are  sick ; 
but  all  sick  men  have  not  gout,  or  fever,  or  ophthalmia.  So, 
too,  all  carpenters,  or  shoemakers,  or  sculptors,  are  craftsmen  ; 
but  all  craftsmen  are  not  carpenters,  or  shoemakers,  or  sculp- 
tors. In  like  manner,  all  madmen  are  unwise ;  but  all  unwise 
men  are  not  mad. 

*  Whosoever  is  a  good  rhapsode,  is  also  a  good  general  ? 
Unquestionably.  And,  of  course,  whoever  is  a  good  general, 
is  also  a  good  rhapsode  ?     No  j  I  do  not  think  that.' 

*  The  objects  bring  up  the  feelings,  and,  conversely,  the  feel- 
ings the  objects.'  In  this  sentence,  is  the  word  *  conversely  * 
used  in  its  proper  meaning  ? 

If  steam  is  passed  over  red  hot  iron,  hydrogen  will  be 
evolved. 

If  virtue  is  knowledge,  it  is  teachable. 

If  the  footmarks  were  made  by  the  prisoner,  he  must  have 
worn  shoes  too  small  for  his  feet.  But  he  could  not  have 
done  so.     What  then  ? 

If  the  soul  is  incorruptible,  it  is  ingenerable. 

Matter  is  either  solid,  or  liquid,  or  gaseous. 

Mr.  de  Morgan  supposes  a  stump  orator  intending  to  say— - 
all  Englishmen  are  lovers  of  liberty ;  and  declaiming  in  these 
terms  : — *  Shew  me  any  number  of  men,  and  I  will  say  with 
confidence,  either  that  they  will  with  one  accord  raise  their 
voices  for  liberty,  or  that  there  are  aliens  among  them.'  This 
might  be  regarded  as  an  equivalent  statement,  without  syllo- 
gistic inference. 

Cromwell,  on  his  death-bed,  is  said  to  have  asked  a  divine 


li 


V    %\ 


EXAMPLES   OF  PROPOSITIONS. 


131 


who  was  with  him,  whether  it  was  possible  to  fall  away  from 
grace.  The  answer  was, — It  is  not  possible.  Then,  said 
Cromwell,  I  am  safe,  for  I  was  in  grace  once. 

No  form  of  polity  is  so  admirable  as  a  limited  constitutional 
monarchy ;  for  it  is,  beyond  all  question,  superior  to  every  other 
species  of  government. 

Honesty  is  deserving  of  reward.  A  negro  is  a  fellow 
creature.      An   honest  negro   is  a  fellow-creature    deserving 

reward. 

Every  man  is  an  animal.     Every  head  of  a  man  is  the  head 

of  an  animal.     De  Morgan. 

In  Book  IV — The  Logic  of  the  Sciences— as  well  as  through- 
out the  work  generally,  there  occur  numerous  examples  that 
may  serve  as  additional  exercises  if  necessary. 


V 


BOOK   II. 

DEDUCTION. 


CHAPTER    L 
THE    SYLLOGISM. 

1.  The  Syllogism  is  the  fully  expressed  form  of  a  De- 
ductive Inference,  that  is,  an  inference  from  the  General  to 
the  Particular. 

When  a  step  of  reasoning  or  argumentation  consists  in  as- 
signing, as  the  proof  of  an  affirmation  (or  denial),  some  more 
general  affirmation,  it  admits  of  being  stated  in  a  peculiar 
form,  in  which  there  *is  sometimes  greater  facility  in  judging 
of  its  soundness.  The  peculiarity  of  the  form  of  statement 
consists  mainly  in  this,  that  everything  belonging  to  the  rea- 
soning is  set  forth  explicitly.  Thus,  when  any  one  maintains 
that  Mathematics  is  useful  as  a  mental  discipline,  and  assigns 
as  the  proof,  that  all  the  exact  sciences  are  nseful  as  mental 
discipline,  the  reasoning,  which  is  Deductive,  and  not  Induc- 
tive, contains  these  two  assertions : — (1)  All  the  exact  sciences 
•  are  useful  as  mental  discipline;  (2)  Mathematics  is  an  exact 
science.      Both   these   are  indispensable    to    the   conclusion 

*  Mathematics  is  a  mental  discipline.'  The  first  is  the  general 
principle,  the  second  an  intermediate  proposition  for  applying 
the  general  principle  to  the  case  in  hand.  Very  often,  one  of 
the  two  propositions  is  left  unexpressed.     In  the  example : 

*  this  man  is  a  rogue,  therefore  he  is  not  to  be  trusted,*  there 
is  an  ellipsis  of  the  general  principle — *  rogues  are  not  to  be 
trusted.*  In  the  form  *you  cannot  trust  rogues,  therefore  you 
cannot  trust  this  man,*  the  omission  is  in  the  second  or  apply- 
ing proposition — *  this  nmii  i«*  a  rogue.' 


If 


^■a.Mnixil& 


-^ 


134 


THE  SYLLOGISM. 


THE  THBEE  TERMS. 


135 


A  Deductive  reasoning  fully  and  formally  expressed  is  a 
Syllogism. 

The  following  arrangement — 

(1)  All  men  are  fallible, 

(2)  John  is  a  man, 

(3)  John  is  fallible— 

is  a  regular  deductive  reasoning,  or  an  argumentation  in  the 
syllogistic  or  complete  form.  The  two  first  propositions 
combine  to  make  the  proof  of  the  third  ;  they  are  called  the 
Premises  of  the  reasoning  or  syllogism ;  the  third  is  the  point 
to  be  proved,  and  is  called  the  Conclusion. 

We  shall  see  hereafter  that,  in  the  departures  made  from  the 
regular  form  of  the  syllogism,  the  order  of  the  propositions 
may  be  reversed ;  the  applying  proposition  coming  first,  and  the 
grounding  proposition  second.  But  whatever  form  the  syllo- 
gism may  assume,  one  feature  can  never  be  absent — a  general 
proposition.  This  is  indispensable.  Unless  one  of  the  premises 
be  more  general  than  the  conclusion,  the  argument  is  not 
deductive. 

2.  A  Syllogism  is  said  to  contain  three,  and  only  three 
Terms ;  the  Subject  and  the  Predicate  of  the  Conclusion, 
and  another  Term,  occurring  in  both  Premises  ;  the  Sub- 
ject of  the  Conclusion  is  the  Mincyr  Term  ;  the  Predicate 
of  the  Conclusion,  the  Major  Term  ;  the  term  occurring  in 
both  Premises,  is  the  Middle  Term. 

By  *  Terms  *  are  meant  the  expressed  notions  entering  into 
the  subjects  and  predicates  of  the  propositions.  A  proposition 
couples  or  unites  two  Terms.  *  X  is  Y '  contains  the  two  terms 
X  and  Y  affirmatively  conjoined.  *  Men  are  not  gods '  contains 
the  two  terms  *  men  '  and  *  gods  '  under  a  negative  copula. 

In  seeking  out  the  Terms,  we  begin  with  the  proposition  to 
be  proved,  that  is,  the  conclusion.  The  subject  of  the  conclusion 
is  the  Minor  or  smaller  term,  the  predicate  the  Major  or  greater 
term.  The  propriety  of  these  designations  is  grounded  on 
the  circumstance,  formerly  adverted  to,  that  in  propositions 
generally,  the  predicate  covers  the  subject,  and  other  subjects 
besides ;  *  kings  are  fallible,'  and  many  other  beings  besides 
kings  are  fallible  ;  hence  *  kings '  are  a  smaller  group  forming 
part  of  a  larger  group  *  fallible ;'  in  compass  or  extent,  there- 
fore, *  kings '  are  a  Minor  tenn^  *  fallible  '  a  Major  term.'* 

♦  Sir  W.  Hamilton  complains  that  those  designations  are  false  and 
erroneous  becauao  they  do  not  apply  to  the  terms  as  considered  in  Com- 
prehentiion.     There  are  more  men  than  kings,  and  so  the  designationa  are 


The  Middle  Term  must  be  sought  not  in  the  conclusion,  but 
in  the  Premises,  or  proving  propositions,  and  must  appear  in 
both.     Thus,  in  the  syllogism — 

Men  are  fallible, 
Kings  are  mew, 
Kings  are  fallible. 
The  term,  absent  from  the  conclusion,  and  present  in  both 
premises,  is  *  men,'  the  subject  of  the  first  and  the  predicate  of 
the  second.     It  is  called  *  middle  '  because  it  is  the  medium  or 
instrumentality  for  bringing  together  in  the  conclusion,  the 
major  and  minor  terms ;  they  being  separated  in  the  premises. 
Also,  as  regards  extent,  compass,  or  denotation,  it  is  inter- 
mediate thus  : — The  minor  *  kings'  is  less  in  extent  than  *  men  ;* 
men  are  more  numerous  than  kings.     Asrain,  *  men  '  is  less  in 
extent  than  *  fallible  beings ; '  there  being  many  fallible  beings 
besides  men.     So  *  men  '  being  more  extensive  than  the  minor 
term  *  kings,'  and  less  extensive  than  the  major  term  *  fallible 
beings,'  is  properly  a  middle  or  intermediate  term.     The  grada- 
tion is  represented  in  a  diagram  thus  : — 

Fallible,  ,  .  .  major,  ^ 

Men,  ....  middle,^ 

Kings,  .  ,  ,  minor.  > 

Although  the  syllogism  contains   three   propositions,  each 
with   two   terms,  making  six  terms  in  all ;    yet,  in  virtue  of 
the  double  occurence  of  each,  there  are  in  reality  only  three 
terms.     The  example  shows : — 
The  Middle  term  in  both  premises. 
The  Minor  term  in  the  conclusion  and  in  one  premise. 
The  Major  term  in  the  conclusion  and  in  one  premise. 
3.  In  the  Syllogism,  there  are  Three,  and  only  three. 
Propositions,  namely,  the  two  Premises  and  the  Conclusion. 
The  Premise  containing  the  Major  Term  and  the  Middle 
Term,  is  called  the  Major  Premise  ;  the  Premise  contain- 
ing the  Middle  Term  and  the  Minor  Term,  is  called  the 
Minor  Premise, 

In  the  foregoing  example,  the  Premise  first  in  order  contains 

applicable  to  the  extension  of  the  terras ;  but,  he  argues,  more  attributes 
are  connoted  by  the  term  '  kings'  than  by  the  term  men,  and  so  major 
and  minor  are  inapplicable  to  the  comprehension.  In  criticism  of  this 
view,  it  may  be  said  that  confessedly  the  designations  wa>r  and  minor 
are  applicable  to  the  terms  viewed  in  their  compass  or  extension,  that  these 
terms  are  used  in  that  sense,  that  they  cannot  be  used  without  confusion 
in  both  senses,  and  that  Uamilton  has  shown  no  good  reason  for  invert- 
ing the  common  usage. 

7 


136 


THE  SYLLOGISM. 


tbe  Major  term  *  fallible/  together  with  the  Middle  terra, 
*  men/—*  men  are  fallible  /  this  is  tbe  Major  Fremise.  ^  The 
Premise  second  in  order  contains  the  Middle  teinn,  *  men/  and 
the  Minor  term,  *  kings/—*  kings  are  men  *— and  is  the  Minor 

We  find  it  convenient  to  represent  the  forms  of  the  syllogism 
by  lettera  or  symbols,  thns  : — Let  X  be  the  minor  term,  Y,  the 
middle  term,  Z,  the  major  term ;  then- 
All  Y  is  Z 
All  X  is  Y 
All  X  is  Z 
is  a  syllogistic  form  on  the  basis  of  affirmation ;  that  is  to  say, 
the  universal  proposition  in  the  first  premise  is  affirmative,  and 
the  conclusion  is  affirmative. 

An  example  on  tbe  basis  of  negation  is — 

No  Y  is  Z 
All  X  is  Y 
No  X  is  Z, 
or,  by  Hamilton's  still  more  expressive  symbols, — 
S  (subject  of  conclusion,  minor  term), 
M  {middle  term), 
P  (predicate  of  conclasion,  major  term) ; 

All  M  is  P  No  M  is  P 

All  S  is  M  All  S  is  M 

All  S  is  P  No  S  is  P. 

4.  Syllogisms,  or  Syllogistic  forms,  are  divided  into 
Figures,  according  to  the  position  of  the  Middle  Term. 
There  are,  in  all,  Four  Figures. 

The  First  Figure  is  exemplified  in  the  forms  hitherto  em- 
ployed. In  it,  the  Middle  Term  is  Subject  in  the  Major  Pre- 
mise, Predicate  in  the  Minor  Premise. 

YisZ  MisP  M  — 
X  is  Y  S  is  M  —  M 
X  is  Z         S  is  P 

The  idea  implied  under  *  Figure  *  is  borrowed  from  the 
Figures  of  Rhetoric,  which  are  departures,  for  effect,  from  the 
the  plain  and  ordinary  forms  of  speech.  On  this  analogy, 
however,  as  remarked  by  Hamilton,  there  ought  to  be  some 
one  regular  or  standard  form,  from  which  all  other  forms  are 
deviations  or  departures^  thence  properly  called  *  Figures.' 
Such  standard  form  is  what  is  mis-named  the  *  First  Figure,' 
which  is  the  pure  type  of  a  deductive  argument.  The  Major 
or  First  Premise  is  tlie  universal  proposition  indispensable  in 


THE  FIGURES. 


137 


deduction,  the  Minor  or  Second  Premise  is  an  affirmative  pro- 
position, whatever  may  be  its  quantity.  As  to  order,  the  Uni- 
versal is  placed  first,  as  being  of  the  two  premises  the  funda- 
mental or  chief;  the  use  of  the  second  premise,  the  minor, 
being  to  apply  the  first  to  a  particular  case;  *  All  thieves  are 
deserving  of  punishment,'  is  applied  to  a  particular  instance, 
by  means  of  an  affirmation  bringing  the  instance  within  the 
sweep  of  the  rule,  that  is,  declaring  such  a  one  to  be  a  thief. 
This  is  the  fiinction  of  the  minor. 

In  the  Second  Figure,  or  the  first  departure  from  the  normal 
syllogism,  the  middle  term  is  predicate  in  both  premises 

Z  is  Y        P  is  M        —  M 
X  is  Y        S  is  M        —  M 

Here  there  is  an  obvious  inversion  of  the  natural  order  of 
things.  In  the  major  premise,  Z  is  Y,  P  is  M,  the  largest  term 
is  made  the  subject,  and  the  middle  term  the  predicate,  of  the 
proposition.  If  the  proposition  be  affirmative,  this  change  is  not 
compatible  with  universality,  and  therefore  the  proposition  can- 
not be  the  major  in  the  same  sense  as  in  the  standard  syllogism. 
If  the  proposition  be  negative,  there  is  only  a  harmless  con- 
version ;  we  may,  for  *  no  Y  is  Z,'  substitute  *  no  Z  is  Y  ;*  *  no 
men  are  gods,*  '  no  gods  are  men.'  This  is  an  insignificant 
and,  for  the  most  part,  useless  alteration  of  the  negative  form 
of  the  standard  syllogism.  Two  of  the  four  forms  of  the 
Figure  (called  Moods)  are  fashioned  out  of  this  trivial  altera- 
tion. The  two  other  forms  containing  affirmative  majors  in- 
volve still  greater  changes  of  the  standard  form.  In  one,  the 
major  is  not  the  universal  proposition  required  as  the  basis  of 
the  deduction,  but  the  applying  proposition,  which  in  the  first 
figure  is  the  second  or  minor  premise.  In  the  concluding 
form,  there  is  a  much  greater  distortion,  consequent  on  presenU 
ing  the  normal  premises  in  obverted  forms. 

In  the  Third  Figure,  the  middle  term  is  subject  in  both 
premises. 

YisZ         MisP        M— 
Y  is  X        M  is  S        M— 

Here  the  major  stands  as  in  the  first,  or  normal  figure.  The 
minor  has  its  terms  transposed ;  the  middle  term  is  subject, 
and  the  minor  term  predicate.  As  before,  this  is  a  harmless 
change,  if  the  proposition  be  a  universal  negative ;  in  which  case, 
however,  the  minor  premise  must  be  the  universal  or  ground- 
ing proposition,  and  not  the  applying  proposition  ;  so  that,  as 
compared  with  the  standard  form,  there  is  an  inversion  of  the 
order  of  the  premises.      If  the  minor  be  affirmative,  either  it 


138 


THE  SYLLOGISM. 


I 


mnst  be  particular,  or  there  is  some  distortion,  rendering  the 
terms  different  in  fact  from  what  they  are  in  appearance. 

In  the  Fourth  figure,  the  position  of  the  middle  term  is  the 
first  figure  reversed  ;  it  is  predicate  in  major,  and  subject  in 
minor. 

Z  is  r        P  is  M         —  M 
risX        MisS         M  — 

This  double  inversion  of  the  order  of  the  terras  implies  still 
greater  deviations  from  the  primary  form.  The  inversion  is 
possible  by  such  devices  as  above  described  for  the  smaller 
inversions  in  the  second  and  third  figures. 

0.  Each  Figure  has  a  certain  number  of  distinct  forms, 
called  the  Moods,  or  modes  of  the  figure.  The  variation  of 
mood  is  determined  by  the  variety  of  the  propositions  con- 
tained, as  regards  Quantity,  and  Quality. 

The  order  of  the  terms  is  fixed  for  each  Figure ;  but  the 
propositions  constituting  the  premises  and  the  conclusion  may, 
within  certain  limits,  be  of  one  or  other  of  the  four  forms, 
A,  I,  E,  0. 

The  First  Figure,  the  normal  syllogism,  has  Four  Moods. 
The  First  Mood  is  composed  of  three  universal  affirmatiouB. 
All  Y  is  Z  1  A,  A,  A  All  men  are  fallible. 

All  X  is  Y  >  (^Barbara)       All  kings  are  men. 
All  X  is  Z  )  All  kings  are  fallible. 

In  the  Second  Mood, 

The  Major  is      a  universal  negative     — BL 
The  Minor  a  universal  affirmative — A. 

The  Conclusion  a  universal  negative     — E. 


No  Y  is  Z 
All  X  is  Y 
No  X  is  Z 


E,  A,  E         No  men  are  gods. 
(Ce/are7it)     All  kings  are  men. 
No  kings  are  gods. 


The  Third  Mood  is  the  first,  with  a  particular  minor,  and 
particular  conclusion  : — 

All  Y  is  Z      I  A,  I,  I  All  men  are  fallible. 

Some  X  is  Y  V  (Darii)  Some  beings  are  men. 

Some  X  is  Z  )  Some  beings  are  fallible. 

The  Fourth  Mood  is  a  similar  variation  on  the  second ;  paiN 
ticular  minor  and  particular  conclusion  : — 

No  Y  is  Z  '^  E,  I,  O  No  men  are  gods. 

Some  X  is  Y        >  {Ferio)  Some  beings  are  men. 
Some  X  is  not  Z  )  Some  beings  are  not  gods. 


FIRST  FIGURE. 


139 


These  four  moods  are  obviously  reducible  to  two ;  the  third 
and  fourth  being  mere  unessential  varieties  of  the  first  and 
second.     The  two  comprehensive  forms  may  be  stated  thus  : — 
All  Y  is  Z  No  Y  is  Z 

All  or  some  X  is  Y      All  or  some  X  is  Y 
All  or  some  X  is  Z  f    No  X  is  Z. 

(    Some  X  is  not  Z. 

The  first  form  is  the  normal  type  of  all  deduction  for  an 
affirmative  conclusion  ;  the  second,  the  type  for  a  negative 
conclusion.  They  present  the  deductive  process  in  its  regular 
order  : — 

First,  a  universal  proposition,  as  the  ground  proposition  of 
the  reasoning  (Major  premise)  ; 

Secondly,  an  affirmative  and  applying  proposition  (Minor 
premise) ; 

Lastly,  the  universal  truth  applied  to  the  particular  case 
(the  Conclusion}. 

We  desire  to  prove  that  kings  are  fallible,  by  applying  to  them 
the  principle  of  the  fallibility  of  all  men.  The  major  states 
the  principle,  the  minor  applies  it.  And  so  for  a  negative  con- 
clusion. 

There  cannot  be  any  valid  deduction  whatsoever  but  must 
conform  to  the  foregoing  type ;  whatever  variation  may  be 
made,  this  is  at  the  bottom. 

The  Second  Figure  has  likewise  four  Moods. 
In  the  First  Moody 

The  Major      is  a  universal  negative     — B. 

The  Minor  a  universal  affirmative- — A. 

The  Conclusion  a  universal  negative     — E. 

No  Z  is  Y  "^  E,  A,  E,     No  gods  are  men. 

All  X  is  Y  >  ( Cesar e)     All  kings  are  men. 

No  X  is  Z  )  No  kings  are  gods. 

This  is  a  case  where  advantage  is  taken  of  the  simple  con- 
version of  the  universal  negative  to  make  a  trivial  departure 
from  the  standard  (negative)  syllogism.  Only  a  slight  change 
is  necessary  to  reconvert  the  present  mood  to  the  second  mood 
of  the  First  Figure  ;  for  *  No  Y  is  Z  '  *  No  men  are  gods,'  we  are 
at  liberty  to  substitute  *  No  Z  is  Y,*  *  No  gods  are  men,'  which 
is  the  whole  difference. 

In  the  Second  Moody 

The  Major      is  a  universal  affirmative — A, 
The  Minor  a  universal  negative — E, 


!(( 


5'    i 


140 


THE   SYLLOGISM. 


The  conclusion  a  universal  negative — B. 
All  Z  is  Y  I  A,  E,  E,      All  kings  are  men. 
No  X  is  Y  >  {Camestres)  No  gods  are  men. 
No  X  is  Z  j  No  gods  are  kings. 

A  much  greater  variation  from  the  standard  (negative)  is 
observable  here.  The  grounding  proposition,  which  must  be 
universal,  is  the  minor  premise  :  so  that  there  is  an  inversion 
of  the  normal  order  of  the  premises.  Moreover,  the  same  pro- 
position has  been  converted  simply,  from  the  form  *  No  men 
are  gods  ;*  and  the  conclusion  is  likewise  the  converse  of  the 
conclusion  in  the  regular  syllogism.  By  first  restoring  the  order 
of  the  premises,  and  next  re-converting  two  universal  negations, 
we  have  the  normal  negative  syllogism  (CeZtirenO. 

No  men  are  gods. 
All  kings  are  men. 
No  kings  are  gods. 
The  grounding  universal  is  the  negative  proposition,  '  no 
men  are  gods ' — the  applying  proposition  is  *  all  kings  are  men.' 

In  the  Third  Mood, 

The  Major       is  a  universal  negative     — B, 
The  Minor  a  particular  affirmative — I, 

The  Conclusion  a  particular  negative     — O. 
No      Z  is  Y      )  E,  I,  O       No  gods  are  men. 
Some  X  is  Y       V  (Festmo)     Some  beings  are  men. 
Some  X  is  notZ  )  Some  beings  are  not  gods. 

Here  we  remark  the  same  trivial  departure  from  one  of  the 
standard  forms,  as  in  the  first  mood.  The  universal  negative— 
the  major  in  the  fourth  mood  of  the  first  figure  (Feno)^is 
simply  converted  (No  Y  is  Z,  into  No  Z  is  Y ;  no  men  are 
gods,  into  no  gods  are  men). 

In  the  Fourth  and  last  Mood,  there  is  a  more  serious  dis- 
tortion. 

The  Major         is  a  universal  affirmative — A, 
The  Minor  a  particular  negative    — O, 

The  Conclusion    a  particular  negative    — O, 
All  Z  is  Y  j  A,  O,  O      All  gods  are  men. 

Some  X  is  not  Y  >  (Baroko)     Some  beings  are  not  men. 
Some  X  is  not  Z  j  Some  beings  are  not  gods. 

A  glance  at  the  premises  shows  us  that  they  are  not  at 
bottom  what  they  appear  on  the  surface.  There  is  indeed  a 
umversal  proposition  in  the  major  premise,  which  might 
answer  for  the  ground  proposition  ;  but  then  the  other  pre- 


SECOND  FIGUKE. 


Ul 


mise,  in  that  case  the  applying  proposition,  is  negative,  which 
is  not  allowable.  The  real  fact  is  that  the  affirmative  major, 
is  a  negative  (universal)  in  disguise,  and  the  negative  minor, 
is  an  affirmative  in  disguise.     The  disguises  may  be  laid  open, 


thus — 


All  Z  is  Y 
Some  X  is  not  Y 
Some  X  is  not  Z 


No  not-Y  is  Z 
Some  X  is  not-Y 
Some  X  is  not  Z 
The  true  middle  term  instead  of  being  Y,  is  the  negative  ol' 
Y,  or  not-Y  (U— Y)     This  is  the  key  to  the  distortion.     The 
remedy  consists  in  (1)  ohverting  and  converting  the  major — All 
Z  is  Y,  which  becomes  No  not-Y  is  Z  ;  and  (2)  in  ohverting 
the  minor — Some  X  is  not  Y,  Some  X  is  not-Y.      There  thus 
emerges  a  form  of  the  third  mood  of  the  first  figure  (^Ferio), 
with  not-Y,  as  the  middle  term. 

This  mood  cannot  be  reduced  to  a  mood  of  the  Krst  Figure 
without  Obversion.  The  older  logicians  sought  to  establish  its 
validity  by  a  cumbrous  process  technically  known  as  Reduciio 
ad  impossibile.  They  showed  that  the  conclusion  cannot  bo 
supposed  false,  without  leading  to  a  contradiction  of  one  o£ 
the  premises,  which  are  given  as  unimpeachable.      Thus : — 

All  Z  is  Y 

Some  X  is  not  Y 

Some  X  is  not  Z 
If  *  Some  X  is  not  Z  *  be  declared  false,  the  universal  *  All  X 
is  Z,* — which  is  its  contradictory, — must  be  admitted  as  true. 
Taking  this  new  proposition,  *  All  X  is  Z  *  along  with  the  major 
of  the  original  syllogism,  *  All  Z  is  Y,*  we  reach  the  conclusion 
that  *  All  X  is  Y:     Thus  :— 

All  Z  is  Y 

AUXisZ 

AllXisY 
is  a  syllogism  in  Barbara,  But  we  know  from  the  original 
premises  that  *  Some  X  is  not  Y ;'  it  cannot  therefore  be  true 
that  '  All  X  is  Y.*  One  of  the  premises  of  the  above  Barbara 
must  be  unsound.  The  major  *  All  Z  is  Y,'  is  one  of  the  origi- 
nal premises,  granted  as  true ;  the  error  must  lie  on  the  minor, 
*  All  X  is  Z.'  Now  this  is  the  proposition  taken  on  trial ;  and 
its  truth  being  shown  to  be  incompatible  with  the  truth  of  the 
original  premises,  its  contradictory,  *  Some  X  is  not  Z  '  must 
be  true.  And  *  Some  X  is  not  Z  *  is  the  conclusion  in  question  j 
which  is  thus  shown  to  be  valid. 

The  Third  Figure  has  six  Moods. 


142 


THE  SYLLOGISM. 


THIRD  FIGXTRE. 


143 


ji* 


In  the  First  Mood, 

The  Major  is         a  nniversal  affirmative— A. 
The  Minor  a  universal  affirmative — A. 

The  Conclusion    a  particular  affirmative — I. 
All  Y  is  Z      ^  A,  A,  I       All  men  are  fallible. 
All  Y  is  X      V  {JDara^U)  All  men  are  living  beings. 
Some  X  is  Z  )  Some  living  beings  are  fallible. 

The  only  departure,  in  this  instance,  from  the  standard 
fiyllogism  (with  a  particular  minor,  Darii)  is  the  universality 
of  the  minor,  All  Y  is  X  By  simple  conversion,  this  premise 
becomes  Some  X  is  Y,  and  the  syllogism  is  then  the  same  as 
the  third  mood  of  the  regular  syilogism. 

This  figure  is  quoted  as  a  useful  form.  Certain  reason- 
mgs  are  considered  to  fall  more  readily  into  the  above  ar- 
rangement, than  into  the  corresponding  mood  of  the  First 
Figure, 

The  Second  Mood  contains  an  inversion  of  the  order  of  the 
Premises.  This  distortion  is  altogether  gratuitous  ;  it  serves 
no  purpose  but  to  seem  a  variety. 

Some  Y  is  Z  "^  I,  A,  I         Some  men  are  kings. 

All  Y  IS  X      WZ>^am2«)    All  men  are  fallible  beings. 

Some  X  IS  Z  )  Some  fallible  beings  are  kings. 

ilere,  it  we  redress  the  order  of  the  premises,  and  simply 
convert  the  new  minor— Some  Y  is  Z,  into  Some  Z  is  Y  -. 
there  arises  a  regular  affirmative  syllogism,  with  a  particular 
minor  {Bara)  ;  there  being  only  the  speciality  that  the  minor 
and  tlie  major  terms  have  changed  places,  thus :— ' 
All  Y  is  X  All  men  are  fallible  beings. 
Some  Z  is  Y      Some  kings  are  men. 

From  this  the  conclusion  would  be  *Sooe  Z  is  X  *  *  some 
kings  are  fallible  beings,'  which,  however,  by  simple  con- 
version, gives  *  Some  X  is  Z,'  *some  fallible  beings  are  men/ 

The  Third  Mood  is  one  of  the  trival  variations  of  syllogistic 

All  Y  is  Z      ^  A,  I,  I,     AH  men  are  fallible. 

feome  Y  is  X  UUatisi),  Some  men  are  kings. 

Some  X  is  Z  )  Some  kings  are  fallible  beings. 

There  is  no  departure  here,  from  the  regular  syllogism 
(affirmative,  with  particular  minor  Darii),  but  in  the  minor 
^rem^e,  which  is  Some  Y  is  X,  instead  of  its  equivalent.  Some 


The  Fourth  Mood  is  exactly  the  counterpart  of  the  previous 
mood,  with  a  negative  major. 

No  Y  is  Z  ^  E,  A,  O       No  men  are  gods. 

All  Y  is  X  >  {Felapton)  All  men  are  living  beings. 

Some  X  is  not  Z  j  Some  living  beings  are  not  gods. 

This  differs  from  the  negative  mood  of  the  first  figure,  with 
a  particular  minor  (Ferio),  only  in  having  a  universal  minor, 
which,  by  conversion,  becomes  particular.  Some  X  is  Y  ;  the 
syllogism  is  then  exactly  the  fourth  mood  of  the  standard 
syllogism. 

The  Fifth  Mood  is,  in  point  of  distortion,  the  parallel  of  the 
last  mood  of  the  Second  Figure  (Baroko).    Both  the  premises 
appear  different  from  what  they  are  in  reality. 
Some  Y  is  not  Z ")  O,  A,  0,    Some  men  are  not  kings. 
All  Y  is  X  >{JBokardo)  All  men  are  fallible. 

Some  X  is  not  Z  )  Some  fallible  beings  are  not  kings. 

If  we  look  for  a  universal  premise,  to  supply  the  ground 
proposition,  we  seem  to  find  it  in  the  minor;  but  then  the 
other  premise  is  negative,  and  therefore  is  not  the  applying 
proposition.  As  in  Bar  oho,  we  must  transfigure  both  pre- 
mises. The  present  major  is  made  affirmative,  by  obversion, — 
*  Some  Y  is  not-Z,'  and  is  then  converted,  *  Some  not-Z  is  Y.' 
This  is  taken  as  the  minor  premise,  the  other  being  the  major, 
thus : — 

All  Y  is  X  All  men  are  fallible. 

Some  not-Z  is  Y  Some  not-kings  are  men. 
which  are  the  premises  of  the  regular  syllogism  (affirmative, 
with  particular  minor,  Darii)  and  would  give  as  a  conclusion, 

Some  not-Z  is  X,  Some  not-kings  are  fallible, 
or,  by  conversion  and  obversion. 

Some  X  is  not  Z,  Some  fallible  beinp^s  are  kings. 

As  in  the  case  of  BaroJco,  the  older  logicians  could  not  refer 
this  mood  to  the  First  Figure,  and  applied  as  a  test  of  its  validity 
the  Beductio  ad  invpossibile.  The  process  need  not  be  repeated 
at  length.  We  assume  the  universal  contrary  to  the  conclu- 
sion, and  taking  it  along  with  the  given  minor,  evolve  a  pro- 
position that  contradicts  the  given  major :  and  argue,  as  under 
Baroko,  that  the  universal  contrary  of  the  conclusion  must  be 
false,  and  therefore  the  conclusion  itself  valid. 

The  Sixth  and  last  Mood  is  the  negative  counterpart  of  the 
third,  and  should  have  been  placed  after  the  fourth ;  it  is  an 
equally  trivial  departure  from  the  regular  syllogism  (negative, 
with  particular  premise,  Ferio), 


144 


THR  SYLLOGISM. 


FOURTH  FIGUBB. 


145 


No  T  is  Z  1  E,  I,  0,    No  men  are  gods. 

Some  Y  is  X  >{Ferison)    Some  men  are  living  beings. 

Some  X  is  not  Z    j  Some  living  beings  are  not  gods. 

The  simple  conversion  of  the  minor  '  Some  Y  is  X/  into  *  Some 
X  is  Y,'  *some  living  beings  are  men,* — reproduces  Ferioy  in  the 
standard  figure. 

The  Fourth  Figure  has  five  Moods.  In  this  figure,  there  is 
an  inversion  of  both  premises  as  compared  with  the  regular 
syllogism.  This,  of  course,  produces  apparently  a  great  degree 
of  distortion  ;  but  there  is  very  little  in  reality.  In  three  of 
the  moods,  the  inversion  is  caused  by  the  transposition  of  the 
premises  ;  this  rectified,  they  need  only  the  simple  conversion 
of  one  or  more  of  the  propositions  to  make  them  standard 
syllogisms. 

Thus,  to  take  the  First  Mood,  which  has  universal  aflirmative 
premises,  and  particular  conclusion  : — 

All  Z  is  Y      j  A,  A,  I  All  kings  are  men. 

All  Y  is  X      >  (BramanU}})     All  men  are  fallible. 

Some  X  is  Z  j  Some  fallible  beings  are  kings. 

Transpose  the  premises,  and  there  emerges  a  standard  syllo- 
gism (affirmative,  with  universal  minor,  Barbara)-^ 
All  Y  is  X  All  men  are  fallible. 

All  Z  is  Y  All  kings  are  men. 

The  conclusion  from  these  premises  is — 

All  Z  is  X  All  kings  are  fallible. 

This  conclusion,  converted  by  limitation,  gives — 

Some  X  is  Z         Some  fallible  beings  are  kings. 

The  Second  Mood  is,  if  possible,  still  closer  to  a  regular 
syllogism,  when  the  order  of  the  premises  is  changed. 
All  Z  is  Y  'I  A,  E,  E,         All  kings  are  men. 
No  Y  is  X  >(^Camenes)     No  men  are  gods. 
No  X  is  Z  J  No  gods  are  kings. 

Restore  the  order  of  the  Premises : — 

No  Y  is  X        No  men  are  gods. 

All  Z  is  Y         All  kings  are  men. 

These  are  the  premises  of  the  regular  syllogism  (negative,  with 

universal  minor,  Celarent),  and  the  conclusion  is 

No  Z  is  X         No  kings  are  gods. 

Whence  No  X  is  Z         No  gods  are  kings. 

The  Tldrd  Mood  is  constructed  on  a  similar  plan ;  the  devia* 
tion  from  regularity  being  caused  by  transposed  premises  : — 


Some  Z  is  Y  "^  I,  A,  I       Some  living  beings  are  men. 

All  Y  is  X      >{Dimaris)  All  men  are  fallible. 

Some  X  is  Z  )  Some  fallible  objects  are  living  beings 

With  re-transposed  premises, — 

All  Y  is  X         All  men  are  fallible. 
Some  Z  is  Y      Some  living  beings  are  men. 
Whence  by  Bariiy  in  the  standard  Figure,  the  conclusion  is,-^- 
Some  Z  is  X         Some  living  beings  are  fallible. 
Or  Some  X  is  Z         Some  fallible  objects  are  living  beings. 


The  fourth  and  fifth  Moods  attain  their  peculiar  form,  not 
through  the  inverted  order,  but  through  the  conversion,  of  the 
Premises.     The  Fourth  runs  thus : — 
No  Z  is  Y  "^  E,  A,  0      No  gods  are  men. 

All  Y  is  X  >  (JFesapo)     All  men  are  living  beings. 

Some  X  is  not  Z  )  Some  living  beings  are  not  gods. 

Convert  both  premises,  the  major  simply,  the  minor  by  limita- 
tion ; — 

No  Y  is  Z  No  men  are  gods. 

Some  X  is  Y        Some  living  beings  are  men. 
These  are  the  premises  of  the  negative  form  in  the  first  figure, 
with  particular  minor  {Ferw)y  whence 

Some  X  is  not  Z         Some  living  beings  are  not  gods. 

The  Fifth  and  last  Mood  differs  from  the  fourth  only  in 
having  a  particular  minor ;  the  universality  of  the  minor  in 
the  fourth  being  superfluous,  as  leading  to  no  stronger  conclu- 
sion than  the  present  form.  The  process  of  assimilation  to 
Ferio  is  precisely  the  same —  i 

No  Z  is  Y  1  E,  I,  O,      No  gods  are  men. 

Some  Y  is  X         >  {Fresison)  Some  men  are  living  beings. 
Some  X  is  not  Z  J  Some  living  beings  are  not  godfl. 

Convert  both  premises  simply  : — 

No  Y  is  Z  No  men  are  gods. 

Some  X  is  Y  Some  living  beings  are  men. 

The  premises  are  now  in  i^enb,  whence, 

Some  X  is  not  Z     Some  living  beings  are  not  gods. 

The  modes  of  the  Fourth  Figure,  are  thus,  with  the  appear^ 
ance  of  great  inversion,  mere  varieties  of  the  primary  Figure. 
The  transposition  of  the  order  of  the  premises  is  the  most 
insignificant  of  all  the  alterations  made  on  a  syllogism.  It 
signifies  nothing  to  the  reasoning,  in  what  order  the  premises 
are  stated.  The  three  first  moods  depart  from  the  standard 
moods  in  very  little  besides.     The  two  last  moods,  as  has 


\l^ 


/ 


146 


THE  SYLLOGISM. 


been  seen,  present  both  premises  converted ;  and  the  first  of 
the  two  is  superfluous,  even  as  a  form. 

The  prime  importance  of  the  Syllogism  attaches  to  its 
standard  forms,  that  is,  to  the  First  Figure.  In  it  we  learn 
the  essential  structure  of  each  valid  deduction— a  universal 
gi-ound  proposition,  affirmative  or  negative,  and  an  applying 
proposition,  which  must  be  affirmative.  These  appear,  in  the 
standard- syllogism,  in  the  order  stated— first,  the  ground 
proposition  (the  major  premise),  secondly,  the  applying  propo- 
sition (the  minor  premise).  In  the  subsequent  figures,  these 
are  sometimes  transposed;  and,  in  two  forms,  BaroJco  and 
Bohardo,  they  are  greatly  disguised.  The  ground  proposition 
is  called  by  Hamilton  the  sumptioyi,  the  applying  proposition, 
the  suhsumpti(m  (more  strictly,  the  subsuming  proposition). 

It  is  not  easy  at  first  sight  to  point  out  any  of  the  forms  of 
the  2nd,  3rd,  or  4th  Figures  that  are  of  special  importance  in 
the  conduct  of  reasoning  or  argumentation.  The  Fourth  Figure 
is  the  least  important  of  all ;  next,  perhaps,  the  second,  which, 
with  the  exception  of  Baroko,  scarcely  disguises  the  standard 
forms.  The  Third  Figure  is  useful  in  overthrowing  universal 
oppositions,  by  exceptions  or  contradictory  particulars. 

It  was  pointed  out  by  Aristotle,  that  in  the  First  Figure  only 
have  we  conclusions  in  all  the  forms.  A,  E,  I,  0.  The  Second 
Figure  is  restricted  to  negative  conclusions ;  the  Third  Figure, 
to  particulars.  The  Fourth  Figure,  which  Aristotle  did  not  re- 
cognize, does  not  admit  of  a  universally  affirmative  conclusion. 

In  explanation  of  the  possible  uses  of  the  Figures  after  the 
first,  two  circumstances  may  be  remarked  that  lead  to  depart- 
ures from  the  typical  form.  In  the  first  place,  the  order  of 
subject  and  predicate  in  either  premise,  and  consequently  the 
figure  wherein  the  syllogism  naturally  falls,  may  vary  with  the 
idea  uppermost  in  the  mind  of  the  reasoner.  **  The  best  form  of 
Government  is  Government  by  a  plurality  of  persons,"  and 
**  Government  by  a  plurality  of  persons  is  the  best  form  of 
Government,"  are  variations  of  the  same  statement  that  would 
cause  a  variation  of  Figure.  In  the  second  place,  the  extent 
of  the  middle  term  relatively  to  the  extent  of  the  major  and 
minor,  gives  rise  to  variations.  When  the  middle  term  is  larger 
than  either  major  or  minor,  it  naturally  forms  the  predicate 
both  of  the  major  and  of  the  minor  premise,  producing  a  syllo- 
gism of  the  Second  Figure.  When,  again,  the  middle  term  is 
smaller  than  either,  it  naturally  forms  the  subject  of  both  pre- 
mises, producing  a  syllogism  of  the  Third  Figure. 


THE  MNEMONIC  LINES. 


147 


It  has  been  shown  in  the  detailed  explanation  above  given, 
that  the  fifteen  moods  of  the  three  last  Figures  are  strict 
equivalents  of  the  Moods  of  the  First  Figure,  and  therefore 
have  the  same  validity  as  these  standard  moods.  The  demon- 
stration of  this  equivalence  is  technically  called  the  Reduction 
of  the  syllogisms,  or  their  revocation  to  the  primitive  forms  of 
affirmative  and  negative  predication.  The  necessity  of  Reduc- 
tion depends  upon  the  nature  of  the  proximate  canons  adopted 
for  the  syllogism.  If  those  canons  are  applicable  only  to 
the  First  Figure,  then,  before  we  can  test  the  validity  of 
irregular  moods,  we  must  reduce  them  to  moods  of  the  First 
Figure.  If  the  proximate  canons  are  applicable  directly  to  all 
syllogistic  moods,  reduction  is  unnecessary. 

Order  of  the  Premises.  Many  logicians  have  inverted  the 
order  of  the  premises,  commencing  with  the  minor.     Thus — 

All  X  is  Y 
All  Y  is  Z 
All  X  is  Z. 
This  is  the  form  that  seems  most  convenient  and  convincing, 
in  a  chain  of  reasoning,  as  in  the  Sorites.     It  suits  the  particu- 
lar form  of  the  syllogistic  axiom,  expressed  by  '  the  mark  of  a 
mark  is    a  mark  of  the  thing ; '  X  is  a  mark  of  Y,  Y  is 
a  mark  of  Z  ;  hence  X  is  a  mark  of  Z.     It,  however,  disguises 
the  genuine  type  of  Deductive  Reasoning,  which  ought  to  be 
exhibited  in  the  standard  syllogism,  even,  if  we  depart  from  it 
in  the  other  figures.     The  universal  proposition  is  rightly  put 
forward  as  the  foundation  of  the  reasoning,  to  which  should 
follow  the  applying  premise,  or  the  minor.     In  the  moods  of 
the  2nd,  3rd,  and  4th  Figures,  inversion  of  premises  occurs  aa 
one  form  of  departure  from  the  First  or  regular  figure. 
Aristotle's  mode  of  writing  Barbara  is — 
A  is  predicated  of  all  B 
B  is  predicated  of  all  C 
A  is  predicated  of  all  C^ 
where  the  minor  is  given  first,  and  the  propositions  inverted 
in  the  wording ;    *  A  is  predicated  of  all  B,'  is  the  same  as  All 
Bis  A. 

6.  The  Mnemonic  Lines  of  the  Syllogism  contain  the 
statement  of  the  different  moods,  with  the  manner  of  reduc- 
ing to  the  First  Figure,  those  of  the  three  last  Figures. 

To  each  of  the  moods,  as  described,  a  technical  name  has 
been  appended,   Barbara,   Celarent,  &c.      These  words  have 


"^„ 


148 


THE  SYLLOGISM. 


r 


been  constructed  for  showing  the  constituent  propositions  of 
each  mood,  and  how  the  moods  of  the  2nd,  3rd,  and  4th 
Figures  may  bo  transmuted  into  moods  of  the  1st  Figure  ;  as 
in  the  process  actually  gone  through  in  the  foregoing  explana- 
tion. 

The  names  are  made  up  in  lines  of  Latin  hexameter  verse. 
Among  artificial  aids  to  memory,  they  stand  unrivalled  : — 

Fig.  1.  bArbArA,  cElArEnt,  dArll,  fErlOque,  prioris. 

Fig.  2.  cEsArE,  cAmEstrEs,  fEstInO,  bArOkO,  secundae. 

Fig.  3.  tertia,     dArAptI,     dIsAmIs,     dAtlsI,      fElAptOu, 
bOkArdO,  fErlsO,  habet :  quarta  insuper  addit. 

Fig.  4.  brAmAntIp,  cAmEnEs,  dImArls,  fEsApO,  frEsIsOn. 

Each  of  these  names  represents  a  mood  ;  the  three  capital 
letters  in  each  standing  for  the  three  propositions,  as  symbo- 
lized in  their  Quantity  and  Quality  by  the  forms  A,  E,  I,  O. 
Of  the  smaller  letters,  or  consonants,  r,  n,  ^,  are  meaningless 
or  dumb  letters.  The  consonants  that  commence  each  name 
— bj  c,  eZ,  / — indicate  the  moods  in  the  First  Figure  that  the 
several  moods  in  the  other  Figures  are  reduced  to ;  Braniantip 
is  reduced  to  Barbara^  Cesar 6  to  Celarentf  and  so  on.  The 
consonants  m,  s,  p,  and  k,  which  signify  the  processes  of  Reduc- 
tion :  m  indicating  that  the  premises  have  to  be  transposed ; 
8  indicating  simple  conversion  ;  p  conversion  by  limitation,  or 
per  accidens ;  while  k  is  the  symbol  of  reductio  ad  impossibile. 
The  application  of  each  is  to  the  vowel  immediately  preceding. 
Thus,  in  Bramantiy  : — 

All  Z  is  Y 
All  Y  is  X 
Some  X  is  Z — 

we  learn  from  m  that  to  obtain  the  form  of  Barbara,  the  first 
mood  of  the  First  Figure,  we  must  transpose  the  premises. 
And  as  we  should  then  see  ourselves  entitled  to  conclude  *  All 
Z  is  X,'  it  has  further  to  be  signified  by  p^  that  to  obtain  the 
conclusion  *  Some  X  is  Z,'  we  must  make  a  limited  conver- 
sion. So  in  Fesapo  to  obtain  Ferio  of  the  First  Figure,  we 
must  convert  E  simply,  and  A  by  limitation.  Although  the 
method  of  reduction  ad  impossibile  may  be  applied  to  any  of 
the  irregular  moods,  the  letter  k  occurs  only  in  two,  Baroko 
and  Bokardo,  these  being  the  only  two  that  the  logicians  found 
irreducible  by  the  processes  of  transposition  and  conversion. 

7.  The  rules  or  Canons  of  valid  reasoning  are  variously 
stated.  They  are  proximate  rules,  being  derived  from  the 
fundamental  axioms  of  all  Deduction. 


CAIIONS  OF  THE  SYLLOGISM. 


149 


Common  Canons. — These  are  six  in  number.* 

(1)  Every  Syllogism  has  Three,  and  only  three.  Terms, 

(2)  There  must  be  Three,  and  only  three,  Propositions, 

(3)  The  Middle  Term  must  be  distributed  once,  at  least,  in  the 
premises. 

That  is  to  say,  the  Middle  Term  must  be  a  universal  in  one 
or  other  of  the  premises.  It  must  be  the  subject  of  a  univer- 
sal proposition  {All  Y  is  Z,  No  Y  is  Z),  or  else  the  predicate  of 
a  negative  proposition  No  X  is  Y,  Some  X  is  not  Y,  As  the 
subject  of  a  particular  proposition  {Some  Y  ia  Z,  Some  Yis 
not-Z),  and  as  the  predicate  of  an  affirmative  proposition  (All 
X  is  Y,  Some  X  is  Y),  the  middle  term  Y  is  particular,  or  un- 
distributed. 

By  a  reference  to  the  nineteen  valid  syllogisms,  it  will  be 
seen  that  in  each  of  them  the  middle  term  is  distributed  once 
in  the  premises.  Thus,  in  the  First  Figure  throughout,  it 
is  the  subject  of  the  major,  which  is  a  universal  {All  Y  is  Z, 
No  Y  is  Z).  This  is  as  it  ought  to  be  in  the  standard  syl- 
logism. In  the  Second  Figure,  it  is  distributed  three  times 
in  the  major,  and  once  in  the  minor  (Some  X  is  not-Y).  In 
the  1st,  2nd,  4th,  and  5th  moods  of  the  Third  Figure,  it  is 
distributed  in  the  minor;  being  also  distributed  in  the  major, 
in  the  1st  and  4th.  In  the  Fourth  Figure,  it  is  distributed  in 
the  minor,  in  all  the  moods  but  the  last. 

In  the  following  couples,  there  is  no  distribution  of  the 
middle  term  (Y),  and  consequently  none  of  the  couples  could 
stand  as  premises  in  a  valid  deduction. 

All  Z  is  Y  Some  Z  is  Y  All  Z  is  Y 

All  X  is  Y  Some  X  is  Y  Some  Z  is  Y 


\' 


Some  Y  is  Z,         Some  Y  is  not  Z  All  Z  is  Y 

All  X  is  Y,  All  X  is  Y  Some  Y  is  not  X. 

A  pretended  syllogism,  in  such  forms  as  these,  or  any  form 
where  the  rule  does  not  hold,  is  said  to  exemplify  the  fallacy 
of  undistributed  middle. 
Such  are  the  following  : — 

Some  Y  is  Z  Some  men  are  kings. 

All  X  is  Y  All  cooking  animals  are  men. 

AH  X  is  Z  All  cooking  animals  are  kings. 

Other  examples  will  occur  afterwards. 

(4)  No  term  undistributed  in  the  premises  must  be  distributed  in 
the  conclusion.      In  other  words,  there  must  not  be  a  greater 

*  After  Whately,  who  gives  them  as  a  condensation  of  the  twelve 
canons  of  Aldrich. 


150 


THE  SYLLOGISM. 


quantity  attaching  to  any  term  in  the  conclnsion,  than  is 
attached  to  the  same  term  in  the  premises.  If  X  be  particular 
m  the  premises,  so  must  it  be  in  the  conclusion  ;  the  same  with 
Z.  This  condition,  likewise,  is  fulfilled  in  the  valid  syllogisms. 
Thus ; — 

All  Y  is  Z  No  Y  is  Z. 

All  X  is  Y  Some  X  is  Y. 

All  X  is  Z  Some  X  is  not  Z. 

In  the  first  of  the  two,  the  subject  of  the  conclusion  is 
universal  in  the  minor  premise,  and  may  therefore  be  universal 
m  the  conclusion  ;  in  the  second,  it  is  particular  in  the  minor, 
and  must  be  particular  in  the  conclusion.  lu  both,  the  predi- 
cate of  the  conclusion  is  particular  in  the  premises,  and  must 
be  particular  in  the  conclusion.  So  if,  in  Dariiy  a  universal 
conclusion  were  drawn,  it  would  be  invalid. 
All  Y  is  Z  All  men  are  mortal. 

Some  X  is  Y         Some  extended  things  are  men. 
All  X  is  Z  All  extended  things  are  mortal. 

We  may  have  premises,  free  from  the  last-named  vice  of 
undistributed  middle,  yet  made  to  yield  a  false  conclusion  by 
overstepping  the  present  rule,  or  raising  a  term  of  particular 
quantity,  in  the  premises,  to  the  rank  of  universal  quantity 
in  the  conclusion.  To  this  error  is  given  the  name.  Illicit 
-process ;  and  according  as  the  unduly  extended  term  occurs  in 
the  major  or  in  the  minor  premise,  the  error  is  called  illicit 
process  of  the  major  or  illicit  process  of  the  minor. 

In  the  foregoing  instance,  the  illicit  process  is  in  the  minor. 
We  give  an  instance  of  illicit  process  of  the  major. 
All  Y  is  Z  All  men  are  fallible. 

Some  X  is  not  Y  Some  beings  are  not  men. 
No  X  is  Z  No  beings  are  fallible. 

The  major  term  *  fallible,'  being  the  predicate  of  an  affir- 
mative proposition,  is  particular  or  undistributed  ;  in  the  con- 
clusion, it  is  the  predicate  of  a  negative  proposition,  and  is 
therefore  distributed. 

(5.)  There  can  he  no  conclusion  drawn  from  negative  premises. 
No  Y  is  Z         No  men  are  gods 
No  X  is  Y        No  trees  are  men 
do  not  supply  the  materials  for  a  deductive  inference.      The 
reason  of  this  is  already  apparent  from  what  has  been  said  as 
to  the  applying  proposition,  which  must  always  affirm.      To 
know  only  that  two  things  are  each  excluded  from  a  third 
thing  is  to  know  nothing  concerning  their  mutual  relation. 
(6.)  If  one  premise  he  negative^  the  conclusion  must  be  negative. 


\i^ 


ha.milton's  canons. 


151 


This  is  illustrated  throughout  the  series  of  valid  syllogisms. 

If  one  premise  be  negative,  all  that  is  predicated  concerning 
one  of  the  terms  is  its  exclusion  in  whole  or  in  part  from  the 
middle  term :  we  cannot,  therefore,  conclude  through  the 
medium  of  the  middle  term  anything  about  its  total  or  partial 
co-extension  with  the  other  term. 

In  order  to  facilitate  the  detection  of  unsound  syllogisms, 
the  two  following  rules,  directly  deducible  from  these  canons, 
are  also  enounced. 

A.  There  is  no  inference  from  particular  fremises. 

Some  Y  is  Z         Some  IT  is  Z 
Some  X  is  Y         Some  X  is  not-Y 
give  no  conclusion.      The  first  example  contains  an  undistri- 
buted middle ;    and  the  weakest  inference  drawn  from  the 
second  (Some  X  is  not  Z)  would  contain  an  illicit  process  of 
the  major. 

B.  If  one  premise  is  particular,  the  conclusion  must  he  par* 
Ocular. 

As  in  Darii,  Ferio^  &c. 

Any  attempt  to  extract  a  universal  conclusion  where  both 
premises  are  not  universal  would  incur  either  undistributed 
middle  or  illicit  process. 

This  last  canon,  and  ako  the  Sixth,  are  embraced  in  one 
statement — *  The  conclusion  always  follows  the  weaker  part.' 

8.  Hamilton's  Canons.  These  are  three  iu  number.  The 
first  contains  the  1st  and  2nd  of  the  foregoing  list  (Three 
Terms  and  Three  Propositions).  The  two  others  are  as 
follows : —  , 

II.  Of  the  Premises,  the  Sumption  must  in  Quantity  be 
definite  (i.e.  nniversal  or  singular)  ;  the  Subsumptioa  in 
Quality  affirmative. 

As  Hamilton  means  by  the  Sumption  the  universal  or 
ground  proposition,  and  by  the  Subsumption,  the  applying  or 
subsuming  proposition,  this  is  declaring  the  characters  of  the 
standard  syllogism.  It  appears  that,  through  all  the  mutations 
of  syllogistic  moods,  there  must  always  be  one  universal 
proposition  (or  else  a  definite  singular),  and  one  affirmative 
proposition.  (The  meaning  of  the  alternative,  a  sm^/uZar  propo- 
sition will  appear  afterwards). 

III.  The  conclusion  must  correspond  in  quality  with  the 
Sumption,  and  in  quantity  with  the  Subsumption. 

Whatever  be  the  quality  of  the  Universal  or  ground  propo- 
sition, that  must  be  the  quality  of  the  conclusion ;   the  one 


152 


THE  SYLLOGISM. 


I 


^\1 


being  affirmative  the  other  is  affirmative ;  the  one  ne<Tative, 
the  other  is  negative.  ° 

Again,  the  quantity  of  the  Applying  proposition  is  the  tme 
quantity  of  the  conclusion  ;  universal  giving  universal,  and 
particular  giving  particular. 

These  two  rules  of  Hamilton's  are  given  as  the  equivalent 
for  Whately's  four  last  They  have  the  advantage  of  placing 
in  a  duo  i)romincnco  the  fundamental  structure  of  deductive 
reasoning,  which  is  altogether  invisible  in  the  foregoing  canons ; 
but  they  arc  not  readily  applicable  to  the  more  distorted 
figures.  Before  using  them,  we  must  first  discover  which  term 
contains  the  sumption,  and  which  the  subsumption ;  and  for 
this,  we  must  refer  to  the  directions  given  respecting  the 
irregular  moods.  In  short,  we  must  first  redress  the  inver- 
sions  and  distortions  of  the  irregular  moods,  which  is  substan- 
tially to  go  through  the  process  of  reducing  each  to  the  fii*st 
figure. 

9.  The  rules  of  the  syllogism  given  in  the  form  of  separate 
canons  for  each  figure,  Jb  or  the  First  or  standard  Figure, 
the  canons  of  Hamilton  are  the  most  suitable  expression. 
For  each  of  .the  other  Figures,  special  canons  may  be 
framed  according  to  the  nature  of  the  Figure. 

Thus,  in  the  second  Figure,  it  can  be  shown  that, 

(1)  One  premise  is  negative. 

(2)  The  major  premise  is  universal. 

The  proof  is  easy.  (1)  If  both  premises  were  affirmative, 
the  middle  term  being  the  predicate  of  both  premises,  it  would 
be  undistributed. 

Again,  (2)  if  the  major  were  particular,  the  weakest  conclusion 
that  could  be  drawn.  Some  X  is  not  Z,  involves  illicit  process 
of  the  major. 

It  follows  from  the  first  of  the  two  rules  (One  premise  must 
be  negative)  that,  in  this  Figure,  it  is  possible  to  prove  negative 
conclusions  only. 

In  the  Third  Figure,  the  canons  are, 

(1)  The  minor  premise  is  affirmative, 

(2)  The  conclusion  is  particular. 

If  the  minor  premise  were  negative,  the  conclusion  must  be 
negative,  and  the  major  term  affirmative,  which  would  involve 
an  illicit  process  of  the  major. 

Again,  the  conclusion  must  be  particular,  whether  the 
syllogisms  be  affirmative  or  negative. 

The  minor  premise  being  affirmative,  there  cannot  be  a  ani- 


8PECIAL  CANONS  OF  THE  FIGURES. 


153 


rersal  affirmative  conclusion  without  illicit  minor.      In  a  uni- 
versal  negative  conclusion  both  terms  are    distributed:  and 
they  cannot  both  be  distributed  in  the  premises,  unless  both 
premises  were  negative,  which  could  not  be. 
In  the  fourth  Figure, 

(1)  In  the  negative  moods,  the  m,ajor  is  universal. 

Some  Z  is  not  Y,  Some  Z  is  Y 

All  Y  is  X,  No  Y  is  X  ^ 

could  not  yield  even  particular  conclusions,  without  illicit 
process  of  the  major*  We  should  have  to  infer — Some  X  is  not 
Z :  and  Z  is  undistributed  in  the  premises  in  consequence  of 
the  particularity  of  the  major. 

(2)  If  the  m^ajor  is  affirmative,  the  minor  is  universal, 

A  particular  minor  to  an  affirmative  major  would  give 
All  Z  is  Y,  All  Z  is  Y 

Some  Y  is  X,  Some  Y  is  not  X 

both  forms  containing  undistributed  middle. 

(3)  Jf  the  minor  is  negative^  both  premises  are  universal.     Try 

All  Z  is  Y,  Some  Z  is  Y, 

Some  Y  is  not  X,  No  Y  is  X. 

There  is,  in  the  first  form,  undistributed  middle  ;  and  in  the 
second,  the  weakest  conclusion,  Some  X  is  not  Z,  contains 
illicit  process  of  the  major. 

This  rule  is  implied  in  the  two  preceding.  By  the  First 
rule,  the  Major  is  universal,  because  the  mood  is  negative.  By 
the  Second  rule,  the  Minor  is  universal,  because  the  major  is 
affirmative. 

(4)  If  the  minor  is  affirmative,  the  conclusion  is  particular. 
With  minor  affirmative,  we  have — 

All  Z  is  Y,  No  Z  is  Y 

All  Y  is  X,  All  Y  is  X, 

In  both  cases,  a  universal  conclusion  v/ould  be  attended  with 

illicit  process  of  the  minor. 

10.  That  the  valid  moods  are  those  above  given,  and  no 
more,  is  shown  by  testing  all  the  other  possible  moods  ac- 
cording to  the  syllogistic  canons. 

The  possible  moods  may  be  arrived  at  by  computing  the 
possible  groups  of  threes  that  can  be  made  out  of  the  four  pro- 
positional  forms — A,  I,  E,  O.  Now,  taking  the  premises  alone, 
there  are  sixteen  different  couples  that  can  be  made  &om  these 
four  letters. 

A,  A        I,  A         E,  A        O,  A 
A,  I        (1,1)         E,I        (0,1) 


/ 


^1  /f 


h 


154 


THE  SYLLOGISM. 


SIFTING   OF  THE   VALID   MOODS. 


155 


4:  i 


I. 


(A,  O,  I) 

(A,  0,  E) 

A,  0,0 


A,B  I,  E  (E.E)  (0,E) 
A,  O  (1,0)  (E,  O)  (0,0). 
Of  these  sixteen  forms,  we  can  reject  at  once,  as  inad- 
missible, first,  those  that  have  both  propositions  particular — 
I  I,  I  O,  O  I,  O  O.  We  can  farther  reject  those  that  have 
both  negative — E  E,  E  0,  O  E  (0  O  is  rejected  on  the  pre- 
vious ground).  After  these  seven  rejections,  there  are  nine 
forms  remaining. 

For  a  farther  sifting,  two  methods  are  open  to  us.  First, 
let  us  try  whether  every  one  of  the  nine  couples  may  stand  as 
premises  to  conclusions  of  all  the  forms,  A,  I,  E,  O. 

A,  A,  A        (A,  I,  A)         (A,E,  A)        (A,  O,  A) 
A,  A,  I  A,  I,  I  (A,  E,  I) 

(A,  A,  E)        (A,  I,  E)  A,  E,  E 

(A,  A,  O)        (A,  I,  O)  A,  B,  O 

and  so  on  through  the  remaining  five  forms. 

Now,  by  applying  the  canon  that  requires  a  particular  con- 
clusion when  one  of  the  premises  is  particular,  we  exclude  two 
in  the  second  column — A  I  A,  A  I  E,  and  two  in  the  fourth — 
A  0  A,  A  O  E.  By  applying  the  canon  that  requires  a  nega- 
tive conclusion  when  one  of  the  premises  is  negative,  we  ex- 
clude, in  the  third  column,  A  E  A,  A  E  I ;  in  the  fourth 
column,  A  0  I  (also  A  0  A  excluded  on  the  previous  ground). 
Although  no  express  canon  is  laid  down  requiring  an  afiirma- 
tive  conclusion  from  affirmative  premises,  such  canon  could  be 
proved  to  be  valid  ;  and  by  means  of  it,  two  exclusions  would 
be  made  in  the  first  column — A  A  E,  A  A  O,  and  one  farther 
exclusion  in  the  second.  Hence,  of  the  sixteen  forms,  six  only 
survive  these  successive  purgations.  By  a  similar  operation, 
extended  to  the  remaining  twenty  forms,  it  would  appear  that 
there  are  in  all  twelve  forms  admissible  ; — 

AAA,     AAI,    AEE,    AEO,     AIT,     AOO 
E  A  E,    E  A  0,    E  I  0,      I  A  I.     I  E  0,    0  A  0, 
If  these  twelve  forms  were  each  admissible  in  all  the  Figures, 
there  would  still   be  forty-eight  valid  syllogisms.     But,  by 
stating  them  under  the   successive  figures,  their  ranks   are 
thinned  still  farther.     Thus,  in  the  First  Figure,  AAI  and 
AEO   are  superfluous  because  they  infer  a  smaller  conclu- 
sion when  a  larger  could  be  drawn ;  with  the  premises  A  A, 
we  can  infer  A  (Barbara)  ;  with  A  E,  we  infer  E  {Celarent), 
Of  the  remaining  ten,  six  would  involve  violations  of  funda- 
mental canons,  as  may  be   seen   by  expressing  them  in  full. 
Two  examples  are  enough.     Thus,  AEE  gives- 
All  Y  is  Z  All  men  are  mortal 


I 


No  X  is  Y  No  molluscs  are  men 

No  X  is  Z  No  molluscs  are  mortal 

which  contains  illicit  process  of  the  major.  The  same  would  hap- 
pen under  a  particular  conclusion,  as  in  A,  E,  0.  Again,  I,  A,  I — 
Some  Y  is  Z  Some  fishes  are  sharks 

All  X  is  "Y  All  salmons  are  fishes 

Some  X  is  Z  Some  salmon  are  sharks — 

has  the  middle  term  undistributed. 

By  operating  in  this  manner,  we  reduce  the  valid  moods  of 
the  First  Figure  to  the  four  formerly  given — A  A  A,  E  A  E, 
A  1 1,  E  I  O. 

The  same  process  repeated  for  the  remaining  figures  has 
the  result  of  reducing  the  admissible  forms  to  those  actually 
given  in  the  scheme  of  the  syllogism. 

The  other  method  of  elimination  is  to  apply  the  special 
canons  of  the  figures  to  the  nine  forms  of  unobjectionable 
premises,  A  A,  A  I,  &c.  By  the  canons  of  the  standard  syllo- 
gism, the  major  is  universal  and  the  minor  affirmative  ;  whence 
the  forms,  A  E,  A  O,  I  A,  O  A,  are  rejected  at  once  ;  and  there 
remain  only  the  four,  A  A,  A  I,  E  A,  E  I,  corresponding  to  the 
four  moods  of  the  First  Figure.  For  the  Second  Figure,  the 
canons  (One  premise  is  negative ;  the  major  is  universal) 
exclude  A  A,  A  I,  I  A,  I  E,  O  A  ;  leaving  A  E  (Gamestres),  A  O 
(Baroko),  E  A.  (Cesare),  E  I  {Festino),  For  the  Third  Figure, 
the  first  canon  (The  minor  is  affirmative)  excludes  A  E,  A  O, 
I  E  ;  and  there  remain  A  A  (Darapti),  A  I  [Datisi)^  I  A  {Bisa" 
mis)^  E  A  (Felapto7i),  E  I  (Ferison),  0  A  (Bokardo), 

For  the  Fourth  Figure,  the  first  canon  (In  the  negative 
moods,  the  major  is  universal)  excludes  I  E,  O  A.  The  second 
canon  (If  the  major  is  affirmative,  the  minor  is  universal) 
excludes  A  I,  A  O.  The  remainder  are  A  A  (Bramantip),  A  B 
{Gamenes)y  I  A  (Blmaris)^  E  A  {Fesapo),  E  I  (Fresison). 

AXIOM   OF  THE  SYLLOGISM. 

11.  Logicians  have  aimed  at  reducing  the  whole  of  the 
special  canons  or  rules  of  the  Syllogism  to  one  comprehen- 
sive Law  or  Principle. 

The  oldest  form  of  this  principle  is  that  named  the 
Dictnm  de  omni  et  nullo.  *  Whatever  is  affirmed  or  denied 
of  a  class,  is  afl&rmed  or  denied  of  any  part  of  that  class.' 

As  stated,  this  maxim  seems  merely  one  of  the  forms  of  Im- 
mediate Inference : — '  all  men  are  mortal,'  hence  *  this  man, 
ten  men,  some  men,  are  mortal.*      This,  however,  is  not  the 


■M 


156 


AXIOM  OF  THE  SYLLOGISM. 


.1 


form  actually  assnraed  by  the  syllogism.  We  have  to  prove 
that  some  object  is  mortal,  not  expressly  named  a  man,  but 
designated  by  some  other  title,  as  *king.'  We  cannot  say 
'  men  are  mortal,*  therefore  *  kings  are  mortal ;'  such  an  infer- 
ence can  be  made  only  through  an  intermediate  assertioo, 
*  kings  are  men.* 

Another  defect  has  been  pointed  out  in  the  dictum  :  namely 
that  it  proceeds  upon  the  old  erroneous  view  of  a  proposition, 
the  reference  of  a  thing  to  a  class.  This,  however,  might  be 
got  over  by  understanding  *  class  *  to  mean  the  class  indefinite^ 
marked  by  the  connotation  of  the  class  name.  Practically, 
such  must  be  the  case ;  we  have  no  means  of  pointing  out  the 
class  *  men,*  except  as  the  possessors  of  human  attributes. 

Considering  the  dictum  as  the  basis  of  all  Deductive  Reason- 
ing, we  might  amend  it  thus  : — *  whatever  is  true  of  a  whole 
class  (class  indefinite,  fixed  by  connotation),  is  true  of  whatever 
thing  can  be  affirmed  to  come  under  or  belong  to  the  class  (as 
ascertained  by  connotation).*  This  supposes  the  need  of  a 
second  affirmation,  the  minor  proposition,  and  is  no  longer  an 
immediate  inference. 

12.  The  defects  of  the  dictum  are  supposed  to  be  remedied 
by  this  form  : — 

Attributes,  or  Things,  co-existing  with  the  same  Attri- 
butes or  Things,  co-exist  with  one  another  (Affirmative). 

If  the  attributes  of  a  king  co-exist  with  those  of  a  man,  and 
the  attributes  of  a  man  co-exist  with  the  attribute  *  fallibility,* 
the  attributes  of  a  king  co-exist,  or  co-inhere  with  the  attribute 
fallibility. 

There  is  a  close  resemblance  between  the  present  form  and 
the  mathematical  axiom — Things  equal  to  the  same  thing,  are 
equal.  The  two  are  alike  axioms  of  mediation ;  they  connect 
two  things  by  a  common  third. 

The  negative  form  is  stated  thus  : — *  One  thing  co-existing 
with  a  second  thing,  with  which  second  thing  a  third  thing 
does  not  co-exist,  is  not  co-existent  with  that  third  thing ;' 
which  resembles  the  axiom — Things  unequal  to  the  same  thing, 
are  unequal. 

This  mode  of  stating  the  axiom  has  often  been  adopted  by 
logicians  : — Ao/a  oiotce  est  nota  rei  ipsius ;  Things  that  agree  in 
the  same  third,  agree  among  themselves.  For  the  negative 
form — re/pugnans  notce^  repugnat  rei  ipd;  Things  whereof  the 
one  agrees,  the  other  does  not  agree,  with  the  same  third,  do 
not  agree  among  themselves. 


NOTA  NOT^. 


157 


The  advantages  of  the  form  are  indicated  by  the  remarks 
already  made.  It  gives  very  great  prominence  to  the  fact  of 
mediation  in  Deductive  Inference,  and  thus  draws  a  broad  line 
between  it,  and  Immediate  or  Apparent  Inference.  It  also 
accommodates  itself  to  such  a  case  as  Darapti,  with  a  singular 
subject,  thus, 

Socrates  was  wise. 

Socrates  was  poor. 

Some  wise  men  have  been  poor. 
Now,  the  treating  of  a  Singular  proposition  as  a  universal, 
which  is  necessary  to  make  the  above  a  regular  syllogistic 
form,  has  always  seemed  a  great  anomaly  in  the  syllogism. 
Indeed,  it  is  a  subversion  of  the  theory  of  Deductive  Reasoning, 
as  supposed  to  consist  in  the  application  of  a  general  or  uni- 
versal principle  to  a  case  coming  under  it.  But,  if  we  accept 
the  present  form  of  the  axiom,  the  above  syllogism  is  rendered 
with  apparent  ease.  *Wise*  co-exists  with  'Socrates  ;'  *Poor* 
co-exists  with  Socrates ;  therefore  *  Wise  *  and  *  Poor '  co-exists 
with  one  another ;  that  is,  *  Some  wise  persons  are  poor.' 

A  farther  advantage  of  the  same  form  consists  in  following 
out  the  the  *  Connotation  *  theory  of  Propositions.  The  exten- 
sion of  the  several  propositions  is  completely  banished  from  it, 
and  nothing  but  Connotation  or  Comprehension  left.  It  is  no 
longer  *  all  A  is  B,*  but  the  attribute  A  co-exists  with  the 
attribute  B,'  and  so  on.  From  the  same  cause,  a  seeming  facility 
is  given  in  chains  of  reasoning,  which  can  be  rendered  thus : 
— A  is  a  mark  of  B,  B  of  C,  C  of  D  ;  wherefore  A  is  a  mark 
ofD. 

Notwithstanding  so  many  advantages,  this  form  of  the  axiom 
now  described  is  unworkable  as  a  basis  of  the  syllogism.  The 
fatal  defect  consists  in  this,  that  it  is  ill  adapted  to  bring  out 
the  difference  between  total  Qj}d  partial  coincidence  of  terms,  the 
observation  of  which  is  the  essential  precaution  in  syllogizing 
correctly.  If  all  terms  were  co-extensive,  the  axiom  would  flow 
on  admirably ;  A  carries  B,  all  B  and  none  but  B  ;  B  carries 
C  in  the  same  manner ;  whence  A  carries  B,  without  limita- 
tion or  reserve.  But,  in  point  of  fact,  we  know  that  while  A 
carries  B,  other  things  carry  B  also,  whence  a  process  of  limita- 
tion is  required,  in  transferring  A  to  C  through  B  : — A  (in  com- 
mon with  other  things)  carries  B  ;  B  (in  common  with  other 
things)  carries  C  ;  whence  A  (in  common  with  other  things) 
caiTies  C.  The  axiom  provides  no  means  of  making  this  limi- 
tation ;  if  we  were  to  follow  A  literally,  we  should  be  led  to 
Buppose  A  and  C  co-extensive  :  for  such  is  the  only  obvious 


158 


AXIOM   OF  THE   SYLLOGISM. 


meaning  of  *  the  attribute  A  coincides  with  the   attribute 

c: 

Unless  the  predicate  is  quantified,  as  Hamilton  recommends, 
the  propositional  form  in  Extension — '  all  men  are  mortal/ 
does  not  explicitly  suggest  that  *  men  are  but  a  part  of  mortals  ;* 
yet  we  can  readily  conceive  the  fact  when  reminded  of  it ;  the 
extent  of  *  mortal  beings  '  is  greater  than  the  extent  of  *  men.' 
But  the  proposition  stated  in  pure  connotation  or  comprehen- 
sion, as  the  present  axiom  requires, — *  the  attributes  of  men  co- 
exist with  the  attribute  mortality' — is  difficult  to  adapt  to  the 
fact  that  mortals  are  more  numerous  than  man.  We  should 
hare  to  make  a  still  greater  circumlocution  : — the  attributes 
of  men  co-exist,  but  are  not  the  only  attributes  that  co-exist, 
with  the  attribute  *  mortality.*  So,  the  attributes  of  a  king 
co-exist,  but  are  not  the  only  attributes  that  co-exist,  with  the 
attributes  of  men.  The  conclusion  would  then  be — The 
attributes  of  a  king  co-exist,  but  are  not  the  only  attributes 
that  co-exist,  with  the  attribute  '  mortality.*  Now,  as  the 
axiom  *  attributes  co-existing  with  the  same  attribute  co-exist 
with  one  another  *  does  not  suggest  these  necessary  limita- 
tions, it  is  not,  as  worded,  an  explicit  basis  for  the  syllogism. 

It  is  only  the  same  objection,  otherwise  put,  that  the  axiom 
does  not  accommodate  itself  to  the  type  of  Deductive  Reason- 
ing, as  contrasted  with  Induction — the  application  of  a  general 
principle  to  a  special  case.  Anything  that  fails  to  make  pro- 
minent this  circumstance  is  not  adapted  as  a  foundation  for  the 
syllogism. 

The  scientific  processes  of  Induction  and  Deduction  are 
habitually  conceived  on  the  basis  pf  Extension  ;  it  is  only  thus 
that  we  readily  appreciate  the  greater  or  less  generality  of 
propositions.  Hence  the  proper  view  of  the  syllogism,  as  of 
the  notion  and  the  proposition,  is  to  base  it  on  Extension,  but 
to  determine  the  extension  by  Connotation  or  Comprehension. 
*  All  men  are  mortal '  is  best  understood  as  the  concrete 
population  of  human  beings,  defined  and  determined  by  the 
class  attributes  of  humanity.  This  double  point  of  view  com- 
plies with  all  the  exigencies  of  reasoning,  and  is  not  advan- 
tageously surrendered  in  favour  of  the  statement  of  propositions 
in  pure  comprehension. 

The  result  of  the  comparison  of  the  two  axiomatic  state- 
ments is,  that  the  Dictum  de  omni  et  nullo,  properly  guarded, 
is  the  most  suitable  and  exact  representation  of  the  essential 
feature  of  Deductive  Reasoning  or  Syllogism. 

The  case  of  Singular  Propositions,  hold   for  the  nonce  to  bt 


SINGULAR   PROPOSITIONS. 


159 


universal,  is  a  grave  exception  to  the  Deductive  process  as  we  have 
uniformly  described  it.  On  examining  such  cases,  however,  we 
may  see  good  reason  for  banishing  them  from  the  syllogism.  Let 
us  take  the  example  already  quoted : — 

Socrates  is  poor 

Socrates  is  wise 

Some  poor  men  are  wise. 
Properly,  the  conclusion  is,  *  one  poor  man  is  wise.'  Now,  if 
*  wise,'  *  poor,*  and  *  a  man,'  are  attributes  belonging  to  the  mean- 
ing of  the  word  Socrates ;  there  is  then  no  march  of  reasoning  at 
all.  We  have  given,  in  Socrates,  inter  alia^  the  facts  *wise,'  'poor,* 
and  '  a  man,*  and  we  merely  repeat  the  concurrence,  whiih  is 
selected  from  the  whole  aggregate  of  properties  making  up  the 
whole,  *  Socrates.'  The  case  is  one  under  the  head  *  Greater  and 
Less  Connotation,'  in  Equivalent  Propositional  Forms,  or  Immedi- 
ate Inference. 

But  the  example  in  this  form  does  not  do  justice  to  the  syllogism 
of  singulars.  We  must  suppose  both  propositions  to  be  real,  the 
predicates  being  in  no  way  involved  in  the  subject.  Thus : — 
Socrates  was  the  master  of  Plato 
Socrates  fought  at  Delium 
The  master  of  Plato  fought  at  Delium. 
It  may  fairly  be  doubted  whether  the  transitions,  in  this 
instance,  are  anything  more  than  equivalent  forms.  For  the 
proposition,  '  Socrates  was  the  master  of  Plato,  and  fought  at 
Delium,'  compounded  out  of  the  two  premises,  is  obviously  nothing 
more  than  a  grammatical  abbreviation.  No  one  can  say  that  there 
is  here  any  change  of  meaning,  or  anything  beyond  a  verbal 
modification  of  the  original  form.  The  next  step  is,  *  the  master 
of  Plato  fought  at  Delium,'  which  is  the  previous  statement  cut 
down  by  the  omission  of  *  Socrates.'  It  contents  itself  with 
reproducing  a  part  of  the  meaning,  or  saying  less  than  had  been 
previously  said.  The  full  equivalent  of  the  affirmation  is  *the 
master  of  Plato  fought  at  Delium,  and  the  master  of  Plato  was 
Socrates  ;'  the  new  form  omits  the  last  piece  of  information,  and 
gives  only  the  first.  Now,  we  never  consider  that  we  have  made 
a  real  inference,  a  step  in  advance,  when  we  repeat  less  than  we 
are  entitled  to  say,  or  drop  from  a  complex  statement  some  portion 
not  desired  at  the  moment.  Such  an  operation  keeps  strictly 
within  the  domain  of  Equivalence  or  Immediate  Inference.  In  no 
way,  therefore,  can  a  syllogism  with  two  singular  premises  be 
viewed  as  a  genuine  syllogistic  or  deductive  inference. 

13.  The  Proof  of  the  Axiom  is  uncontradicted  experi- 
ence. 

The  Dictum  is  not  a  mere  rule  of  consistency,  exacting  the 
admission,  in  equivalent  forms,  of  all  that  has  Ijeen  conceded 
in  one  form.  It  is  a  mediate  process,  and  the  mediation  has 
to  be  justified  by  an  appeal  to  the  facts.     As  far  as  proof  goes, 


160 


AXIOM   OF  THE   SYLLOGISM, 


it  resembles  in  character  the  second  form  above  given—*  Thm^ 
co-existing  with  the  same  thing,  co-exist,'  and  the  mathema- 
tical axiom  *  Things  equal  to  the  same  thing  are  equal/  All 
the  three  principles  stand  upon  the  same  foundation;  some 
philosophers  refer  them  to  intuition,  others  to  experience ;  but 
the  mode  of  proof  i'or  one  is  the  mode  for  all.  The  dictum 
seems  to  approach  nearest  to  a  mere  rule  of  consistency ;  yet 
the  fact  of  mediation  makes  all  the  difference  ;  *  the  identical 
of  an  identical  is  identical  '  is  a  new  step  and  needs  a  new  jus- 
tification. Nobody  would  accept  even  so  obvious  an  inference 
— as  '  men  are  mortal,  kings  are  men.  kings  are  mortal,*  with- 
out first  verifying  upon  cxam])les  the  peculiar  kind  of  transi- 
tion involved.  Wo  are  so  alive  to  the  snares  lurking  in  the 
most  obvious  and  plausible  forms  of  language,  that  we  do  not 
trust  any  of  them  without  the  check  of  actual  trials.  Nothing 
could  seem  more  satisfactory  than  *  A  co-exists  with  B,  B  with 
C,  therefore  A  co-exists  witli  C  wholly  and  unconditionally,'  yet 
until  we  have  elaborately  fenced  the  operation  against  the 
simple  conversion  of  a  universal,  the  conclusion  is  unwarranted. 

Viewing  together  the  Mathematical  axiom  of  Equality  and  the 
axiom  of  the  Syllogism,  Mr.  de  Morgan  remarks  :— '  In  both  there 
is  a  law  of  thought  appealed  to  on  primary  subjective  testimony  of 
consciousness ; '  '  equal  of  equal  is  equal  *  in  the  one ;  '  identical  of 
identical  is  identical '  in  the  other.  The  two  laws  are  equally 
necessary,  equally  self-evident,  equally  incapable  of  being  resolved 
into  simpler  elements. 

14  There  are  other  modes  of  stating  the  Axiom.  Hamil- 
ton has  two  forms.  The  fiirst  is  for  what  he  calls  Informal 
Keasoning:— In  so  far  as  two  notions  (notions  proper  or 
individuals)  either  both  agree,  or  one  agreeing  the  other 
does  not,  with  a  common  third  notion  ;  in  so  far,  these 
notions  do  or  do  not  agree  with  one  another. 

This  is  simply  one  way  of  wording  the  Nota  noics,  and  is 
liable  to  the  objections  urged  against  that  form.  There  is  no 
provision  for  distinguishing  total  from  partial  agreement,  and 
therefore  no  basis  for  the  working  of  the  syllogism.  The 
words  *  agreement  'and  *  disagreement '  are  less  apt  than  *  co- 
existence '  and  '  non-coexistence '  for  expressing  the  axiom  ; 
they  have  the  defects  inherent  in  the  *  judgment'  theory  of 
Propositions. 

15.  For  the  Figured  Syllogism,  where  the  terms  are  re- 
lated as  subject  and  predicate  of  propositions  in  a  given 


Hamilton's  forms. 


161 


.order,  Hamilton  enounces  this  form: — What  worse  re- 
lation of  subject  and  predicate  subsists  between  either  of 
two  terms  and  a  common  third  term,  with  which  one,  at 
least,  is  positively  related ;  that  relation  subsists  between 
the  terms  tiiemselves. 

The  peculiar  phraseology  *  What  worse  relation  '  is  a  man- 
ner of  saying  that  the  conclusion  must  carry  the  weakest  re- 
lationship signified  by  the  premises.  If  there  be  a  negative  in 
the  premises,  there  must  be  a  negative  in  the  conclusion ;  if 
there  be  particularity  in  the  premises,  there  must  be  particu- 
larity in  the  conclusion.  The  same  thing  is  otherwise  ex- 
pressed— *  The  conclusion  must  follow  the  weaker  part.' 

This  is  the  Axiom  given  in  Extension,  and  is  in  accordance 
with  the  Diclum,  although  not  stated  with  the  same  generality. 
It  more  resembles  one  of  the  canons  for  workiug  oat  the  syllo- 
gistic details,  itself  resting  on  the  Dictum. 

16.  The  first  of  Hamilton's  two  forms  is  expressed 
otherwise  thus  (Thomson) : — The  agreeuient  or  disagree- 
ment of  one  conception  with  auother,  is  ascertained  %y  a 
third  conception,  inasmuch  as  this,  wholly  or  by  the  same 
part,  agrees  with  both,  or  with  ojily  one  of  the  conceptions 
to  be  compared. 

This  form  appears  to  be  based  upon  Comprehension,  or  the 
Notanotoi,  but  endeavours  to  introduce  the  limitations  requisite 
for  discriminating  total  and  partial  quantity.  The  phiaseology, 
however, — '  conception,  &c.' — is  ambiguous  ;  it  may  express 
either  extension  or  comprehension— *  men'  or  the  attributes 
*  human.'  If,  taken  in  extension  (which  is  most  probable),  is 
closely  reproduces  Hamilton's  second  form,  and  puts  stress 
upon  the  difference  between  total  and  partial  coincidence. 
Nevertheless,  it  does  not  rise  to  the  sweep  of  the  Dictuin, 
in  declaring  the  paramount  circumstance  of  deductive  reason- 
ing,—-the  carrying  out  of  a  genei-al  law  to  particular  cases. 

If  *  conception  *  means  attributes,  comprehension,  or  conno- 
tation, the  phraseology  would  indicate  Hamilton's  syllogism  of 
Comprehension,  and  would  not  suggest  the  common  syllogism. 
The  attributes  *  king '  and  the  attribute  *  mortal '  agree  (better 
*  coincide  ')  by  agreeing  (coinciding)  with  the  same  part  of  the 
attributes  *  human.'  Hamilton's  syllogism  is  more  explicit ; 
thus — The  attributes  *king'  contain  the  attributes  *man-' 
the  attributes  *  man  '  contain  the  attribute  *  mortal ;'  the 
attributes  *ki!)g  '  contain  the  attribute  'mortal.* 


162 


AXIOM   OF  THE    SYLLOGISM. 


»# 


17.  In  the  comprehensive  scheme  of  De  Morgan,  the 
axiom  is  a  generalization  of  many  special  axioms.  The 
syllogism  is  treated  as  the  composition  of  two  relations 
into  ODC  ;  the  axiom  is  '  the  relation  of  a  relation  is  a  rela- 
tion compounded  of  the  two.' 

The  truth  of  this  is  seen,  and  its  application  controlled,  by 
the  special  instances  of  relationship.  One  of  these  instances  is 
the  axiom  of  the  common  syllogism.  Others  are  the  mathe- 
matical axioms,  *  Eqnal  of  equal  is  equal,'  and  *  greater  of 
greater  is  still  greater*  (a  fortiori).  Among  more  special  in- 
stances are  *  antecedent  and  consequent,'  *  ancestor  and 
descendant. 

18.  It  has  been  supposed  by  some  that  the  common 
axiom,  as  expressed  by  the  '  dictum  de  omni  et  nuUo,'  is 
a  consequence  of  the  Laws  of  Thought  (Identity,  Contradic- 
tion and  Excluded  Middle). 

Hamilton  maintains  that  categorical  syllogisms  are  regulated 
by  the  fundamental  laws  of  Identity  and  Contradiction.  Ho 
interprets  the  law  of  Identity  as  the  identity  of  a  whole  and 
the  sum  of  its  parts,  whence  he  considers  it  right  to  infer 
that  what  belongs  to  a  whole  belongs  to  its  part.  Mr.  Mansel 
agrees  with  Hamilton  in  referring  the  syllogistic  laws  to  the 
same  principles. 

The  eflfect  of  this  doctrine  is  to  abolish  the  difference  be- 
tween Immediate  and  Mediate  Inference,  by  bringing  mediate 
inference  under  Immediate,  or  under  the  law  of  Consistency. 
On  the  face  of  it,  the  supposition  is  unlikely  ;  and  accordingly 
it  has  been  denied  by  other  logicians.  Thus,  Mr.  de  Morgan 
(Syllabus,  p.  47)  remarks  of  the  attempts  to  reduce  the  syllog- 
ism to  the  three  so-called  Laws  of  Thought,  *  When  any  ono 
attempts  to  show  li&w,  I  shall  be  able  to  judge  of  the  process; 
as  it  is,  I  find  that  others  do  not  go  beyond  the  simple  asser- 
tion, and  that  I  myself  can  detect  the  petitio  principii  in  every 
one  of  my  own  attempts.* 

The  law  of  Consistency  requires  us  to  concede  that  what  is 
true  of  a  class  is  true  of  every  individual  in  the  class  ;  *  all  men 
are  fallible,*  *  the  half  of  men  are  fallible,  this  man  is  fallible  ' ; 
here  there  is  no  transition,  it  is  the  same  fact,  repeated  only  to 
a  less  extent.  But  when  we  say  *  kings  are  men,*  *  kings  are 
fallible,*  there  is  a  transition  to  a  difierent  subject,  a  subject 
not  present  to  the  mind  as  a  part  of  the  original  whole,  but 
brought  under  it  by  a  second  assertion.    Now  a  distinct  axiom, 


DERIVATION  OF  SPECIAL   CANONS. 


163 


18  needed  to  transfer  the  attribute  under  this  new  case.  The 
axiom  may  be  in  its  nature  self-evident,  but  the  conclusions 
regulated  by  it  are  not  identical  with  either  of  the  premises,  as 
an  immediate  inference,  properly  so  called,  is  identical  with  the 
original  form. 

19.  The  special  canons  of  the  Syllogism  are  derivable 
from  the  Axiom. 

*i,^^^  ^*  easily  follows  from  the  Dicfuin,  as  explained,  that 
there  are  three  terras,  and  no  more.  There  is  a  Universal  Pro- 
position containing  a  subject  and  a  predicate,  an  applying  or 
Interpreting  proposition,  adding  a  third  term,  and  repeating 
one  ot  the  terms  of  the  universal :— All  or  no  Y  is  Z,  All  X 
wu  "^^^  conclusion  contains  no  new  term—i^Jl  X  is  Z. 
Whence  there  are  three  terms  in  all. 

(2)  The  same  examination  shows  that  there  are  three  and 
no  more  than  three  propositions ;— the  Universal,  the  Inter- 
preting Proposition,  and  the  Conclusion. 

(3)  The  third  special  canon  is~*  The  middle  term  must  be 
distributed  once  in  the  premises.*  Distribution  or  Universal 
(Quantity  m  the  middle  term  is  essential  to  the  total  coincidence 
or  non-coincidence  of  at  least  one  of  the  other  terms  with  the 
middle  term  ;  without  which  the  two  extreme  terms  could  not 
be  shown  either  to  coincide,  or  not  to  coincide,  in  whole  or  in 
part.  Some  men  are  fallible,*  *  kings  are  some  men,'— would 
not  bring  about  a  coincidence  between  *  fallibility*  and  *  kinoes  •' 
one  portion  of  men  might  be  fallible,  and  a  different  portion 
might  be  kings.  This  is  obviated  if  fallibility  adheres  to  all 
men  ;  it  must  then  adhere  to  whatever  objects  are  found  to  be 
men. 

(4)  The  fourth  special  canon  is—'  No  term  undistributed 
m  the  premises  must  be  distributed  in  the  conclusion.*  It  may 
be  brought  under  the  Dictum  thus :— The  distribution  of  a 
term  in  the  conclusion  means  universal  or  total  coincidence 
with  the  other  term  of  the  conclusion  ;— *  All  X  is  Z  '  means 
^at  X  18  wholly  coincident  with,  wholly  included  in  Z.  Now 
X  and  Z  are  brought  together  by  a  middle  term  Y  ;  and  if  X 
did  not  wholly  coincide  with  Y  in  the  first  instance,  it  could  not 
be  transferred,  in  total  coincidence,  to  Z.  If  we  had  only  some 
u  '^     'rSr""  ^^*^^°^&^  al^  Y  is  Z,  we  could  not  declare  aZZ  X  to 

•xfv  .r®,'®  carried  over  to  Z  only  so  much  of  X  as  ^oes 
with  Y ;  if  that  be  the  whole,  the  whole  is  carried ;  if  a  part, 
part  is  carried.  If  *  all  men  are  fallible.*  and  *  some  beings  are 
men,  only  some  beings  are  fallible,  namely,  as  many  as  are  mea. 


i«i 


I 


164 


AXIOM   OF  THE  SYLLOGISM. 


M 


(5)  *  From  negative  premises,  there  is  no  inference.*  Nega- 
tive premises  do  not  coniply  with  the  essential  fact  of  the  in- 
terpreting proposition,  which  is  to  declare  that  a  given  case 
comes  under  the  sweep  of  the  rule.  Whether  the  universal 
be  affirmative  or  negative,  the  applying  proposition  must,  from 
its  nature,  be  affirmative.  No  Y  is  Z,  no  X  is  Y,  could  not  be 
the  means  of  bringing  X  under  Z,  or  of  bringing  these  two 
terms  together  in  a  conclusion  ;  we  could  not,  from  such  pre- 
mises, infer  even  No  X  is  Z.  '  No  matter  is  destructible  *  re- 
quires to  be  followed  up  with  *  ether  is  matter  '  to  prove  that 
*  no  ether  is  indestructible.' 

(6)  *  If  one  premise  be  negative,  the  conclusion  is  negative,*  ex- 
presses exactly  what  happens  in  the  negative  form  of  the  axiom. 

In  the  enlarged  scheme  of  De  Morgan,  some  of  these  rules 
are  violated  in  appearance,  but  only  in  appearance.  Thus 
from  '  two  negative  premises  *  he  draws  a  conclusion  in  the 
affirmative.  This,  however,  arises  from  the  elasticity  of  ex- 
pression allowed  by  the  use  of  contrary  forms.  Every  affirma- 
tive proposition  may  be  given  as  a  negative ;  and  there  may 
be  the  semblance  of  negation,  with  the  reality  of  affirmation 
in  conformity  with  the  axiom.     Thus — 

All  Y  is  Z     =     No  Y  is  not  Z. 

AUXisY     =     No  X  is  not  Y. 

All  X  is  Z  All  X  is  Z. 

20.  The  axioms — *  Equals  added  to  equals,  give  equal 
sums,*  and  the  argumentum  a  fortiori,  if  received  as  axioms 
in  Logic,  are  distinct  from  the  axiom  of  the  Syllogism,  and 
must  be  independently  proved. 

The  argumentum  a  fortiori  is  represented  thus  : — If  A  is 
greater  than  B,  and  B  greater  than  C,  still  gi'eater  is  A  than 
(J.  This,  and  the  other  axiom  stated,  are  purely  mathematical 
in  their  character ;  they  serve  for  the  comparing  of  quantities 
as  equal  or  unequal.  They  rest  on  their  own  special  evidence 
of  fact. 

It  will  be  seen  that  Boole  draws  the  Syllogism  under  the 
axiom  that  suffices  for  the  reduction  of  equations.  He  assumes 
that  the  analogy  of  the  logical  method  and  the  algebraical  is 
sufficiently  close  to  allow  of  the  substitution. 

The  conflicting  opinions  as  to  the  evidence  of  axioms  gener- 
ally, whether  of  logic,  of  mathematics,  or  of  other  sciences,  will 
be  discussed  in  a  succeeding  chapter. 


TESTING  OF  AKGUMENXa 


165 


EXAMPLES   OF  THE   SYLLOGISM. 

21.  The  chief  application  of  the  theory  and  the  forms  of 
the  syllogism  is  to  detect  fallacies  in  deductive  reasoning^ 

There  are  certain  forms  of  deductive  reasoning  or  argument, 
that  are  specious  to  appearance,  and  fallacious  in  reality ;  and 
the  analysis  of  the  syllogism  is  useful  in  disclosing  the  fallaci- 
ousness. 

22.  The  course  of  procedure,  in  dealing  with  an  ar^- 
ment  m  any  way  uncertain  or  perplexed,  is  as  follows  :— 

I.  Ascertain  what  is  the  conclusion,  or  the  point  to  be 
proved.  State  this  distinctly  in  a  proposition  so  as  to  dis- 
tinguish the  Subject  {minor  term  of  the  syllogism)  and  the 
Predicate  {major  term). 

II.  Find  out  the  middle  term  of  the  argument.  In  a  valid 
syllogism  there  must  be  a  middle  term,  and  only  one  :  and  it 
must  be  something  not  occurring  in  the  conclusion. 

•■^u\^^°^  ^^^  ^^^^  proposition  connecting  the  middle  term 
with  the  major  term ;  this  is  the  major  premise  of  the  syllogism. 
Also  some  proposition  connecting  the  middle  term  with  the 
minor  term  ;  giving  the  minor  premise  of  the  syllogism. 

IV.  The  two  premises  and  the  conclusion  being  stated  in 
form  and  order,  the  validity  may  be  judged  according  to  the 
laws  of  the  syllogism. 

(1)  If  the  deduction  coincides  with  any  of  the  valid  moods 
it  is  valid ;  if  not,  not.  * 

(2)  It  being  seen  what  Figure  the  argument  comes  under,  it 
may  be  tested  by  the  special  canons  of  that  figure. 

(3)  The  general  canons  of  the  syllogism  may  be  applied  to 
discover  errors,  if  there  be  any  such. 

Any  one  of  these  three  modes  may  be  adopted  at  choice  • 
inasmuch  as  each  of  them  singly  is  conclusive.  ' 

The  easiest  remembered  mode  of  testing  a  syllogism,  when 
once  m  form,  is  by  the  six  general  canons  of  the  syllogism. 
Of  these,  the  two  that  are  most  usually  violated  in  sophistical 
reasonings  are  the  3rd  (Distribution  of  the  Middle  Term)  and 
the  4th  (The  quantity  of  the  terms  in  the  conclusion  not  greater 
than  in  the  Premises).  An  argument  with  negative  premises 
(5)  would  deceive  no  one.  It  would  also  be  obvious,  without 
much  Logic,  that  one  premise  being  negative,  the  conclusion 
must  be  negative  (6). 

23.  As  an  alternative,  we  may  discard  the  consideration 


HI 


II  r* 


166 


EXAMPLES   OP  THE   SYLLOGISM. 


of  the  separate  Figures,  and  reduce  every  argument  at  once 
to  the  standard  form  of  Deduction. 

From  the  very  nature  of  deductive  reasoning,  the  conclusion 
is  a  special  application  of  some  more  general  proposition. 
This  more  general  proposition  must  be  found  in  the  premises ; 
it  is  the  ground  proposition  ;  in  Hamilton's  phraseology,  the 
Sumption.  There  must  also  be  found  another  proposition 
declaring  its  applicability  to  a  particular  case,  namely,  the 
case  given  in  the  conclusion.  These  two  indispensable  proposi- 
tions may  occur  under  distorted  forms,  which  we  must  be  able 
to  redress  by  the  methods  already  pointed  out,  that  is,  by 
obversion  and  conversion,  as  the  case  may  be.  Also,  the 
conclusion  may  require  to  be  obverted  or  converted,  or  both. 
By  such  methods,  we  may  evade  all  the  variations  of  figure, 
and  come  at  once  to  the  regular  type  of  deduction. 

EXAMPLES. 

All  men  are  mortal  AH  T  is  Z. — (A)  \ 

No  dogs  are  men  No  X  is  Y. — (E)  >  1st  Fig. 

No  dogs  are  mortal  No  X  is  Z. — (E)  j 

(1)  This  syllogism  is  in  the  First  Figure,  but  there  is  no 
mood  in  that  Figure  containing  the  propositions  A,  E,  E. 

(2)  Otherwise  :  The  major  term,  mortal,  is  distributed  in 
the  conclusion,  and  not  in  the  premises  ;  there  is  illicit  process 
of  the  major. 

(3)  Or  lastly  :  It  contradicts  the  canon  of  the  normal  syllo- 
gism, whereby  the  minor  is  declared  to  be  affirmative. 

All  planets  are  round         All  Z  is  Y. — A    ) 

A  wheel  is  round  All  X  is  Y. — A     >  2nd  Fig. 

A  wheel  is  a  planet  All  X  is  Z. — A     j 

(1)  There  is  no  such  mood  in  the  Second  Figure, 

(2)  The  middle  term,  *  round,*  is  undistributed. 

(3)  There  is  a  violation  of  the  special  canon  of  the  Second 
Figure — One  premise  must  be  negative. 

*  Every  honest  man  attends  to  his  business ;  this  person 
attends  to  his  business  ;  this  person  is  an  honest  man.*  This 
is  the  exact  counterpart  of  the  foregoing.  The  conclusion 
being  *  this  person  is  an  honest  man  ;'  the  minor  term  is  *  this 
person,*  the  major,  *  an  honest  man.*  The  middle  term  is 
*  attends  to  his  business.*  The  major  premise  (major  and 
middle),  *  Every  honest  man  attends  to  his  business,'  A  ;  the 
minor  premise,  *  this  man  attends  to  his  business,*  A  (a  definite 


FALLACY  OF  CONVEBSION. 


167 


individual  may  be  considered  as  either  A  or  I).  On  any  one  of 
the  three  grounds  given  In  the  foregoing  example,  the  reason- 
ing is  fallacious. 

These  two  examples  are  regarded  by  logicians  as  of  a  type 
calculated  to  mislead,  and  therefore  exemplifying  the  use  of 
the  laws  of  the  syllogism.  It  is  interesting  to  enquire  what 
circumstance  gives  them  their  fallacious  plausibility.  With 
this  view,  we  may  proceed  by  the  alternative  method  above 
pointed  out,  namely,  by  ascertaining  whether  these  be  the 
regular  premises  of  deduction. 

To  prove  that  a  wheel  is  a  planet,  we  must  have  a  more 
general  proposition,  of  which  this  shall  be  a  particular  case. 
Such  a  proposition  would  be  *all  round  bodies  are  planets:* 
We  should  then  require  an  applying  or  subsuming  proposition, 
namely,  *  wheels  are  round  bodies.'     With  these  two  proposi- 
tions, the   conclusion   would  be  legitimate,  that   wheels   are 
planets.     Looking  at  the  premises  given,  however,  we  do  not 
find  a  proposition  corresponding  to  the  first,  or  the  general 
proposition.      It   is   stated,  not   that  *all   round   bodies   are 
planets,'  but   only   that  *  all   planets  are   round,*  a  different 
proposition.     The  confounding  of  the  two  is  effected  by  the 
simple  conversion  of  a  universal  affirmative ;    by  arguing  from 
*all  planets  are  round,'  that  *all  round  bodies  are    planets,* 
which  we  can  do  only  if  there  are  no  round  things  but  planets. 
In  short,  the  fallacy,  traced  to  its  root,  is  2k  fallacy  of  conversion ; 
and  if  we  are  liable  to  be  deceived  by  such  syllogisms  as  the  pre- 
sent, it  is  because  we  are  liable  to  slip  into  this  fallacy.    There  is 
something  in  the  form  of  the  universal  affirmative  that  throws 
ns  off"  our  guard  ;  from  the  expression  All  X  is  Y,  we  are  apt 
to  assume  the  co-extension  of  X  and  Y,  unless  cautioned  and 
educated  to  the  contrary.     In  cases  where  the  co-extension 
exists,  and  only  in  such  cases,  could  the  argument  in  question 
give  a  sound  conclusion.     Thus — 
All  matter  gravitates. 
Air  gravitates. 
Air  is  matter. 
Now,  by  the  same  process  as  before,  it  is  shown  that  the 
genei'al  proposition  needed  for  this  conclusion  is  *  All  gravi- 
tating things  are  matter,*  which  happens  to  be  true,  but  is  not 
justified  by  the  assertion  in  the  major,  *  all  matter  gravitates  ;* 
for  there  might  be  other  gravitating  things. 

So  in  the  second  example  *  Every  honest  man  attends  to  his 
business,'  &c.,  we  should  require  the  terms  *  honest  man  *  and 
•  attention  to  business  *  to  be  co-extensive,  which  they  are  not. 


I 


i 


tn 


168 


EXAMPLES  OP  TUE  SYLLOGISM. 


1' 


'i'. 


i\ 


Whatever  tendency  we  have  to  be  deceived  by  such  reasonings 
depends  solely  upon  the  intellectual'  weakness  of  presuming 
co-extension  of  terms,  in  universal  affirmations. 

Hume  says: — *  We  have  no  perfect  idea  of  anything  but  a 
perception .  A  substance  is  entirely  difl'erent  from  a  perception, 
We  have  therefore  no  idea  of  substance.  * 

The  first  step  is  to  resolve  the  conclusion  into  its  two  terms. 
As  often  happens,  in  Logic,  these  terms  are  not  the  grammati- 
cal subject  and  grammatical  predicate  ;  a  transformation  must 
be  given  to  suit  the  tenor  of  the  premises.  Comparing  the 
first  proposition  with  the  last,  we  see  that  the  minor  terra,  or 
subject  of  the  conclusion,  must  be  *  having  an  idea ; '  the 
major  term  is  *  substance.'  The  affirmation  is  negative ; 
literally,  our  *  having  an  idea  '  is  not  true  of  substance.  It  is 
denied  that  substance  is  one  of  the  things  included  under 
having  an  idea.  The  next  point  is  to  single  out  the  m^iddle 
term,  namely,  *  perception.*  Joined  with  the  major  and  minor 
terms  respectively,  this  yields  as  premises — 

No  *  having  an  idea  *  is  not  perception. 

All  substance  is  not  perception. 

No  *  having  an  idea '  is  true  of  substance. 

In  the  present  form,  the  reasoning  is  wholly  inadmissible ;  the 
premises  are  both  negative.  We  might,  however,  obvert  the 
middle  term  *  perception,'  and  regard  not-perception  as  the 
true  middle  (like  changing  '  not  wise '  into  not-wise,  or  foolish). 
We  have  thus — 

No  *  having  an  idea '  is  not-perception  E  ] 
All  substance  is  not-perception  A  >  2nd  Fig.  {Cesare). 

No  *  having  an  idea  '  is  substance.       E  j 
In  this  form  the  argument  is  sound. 

It  is  often  desirable  to  express  arguments  of  great  subtlety, 
such  as  the  present,  in  the  standard  form  of  deduction.  The 
requisite  transmutation  would  have  to  be  effected  thus.  The 
conclusion,  *  "  having  an  idea  '*  is  not  true  of  substance,'  is  to 
bo  converted  *No  substance  is  included  in  our  having  an 
idea.'  For  this,  the  universal  proposition  would  be  a  proposi- 
tion of  denial  more  comprehensive  than  substance  : — No 
not-perception  is  included  in  our  having  an  idea.  The  minor 
is  then.  All  substance  is  not-perception  ;  whence  we  conclude 
according  to  the  regular  form  for  the  negative  deduction. 
From  the  middle  term  being  a  negation,  however,  this,  can 
never  be  an  easy  form  of  argument ;  and  more  especially  so  in 


li 


RX.VMPLES  OF  TUE   SYLLOGISMS 


169 


the  present  argument,  where  perception  is  as  wide  as  exist- 
ence, and  has  only  a  formal,  and  not  a  real  obverse. 

Thus,  then,  we  have,  in  the  First  Figure,  as  Gdarent 

Nothing  that  is  not  a  perception  (no  not-perccpfcion)  can 

be  perfectly  conceived,  g 

Substance  is  not  a  perception  (a  not-perception),  A.* 

Substance  cannot  be  perfectly  conceived.  ]B, 

'None  but   Whites  are   civilized;     the   Hindoos  are  not 
Whites  ;  therefore  they  are  not  civilized.' 
In  a  syllogism  thus  : — 

No  not- Whites  are  civilized  E  ) 
The  Hindoos  are  not  Whites  A  I  {Gelaren^, 
The  Hindoos  are  not  civilized  E  J 
A  correct  argument,  the  middle  term  being  *  not- Whites,'  for 
which  the  positive  equivalent  would  be  the  remaining  meuibers 
of  the  Universe,  *  races  of  men  '  (Black,  brown,  yellow  &c  ) 
This  would  give  a  more  intelligible  form  : —  ' 

No  communities  of  the  black,  browu,  or  yellow  races  are 
civilized ; 

The  Hindoos  are  of  the  black  or  brown  races. 
The  Hindoos  are  not  civilized. 

*  Abstinence  from  the  eating  of  blood  had  reference  to  the 
divine  institution  of  sacrifices ;   one  of  the  precepts  delivered 
to  Noah  was  abstinence  from  the  eating  of  blood  ;    therefore 
one  of  the  precepts  delivered  to  Noah  contained  the  divine 
institution  of  sacrifices  '  (Whately). 

Although  prolix  in  the  wording,  there  is  little  distortion  in 
this  example.  The  minor  term  is  obviously  *  one  of  the 
precepts  delivered  to  Noah,'  the  major,  *  contained  or  had 
reference  to  the  divine  institution  of  sacrifices.'  The  middle 
term  is  *  abstinence  from  the  eating  of  blood  ;'  and  the  arrange- 
ment is  exactly  as  in  the  standard  syllogism. 

*  Few  treatises  of  science  convey  important  truths,  without 
any  mtermixture  of  error,  in  a  perspicuous  and  interesting 
form ;  and  therefore,  though  a  treatise  would  deserve  much 
attention  which  should  possess  such  excellence,  it  is  plain  that 
few  treatises  of  science  deserve  much  attention.'     (Whately). 

The  conclusion  gives  as  minor  term  *  few  treatises  of 
science,'  as  major  *  deserve  much  attention.*  The  middle  term 
is  'convey  important  truths,  &c.'  The  major  premise,  there- 
fore,  is— 


X 


ill 


170 


EXAMPLES  OF  THE  SYLLOGISM. 


EXAMPLES   OF  THE  SYLLOGISM. 


171 


f 


All  treatises  of  science  that  convey  &c.,  deserve  attention: 
The  minor  premise — 

Few  treatises  of  science  are  works  conveying  important,  &o. 
The  conclusion — 

Few  treatises  of  science  deserve  attention  (Darii). 

It  was  formerly  remarked  (p.  82)  that  for  Some,  in  the  minor 
term,  we  may  have — Few,  most,  many,  one,  two, — provided 
that  the  same  quantity  is  used  in  the  premises  and  in  the 
conclusion.       rh^  *  f^-^r^  -^^iffr-j 

*  Enoch  (according  to  the  testimony  of  Scripture)  pleased 
God  ;  but  without  faith  it  is  impossible  to  please  Him  ;  there- 
fore Enoch  had  faith  '  (Whately). 

The  minor  and  major  terms  are  obvious.  The  middle  is 
•pleasing  God/  The  major  premise  is — *  pleasing  God  is  im- 
possible without  faith,'  which  is  a  circumlocution  by  way  of 
expressing  emphatically  the  proposition  *  pleasing  God  is 
having  faith  ' — '  all  persons  that  please  God  have  faith.'  The 
minor  premise  being  *  Enoch  pleased  God/  the  conclusion  fol- 
lows from  the  regular  type  of  deduction; 

It  was  said  by  some  one  during  the  Reform  discussions  of 
2867  : — *  Every  reasonable  man  wishes  the  Reform  Bill  to 
pass.  I  don't.*  There  was  but  one  inference.  The  speaker 
was  not  a  reasonable  man  (Camestres),  This  is  a  good  example 
to  show  that  an  effective  argument  may  be  given  out  of  the 
First  Figure. 

If  we  follow  the  ordinary  method  of  reduction  in  this  case, 
we  find  ourselves  in  a  difiBculty.  Camestres  is  usually  reduced 
to  the  First  Figure  by  transposing  the  premises  and  simply 
converting  the  original  minor ;  if  we  do  so  in  this  case,  we 
find  a  singular  proposition  in  the  major  premise,  which  cannot 
be  converted  without  doing  great  violence  to  the  ordinary 
forms  of  language,  and  cannot  stand  as  the  grounding  pro- 
position conceived  as  a  general  rule.  The  general  rule  in  this 
case  is  obviously  the  existing  major — *  Every  reasonable  man 
wishes  the  Reform  Bill  to  pass.'  But  if  we  view  this  as  the 
general  rule,  then  we  appear  to  have  a  negative  applying  pro- 
position— *  I  don't.'  Looking  more  closely  at  the  premises,  we 
see  that  the  true  nature  of  the  predication  is  disguised.  The 
major  proposition  is  really  negative,  and  the  minor  really  affir- 
mative. The  remedy  for  the  distortion  is  to  obvert  the  major 
into — ^  No  reasonable  man  wishes  the  Reform  Bill  to  fail ;'  or 
*  No  man  that  wishes  the  Reform  Bill  to  fail  is  reasonable.* 


The  minor  when  altered  to  correspond  becomes — *  I  do  ;'  and 
we  have  a  syllogism  m  Celarent, 

Another  example  of  this  same  mood,  Camestres,  illustrates 
the  occurrence  in  ordinary  reasoning  of  other  syllogistic  forms 
than  the  moods  of  the  standard  figure.  We  are  presented  with 
-  the  assertion  that  *  No  despotism  is  a  good  form  of  govern- 
ment,' and  on  asking  the  ground  of  such  an  assertion,  are 
told — *  Every  good  form  of  government  promotes  the  intelli- 
gence of  its  subjects,  and  no  despotism  does  that.'  This  is  an 
argument  in  Camestres, 

Everygoodformof  government  promotes  )       . 
the  intelligence  of  its  subjects.  j         °^ 

No  despotism  promotes,  &c.  Es 

No  despotism  is  a  good  form  of  govern-  )     i  tti 
ment.  /    *^^^ 

The  above  statement  of  the  Major  is  the  natural  statement  of 
the  proposition  ;  the  order  of  subject  and  predicate  is  such  as 
a  reasoner  would  naturally  observe.  That  it  promotes  the  in- 
telligence of  its  subject!  is  affirmed  of  every  good  form  of 
government ;  the  order  of  the  terms  conforms  to  the  usual 
arrangement  of  having  the  largest  term  in  the  predicate ; 
other  agencies  than  good  government  promote  the  intelligence 
of  the  people. 

As  in  the  former  Camestres,  this  syllogism  cannot  be  reduced 
to  the  First  Figure  by  the  process  indicated  in  the  Mnemonic 
letters  without  putting  the  real  Major,  or  grounding  proposi- 
tion, in  the  Minor  place.  We  may  retain  the  present  order 
without  violating  the  rule  that  the  applying  proposition  must 
be  affirmative.  For  the  present  major,  affirmative  in  form,  is 
obviously  negative  in  its  bearing  ;  while  the  minor,  negative 
in  form,  is  really  of  an  affirmative  nature,  asserting  that  a 
despotic  form  of  government  possesses  the  character  contem- 
plated in  the  ground  proposition  as  precluding  the  title  of 
good.  By  ob verting  the  predicate  of  the  major,  the  middle 
term,  we  manifest  the  real  character  of  the  premises  : — 

No  form  of  government  that  fails  to  promote  the  intelli- 
gence of  its  subjects  is  a  good  from  of  government. 

A  despotism  fails  to  promote  the  intelligence  of  its  subjects. 

No  despotism  is  a  good  form  of  government. 

In  speaking  of  the  general  uses  of  the  Figures,  we  remarked 
that  the  Third  Figure  is  sometimes  useful  in  making  good  an 
unobtrusive  and  timid  contradictory.     The  three  first  moods 


172 


EXAMPLES   OF  THE  SYLLOGISM. 


i 


supply  mild  contraries  to  a  nniversal  nej^ative ;  the  two  last 
mild  contraries  to  a  universal  affirmative.  We  give  an  ex- 
ample of  each. 

Suppose  a  speaker  to  maintain  absolutely  and  without 
reservation  that  speculation  is  of  no  value.  His  position  in 
logical  form  is—*  No  speculation  is  valuable.'  We  subvert  this 
and  extort  from  the  speaker  a  concession  that  his  position  is 
too  extreme,  when  we  obtain  his  assent  to  the  two  proposi- 
tions— *  Some  truths  affecting  human  conduct  are  speculations', 
and  *  All  truths  affecting  human  conduct  are  valuable.'  These 
two  propositions  involve  the  sub-contrary  of  the  extreme 
negative  ; — namely,  Some  speculations  are  valuable.  They  are 
given  in  the  order  of  subject  and  predicate  natural  to  the 
occasion,  and  they  fall  into  the  Third  Figure.  They  serve  as 
premises  either  for  Disamis^  or  Datisi,  according  to  the  order 
we  observe  in  enouncing  them.     Thus : — 

Some  truths  affecting  human  conduct")  ^j 
are  speculations  > 

All  truths  affecting  human  conduct  11  ^m 
are  valuable  j 

Some  speculations  are  valuable  Is 

This  is  a  syllogism  in  Disamis.  But  it  is  to  be  observed  that 
we  invert  the  normal  order  of  the  major  and  minor  terms  in 
the  conclusion.     The  most  natural  form  is  Datisi — thus  :— 

All  truths  affecting  human  conduct  )  i  * . 

are  valuable  ) 

Some  truths  affecting  human  conduct )  j 

are  speculations  j 

Some  speculations  are  valuable  I 

If  our  opponent  should  concede  that  all  truths  affecting 
human  conduct  are  speculations,  we  should  have  a  syllogism 
in  Darwpti,  In  that  case,  our  partial  contradiction  would 
seem  peculiarly  bland,  because  our  premises  would  then  be 
superfluously  strong,  and  we  should  have  the  appearance  of 
remitting  something  in  the  conclusion. 


of  a 


Our  next  example  illustrates  the  partial  subversion 
universal  affirmative  by  making  good  its  sub-contrary,  a 
particular  negative.  It  is  maintained  that  no  attention  should 
be  given  to  what  is  not  practical.  This  may  assume  the  logical 
form  of  a  universal  affirmation, — *  Everything  that  is  unprac- 
tical should  be  neglected.'  Desiring  to  Contradict  this  iu  a 
mild  form,  we  may  use  the  following  argument : — 


i 


ARNAULD'S  UNIVERSAL  TEST.  173 

Xo  truth  applicable  to  practice  should  be  )   ^p, 
neglecteu.  j   *-*^* 

Every  truth  applicable  to  practice  may"! 
seem  unpractical.  j    "^P 

Some  seemingly  unpractical  truths  should  }     ^ 
not  be  neglected.  j-  tUa 

This  is  a  syllogism  in  Felapion.  The  major—*  Some  truths 
applicable  to  practice  should  not  be  neglected,'  would  equally 
suit  our  purpose,  and  with  the  above  minor  would  give  a 
BoTcardo.  In  such  cases  as  the  above,  it  is  difficult  to  say 
which  is  the  grounding  proposition.  There  is  no  violation  of 
the  essential  nature  of  Deduction  in  regarding  a  particular 
proposition,  or  approximate  generalization,  as  the  ground  of 
the  argument.  To  make  the  reasoning  a  genuine  deduction,  it 
is  required  only  that  the  grounding  proposition  be  more 
general  than  the  conclusion. 

Arnaulcfs  Universal  Test, 

It  may  be  worth  while  to  give  an  example  of  Amauld's 
mode  of  testing  a  deductive  argument  without  reference  to  its 
logical  form. 

He  directs  the  pupil  simply  to  observe  whether  the  conclusion 
is  contained  in  the  premises.  He  gives  the  following  example 
of  his  method  :  — 

*  I  am  in  doubt  whether  this  reasoning  be  good  : 

The  duty  nfa  Christian  is  not  to  praise  those  that  commit  criminal 
actions, 

Noiv  those  that  engage  in  a  duel  commit  a  criminal  action. 
Therefore  it  is  the  duty  of  a  Christian  not  to  praise  tlwse  thai 
engage  in  duels. 

*  Now  I  need  not  trouble  myself  as  to  the  figure  or  mood  to 
which  this  may  be  reduced.  It  is  sufficient  for  me  to 
consider  whether  the  conclusion  be  contained  in  one  of  the  two 
first  propositions,  and  if  the  other  show  this.  And  I  find  at 
once  that  the  first  proposition,  since  it  differs  in  nothing  from 
the  conclusion,  except  that  there  is  in  the  one,  those  thai  com- 
mit criminal  actions,  and  in  the  other  those  that  engage  in  duels 
— that  in  which  there  is  commit  criminal  actions,  will  contain 
that  in  which  there  is  engage  in  duels,  provided  that  committing 
criminal  actions  contains  engaging  in  duels. 

*  Now  it  is  clear  by  the  sense  that  the  term  those  that  commit 
criminal  actions  is  taken  universally,  and  that  it  extends  to  all 
those  that  commit  any  such  actions  whatever ;  and  thus  the 


m\ 


174 


EXAMPLES   OF  THE   SYLLOGISM. 


MISCELLANEOUS  EXERCISES. 


175 


minor.  Those  that  engage  m  a  duel  commit  a  cnminal  action, 
showing  that  to  engage  in  a  duel  is  contained  under  this  term, 
commit  criminal  actions,  shows  also  that  the  first  proposition 

contains  the  conclusion.'  ^       ,.    x-      j.  •  «« 

This  test  of  Arnanld's  is  the  simplest  of  application  to  premises 
not  couched  in  syllogistic  terms.  It  is  easily  applied  in  any 
case :  the  only  change  of  form  that  could  aid  m  the  scrutiny, 
would  be  to  make  the  containing  proposition  of  the  same  form 
with  the  conclusion. 

To  the  following  arguments,  the  student  may  supply  such 
grounding  propositions  as  would  give  them  validity :-- 

A  true  philosopher  is  independent  of  the  caprices  of  fortune, 
for  he  places  his  chief  happiness  in  moral  and  mtellectual  ex- 

^^  aXvc  is  a  human  being,  therefore  he  should  not  be  held  in 

bondage.  «,    .       /.        r 

Not  being  thirsty,  he  cannot  be  suffering  from  fever. 

The  Reformation  was  accompanied  and  followed  by  many 
disturbances,  and  is  therefore  to  be  condemned. 

Solon  must  be  considered  a  wise  legislator,  seeing  that  he 
adapted  his  laws  to  the  temper  of  the  Athenians. 

He  was  too  impulsive  a  man  not  to  have  committed  many 

^"^  Educated  among  savages,  he  could  not  be  expected  to  know 
the  customs  of  polite  society. 

Not  every  advice  is  prudent,  for  many  advices  are  not  sate. 

Many  assertions  that  are  open  to  doubt  are  nevertheless 
worth/of  attention,  for  many  assertions  that  are  open  to  doubt 

may  be  true.  ii»»»     t         a* 

*  Napoleon  never  cared  for  anybody  but  himself.  An  modi- 
fied opposition  to  this,  it  may  be  urged  that,  after  all,  he 
was  human.'  Supposing  this  rejoinder  is  intended  to  establish 
that  Napoleon  had  some  disinterested  affections,  what  ground- 
ing proposition  does  it  require  ? 

In  like  manner,  subvert  the    assertion,      Napoleon  never 

knew  fear.'  j.   -u^ 

Volcanic  eruptions,   earthquakes,   and  plagues  cannot    be 

interpreted  as  a  warning  to  evil-doers,  for  they  involve  alike 

the  innocent  and  the  guilty. 

Some  dogs  are  useful  animals,  for  is  not  the  retriever  useful  f 
All  zeal  is  not  virtuous,  there  being  a  zeal  that  has  no  dis- 

*  TaUe-tuming;  (you  may  say,)  *  is  a  thiny  I  donH  under^ 


itand*     Admitting  this,  I  ask  you  to  construct  in  an  affirma- 
tive form,  an  argument  which  would  entitle  you,  logically,  yet 
not    convincingly,  to   deny   the  existence   of  table-turning. 
(Spalding). 

Miscellaneous  Syllogisms. 

*  Suppose  a  man  says,  '  I  dislike  all  foreigners ; '  find  a 
premise  which,  with  his  own  assertion,  would  entitle  him  to 
say  also,  *  No  foreigner  deserves  to  he  liked,*     (Spalding). 

All  cold  is  to  be  expelled  by  heat :  this  person's  disorder  is 
a  cold ;  and  must  therefore  be  expelled  by  heat. 

No  carnivorous  animals  have  four  stomachs :  all  ruminants 
have  four  stomachs  :  no  ruminants  are  carnivorous. 

Some  men  of  inferior  ability  are  legislators.  All  peers  are 
legislators,  and  some  peers  are  men  of  inferior  ability. 

'  No  war  is  long  popular :  for  every  war  increases  taxation  ; 
and  the  popularity  of  anything  that  touches  our  pockets  is  very 
short-lived.*  (Spalding). 

He  that  will  not  learn  cannot  become  learned.  This  being 
so,  there  are  many  clever  young  men  that  we  cannot  expect 
to  become  learned. 

There  is  some  anger  that  is  not  blameworthy.  What  pre- 
mise do  you  need  for  the  conclusion, — *  Some  passions  are  not 
blameworthy.' 

*  No  truth  is  without  result ;  yet  many  truths  are  misunder- 
stood.*    What  is  the  conclusion  ? 

Some  deserve  to  be  imitated  that  are  nevertheless  fools. 
Whoever  speaks  the  truth  deserves  to  be  imitated. 

Humanity  is  a  moral  virtue  :  the  study  of  polite  letters  is 
humanity ;  the  study  of  polite  letters  is  a  moral  virtue. 

White  is  a  good  fellow  :  if,  therefore,  linen  is  white,  it  is  a 
good  fellow. 

*  He  that  says  you  are  an  animal  speaks  truly  :  he  that  says 
you  are  a  goose,  says  you  are  an  animal ;  he  that  says  you  are 
a  goose  speaks  truly.'  (Arnauld). 

'  You  are  not  what  I  am:  I  am  a  man  :  therefore  you  are 
not  a  man.'  (Arnauld). 

One  symptom  of  the  plague  is  fever;  this  man  has  fever; 
therefore  he  has  the  plague. 

Some  objects  of  great  beauty  answer  no  other  perceptible 
purpose,  but  to  gratify  the  sight :  many  flowers  have  great 
beauty ;  and  many  of  them  accordingly  answer  no  other  pur- 
pose but  to  gratify  the  sight. 

Every  good  statesman  is  favourable  to  progress.      Some 


176 


EXAMPLES  OF  THE  SYLLOGISM. 


EXAMPLES  OF  CHAINS  OF  REASONING. 


177 


I 


members  of  Parliament,  not  being  favourable  to  progress,  are 
not  good  statesmen. 

*  Unpleasant  things  are  not  always  injurious ;  afflictions  are 
often  salutary.*     Supply  the  missing  premise. 

John  is  taller  than  William  ;  William  is  taller  than  Charles ; 
John  is  taller  than  Charles. 

*  Of  two  evils  the  less  is  to  be  preferred  ;  occasional  turbu- 
lence, therefore, being  a  less  evil  than  rigid  despotism,  is  to  be 
preferred  to  it/  (Whatleyj. 

All  fixed  stars  twinkle  j  yonder  star  twinkles  ;  therefore  it 
is  fixed. 

All  that  do  not  act  foolishly  are  respectable ;  all  fools  act 
foolishly  ;  no  fools  are  respectable. 

*  Most  men  that  make  a  parade  of  honesty  are  dishonest ; 
this  man  makes  a  parade  of  honesty.'  Can  we  conclude  that 
be  is  dishonest  ? 

Ill  doers  are  ill  dreaders.  This  man  dreads  evil,  and  is, 
therefore,  a  scoundrel. 

All  aristocracies  are  self-willed ;  some  self-willed  people  are 
not  cruel ;  some  aristocracies  are  not  cruel. 

Some  democracies  are  not  persistent  in  their  designs ;  the 
Government  of  the  United  States  is  a  democracy  ;  the  Govern- 
ment of  the  United  States  is  not  persistent  in  its  designs. 

All  plants  contain  cellular  tissue  ;  no  animals  are  plants  ;  no 
animals  contain  cellular  tissue. 

*  I  snatch  at  the  conclusion  that  every  eager  desire  is  an 
evil  thing ;  since  I  know  that  the  desire  of  evil  is  evil,  and 
that  not  a  few  eager  desires  have  evil  objects.'  (Spalding). 

A  good  marksman  must  have  a  steady  hand  ;  George  has  a 
steady  hand  ;  therefore,  George  is  a  good  marksman. 

Flotation  is  possible  only  in  liquids,  and  so  not  possible  in 
this  water,  which  is  frozen. 

Poetry  is  not  Science.  The  characteristics  of  Science  are 
truth  and  generality,  and  Poetry  possesses  neither. 

Nothing  that  is  not  possible  for  man  to  do  has  ever  been 
done  by  man.  Raising  the  dead  is  not  possible  for  man,  and, 
consequently,  has  never  been  done  by  man. 

'  If  I  know  that  Messieurs  A.  B.  and  C.  are  not  only  learned, 
men  but  also  silly  ones,  will  you  allow  me  to  draw  any  infer- 
ence?'    (Spalding). 

Irrational  prejudice  is  symptomatic  of  a  weak  mind,  and  we 
sometimes  see  it  in  very  learned  men.  State  this  in  syllogistic 
form,  and  di*aw  the  legitimate  conclusion. 

One  who  misapplies  i-iches  deserves  poverty ;  which  one  who 


is  benevolent  does  not  deserve.     Is  the  legitimate  conclusion 
consonant  with  fact  ? 

*  If  a  rule  never  is,  and  a  principle  always  is,  a  law  admitting 
no  exception,  judge  that  a  rule  must  be  something  different 
from  a  principle.'     (Spalding). 

No  branch  of  science  can  be  made  absolutely  perfect,  yet 
all  branches  of  science  are  worthy  of  diligent  culture.  What 
inference  do  you  draw  from  this  ? 

*  What  was  it  that  first  gained  him  the  public  ear  ?     It  cer 
tainly  was  not  the  pure  Saxon-English  in  which  his  sentences 
are  clothed,  for,  alas  !  we  find  that  many  writers  who  neglect 
their  grammar  even,  secure  an  immence  audience,  to  the  de- 
light of  their  publishers,  and  their  own  gratification.' 

*  It  has  been  supposed  by  some  philosophers,  that  electricity  is 
the  real  agent  by  which  the  nerves  act  upon  the  muscles.  But 
there  are  many  objections  to  such  a  view  ;  and  this  very  im- 
portant one  among  the  rest, — that  electricity  may  be  trans- 
mitted along  a  nervous  trunk  which  has  been  compressed  by 
a  string  tied  tightly  round  it,  whilst  the  passage  of  ordinary 
nervous  power  is  as  completely  checked  by  this  process  as  if 
the  nerve  had  been  divided.' 

The  following  are  examples  of  chains  of  reasonmg,  resolvable 
into  consecutive  syllogisms. 

*  The  concept  *  horse  *  cannot,  if  it  remain  a  concept,  that  is, 
a  universal  attribution,  be  represented  in  imagination  ;  but  ex- 
cept it  be  represented  in  imagination,  it  cannot  be  applied  to 
any  object ;  and  except  it  be  so  applied,  it  cannot  be  realized 
in  thought.'     (Hamilton). 

*  But,  to  prove  that  moral  sentiments  are  instinctive  or 
inscrutable,  it  is  boldly  asserted,  by  the  advocates  of  the 
hypothesis  in  question,  that  the  moral  sentiments  of  all  men 
are  precisely  alike. 

*  The  argument,  in  favour  of  the  hypothesis,  which  is  raised 
on  this  hardy  assertion,  may  be  stated  briefly  in  the  following 
manner ; — No  opinion  or  sentiment  which  is  a  result  of  observa- 
tion and  induction  is  held  or  felt  by  all  mankind.  Observation 
and  induction,  as  applied  to  the  same  subject,  lead  different 
men  to  different  conclusions.  But  the  judgments  which  are 
passed  internally  upon  the  rectitude  or  pravity  of  actions,  or 
the  moral  sentiments  or  feelirjgs  which  actions  excite,  are 
precisely  alike  with  all  men.  Consequently,  our  moral 
sentiments  or  feelings  were  not  gotten  by  our  inductions  from 


t! 


178 


RECENT  ADDITIONS  TO  THE   SYLLOGISM. 


QUANTIFICATION  OF  THE  PREDICATE. 


179 


the  tendencies  of  the  actions  which  excite  them:  ^or  were 
these  sentiments  or  feelings  gotten  by  md notions  of  others  and 
then  impressed  npon  onr  minds  by  hnman  anthority  and  ex- 
ample.  Consequently,  onr  moral  sentiments  are  instinctive,  or 
are  ultimate  or  inscrutable  facts.*     (Austin.) 

« The  creneral  object  which  all  laws  have,  or  ought  to  have, 
in  comn^on,  is  to  augment  the  total  happiness  of  the  commun- 
ity  •  and  therefore,  in  the  first  place,  to  exclude,  as  far  as  may 
be  everything  that  tends  to  subtract  from  that  happmess: 
in 'other  words,  to  exclude  mischief.  But  all  punishment  is 
mischief:  all  punishment  in  itself  is  evil.  Upon  the  Principle 
of  utility,  if  it  ought  at  all  to  be  admitted,  it  ought  only  to  be 
admitted  in  as  far  as  it  promises  to  exclude  some  greater  evil. 
(Bentham). 

*  If  our  intellectual  part  is  common,  the  reason  also,  in  respect 
of  which  we  are  rational  beings,  is  common:  if  this  is  so,  com- 
mon also  is  the  reason  which  commands  us  what  to  do,  and 
what  not  to  do  ;  if  this  is  so,  there  is  a  common  law  also ;  it 
this  is  so,  we  are  fellow-citizens  ;  if  this  is  so,  we  are  members 
of  some  political  community ;  if  this  is  so,  the  world  is  m  a 
manner  a  state.'  (Marcus  Antoninns).  It  is  not  to  be  sup- 
posed that  all  these  transitions  make  distinct  syllogisms  ;  some 
are  at  best  but  immediate  or  equivalent  transitions. 


CHAPTER   n. 
BECENT  ADDITIONS  TO  THE  SYLLOGISM. 

HAMILTON'S  ADDITIONS. 

Sir  William  Hamilton's  extensions  of  the  theory  and  the 
forms  of  the  syllogism  are  chiefly  based  on  the  Quantification 
of  the  Predicate,  and  on  the  fuU  development  of  the  two 
modes  of  Quantity— Extension  and  Comprehension.  He. hag 
also  much  criticism  in  detail  on  many  parts  of  the  syllogistic 

^'^  It^has  been  seen  (p.  86)  that  the  thorough  quantification  of  the 
predicate  yields  four  new  prepositional  forms,  making  eight 
in  all.     Two  of  these,  the  affirmative  forms,     All  X  is  all  Y, 
*  Some  X  is  all  Y,'  which  are  held  by  De  Morgan  and  by  Mill, 


to  be  compound  propositions,  have  been  adopted  by  some  other 
logicians,  as  Thomson  ('Laws  of  Thought')  and  Spalding. 
The  remaining  two  forms — the  negative  '  All  X  is  not  some  Y,' 
'  Some  X  is  not  all  Y  '  have  been  set  aside  as  not  occurring  in 
actual  instances. 

The  addition  of  two  new  forms  greatly  increases  the  number 
of  possible  syllogistic  moods.  By  trying  all  the  combinations 
of  three  propositions  out  of  six,  and  by  rejecting  all  that  violate 
laws  of  the  syllogism,  and  all  that  repeat  others,  Dr.  Thomson 
makes  out  22  moods  in  the  First  Figure,  20  moods  in  the 
Second  Fi<Tnre,  20  moods  in  the  Third  Figure ;  so  that  apart 
from  the  Fourth  Figure,  of  which  no  account  is  taken,  there 
are  62  moods.     We  give,  as  examples,  some  of  the  new  moods. 

U  U  U  contains  three  universal  affi.rmatives  with  universal 
predicates. 

All  Y  is  all  Z 
All  X  is  all  Y 
AH  X  is  all  Z 
a  syllogism,  to  which  there  is  no  counterpart  in  nature,  unless 
the  terms  are  merely  different  names  for  the  same  thing ;  as 
*all  water  is  all  oxide  of  hydrogen.'     We  .may  find  a  proposi- 
tion whose  terms  are  of  co-equal  extent  to*  constitute  a  mejor, 
(all  matter  are  all  gravitating  things) ;  but  we  shall  probably 
never  be  able  to  couple  with  this  a  minor  also  co-extensive  in 
its  terms,  if  these  terms  really  mean  different  things. 

U  E  E  is  an  example,  constituting  an  exception  to  the  canon 
requiring  the  minor  in  the  First  Figure,  or  normal  deductive 
syllogism,  to  be  affirmative. 

All  Y  is  all  Z  All  matter  is  all  gravitating  things 

No  X  is       Y  No  mind  is  matter 

No  X  is       Z  No  mind  gravitates 

Here  the  quantification  of  Z  (universal)  avoids  illicit  process 
of  the  major. 

It  is  not  pretended  that  any  useful  form  grows  out  of  these 
additions  to  the  syllogistic  moods;  and  even  as  a  formal 
exercise,  no  one  has  thought  it  worth  while  to  state  them  in 
full ;  far  less  to  provide  examples  of  them  in  the  concrete. 

Only  Hamilton  himself  (followed  by  Professor  Spencer 
Baynes)  has  endeavoured  to  enumerate  the  syllogistic  moods 
growing  out  of  the  eight  quantified  prepositional  forms.  He 
even  gives  the  number  variously.  The  earliest  statement  is 
thirty-six  valid  moods,  for  each  figure  (excluding  the  Fourth), 
that  is,  twelve  affirmative,  and  twenty-four  negative.  Dr. 
Thomson  has  tabulated  the  foi-ms.  agreeing  with  Hamilton  so 


m 


180  HAMILTON'S   ADDITIONS   OF  THE   SYLLOGISM. 


i 


far,  but  deducting  from  Hamilton's  complete  list  as  useless 
though  possible  varieties,  14  moods  in  the  first  figure,  16  in 
the  second,  and  16  in  the  third.  He  thus  reduces  Hamilton's 
]  08  moods  to  62.  In  a  later  statement  Hamilton  gives  42 
syllogisms,  reducible  to  21. 

Syllogisms  viewed  either  in  Extension  or  in  Comprehension,  It 
is  a  great  point  with  Hamilton  to  show  that  the  common  syl- 
Joo-ism  is  defective,  from  not  being  expressed  both  in  Extension 
and  in  Comprehension.  He  complains  that  all  logicians,  with 
the  doubtful  exception  of  Aristotle,  have  limited  their  con- 
sideration to  reasoning  as  given  in  the  quantity  of  Extension. 
He  exemplifies  the  difference  of  the  two  syllogisms  thus  . — 
Extension,  Comprehension, 

B  is  A  C  is  B 

C  is  B  B  is  A 

C  is  A  C  is  A 

All  men  are  mortal  Caius  is  a  man 

Caius  is  a  man  All  men  are  mortal 

Caius  is  mortal  Caius  is  mortal 

In  the  first  example  the  class  *  mortal  *  contains  under  it 
the  class  man  ;  in  the  second  example,  the  atti-ibutes  of  *  man  ' 
contain  in  them  the  attribute  *  mortal.' 
The  following  is  an  example  in  Celarent, 

Extension.  Comprehension, 

No  men  are  gods  Kings  are  men 

All  kings  are  men  Men  are  not  gods 

No  kings  are  gods  Kings  are  not  gods 

The  second  form  (Comprehension)  may  be  read  thus  : — 
The  attributes  of  a  king  contain  the  attributes  of  a  man. 
The  attributes  of  a  man  do  not  contain  the  attributes  of  a  god. 
The  attributes  of  a  king  do  not  contain  the  attributes  charac- 
teristic of  a  god. 

It  is  to  be  remarked,  with  reference  to  this  scheme  of  double 
syllogisms,  according  as  the  terms  are  taken  in  extent,  or  in 
intent — breadth  or  depth — that  the  two  modes  express  one 
and  the  same  meaning;  and  that  the  really  fundamental 
meaning  is  Intent,  or  the  Connotation  of  the  Terms  employed. 
The  real  meaning  of  the  last  example  is,  first,  that  the 
attributes  coimoted  by  the  term,  man,  fail  to  accompany,  or 
are  incompatible  with,  the  attributes  connoted  by  the  term, 
'god'  (major);  that  the  attributes  connoted  by  'king'  are 
accompanied  with  the  attributes  connoted  by  '  man.'  The 
other  form,  however,  falls  readiest  into  common  language, 
the  form   of  Extension,  that  is,  of  inclusion  or  exclusion  of 


SYLLOGISMS  IN  COMPHEHENSION. 


181 


classes;  men  are  out  of  the  class  of  gods;  kings  are 
in  the  class  men;  therefore,  kings  are  our.  of  the  class 
gods.  This  is  a  more  concrete  and  intelligible  form ;  still,  it 
IS  not  the  contrast  or  the  opposite  of  the  other.  We  do  not 
think  of  this  form  justly,  correctly,  unless  we  conceive  the 
terms  as  determined  by  their  connotation.  The  extent  is 
bounded  solely  by  the  intent.  It  is  not  as  if  we  had  a  com- 
plete list  of  men,  and  a  complete  list  of  kings,  and  saw  the 
kmgs  inserted  among  the  men,  while  the  list  of  men  had 
nothing  in  common  with  the  list  of  gods.  This  is  the  full  and 
literal  rendering  of  the  reasoning  in  extension  ;  and  the  very 
statement  of  it  is  enough  to  show  that  we  do  not  reason  so. 
When  we  speak  of  a  class,  we  do  so  in  a  figurative  manner ; 
we  suppose  an  actual  array  of  individuals  when  there  is  no 
such  array ;  there  being  only  the  defining  mark,  the  connota- 
tion of  them,  to  define  them  whenever  they  appear.  The 
extent  of  '  man  '  is  the  imaginary  aggregate  of  all  objects 
agreeing  in  the  marks  connoted  by  the  term,  the  defining 
characteristics  of  man  ;  if  we  lose  sight  of  this  condition  for  a 
moment,  we  have  nothing  fixed  in  our  grasp.  Accordingly, 
comprehension  is  inseparable  from  extension  in  every  case ;  it 
IS  an  ever  present  fact,  without  our  topsy-tur vying  the 
syllogism,  or  constituting  a  parallel  array  of  moods  to  match 
the  moods  in  extension. 

Hanailton's  forms  in  comprehension  depend  solely  on  his  in- 
troducing the  idea  of  '  containing  and  contained  *  into  the 
groups  of  attributes  signified  by  the  terms  of  the  proposition. 
A  king  has  more  attributes  than  a  man  ;  the  individual  person 
'Frederick  the  Second'  has  more  attributes  than  a  king.  Thus, 
Frederick  is  the  largest  term,  in  point  of  number  of  attributes,* 
man  is  the  smallest.  Hence  we  may,  by  straining  a  metaphor, 
apply  the  relation  of  whole  and  part,  containing  and  contained, 
to  this  circumstance,  as  well  as  to  the  groups  (in  extension) 
men,  kings,  Frederick  ;  and  may  carry  the  analogy  so  far  as 
to  construct  syllogisms  to  match.  But  no  new  or  distinct 
meaning  is  conveyed  ;  and  there  is  not  even  a  more  int€liigible 
rendering  of  an  old  meaning. 

Hamilton,  in  discussing  the  conditions  of  the  Distinctness  of 
Notions,  remarks  justly  that  the  highest  degree  of  distinctness 
cannot  be  attained  without  fixing  the  Comprehension,  in  other 
words,  the  meaning,  definition,  or  connotation  of  the  term. 
(Lectures  on  Logic  1, 108).  He  remarks  also  that  the  quantity 
of  Extension  js  a  creation  of  the  mind  itself,  and  only  created 
througli,  as  abstracted  from,  the  quantity  of  comprehension ; 


'I 


182      DE  morgan's  additions  to  the  syllogism. 


whereas  the  quantity  of  comprehension  is  at  once  given  in  the 
nature  of  things  (p.  218).  All  which  tends  to  the  conclusion 
that  the  comprehension  is  what  we  think  of  in  a  notion ;  and 
consequently  the  comprehension  cannot  be  left  out  of  the  ac- 
count in  any  syllogistic  form.  It  is  the  power  behind  the 
throne,  even  when  extension  is  the  ostensible  reigning  circum- 
stance. 

In  objecting  to  the  Fourth  Figure,  Hamilton  grounds  his 
dislike  on  the  circumstance,  that  the  premises  proceed  in  the 
whole  of  comprehension,  while  the  conclusion  is  drawn  in  the 
counter  whole  of  extension.  He  explains  the  matter  thus. 
The  scheme  of  the  Figure  is — 

PisM 
Mis  S 
SisP 

Now  in  the  premises  P  is  contained  under  M  ;  and  M  con- 
tained under  S ;  whence  in  the  conclusion  we  should  expect  P 
to  be  contained  under  S.  In  this,  however,  we  are  disappointed  ; 
for  the  reasoning  suddenly  turns  round  in  the  conclusion,  and 
affirms  S  as  a  part  of  P.  [Not  strictly  correct ;  for  S  is  qualified 
by  *some,*  which  may  still  leave  it  the  larger  term ;  *  Some  S 
is  P.']  If  we  had  an  affirmative  syllogism  in  the  form 
All  P  is  M  All  kings  are  men 

All  M  is  S  All  men  are  fallible 

All  S  is  P  All  fallible  beings  are  kings 

we  should  have  an  illegitimate  inference ;  which  might  no 
doubt  be  evaded  if  the  conclusion  could  be  read  thus — 

All  the  attributes  of  fallible  beings  are  coyitained  in  the  at- 
tributes of  Kings. 

But  no  one  ever  reads  the  figure  in  this  way. 


i 


DE   MORGAN  S   ADDITIONS. 

We  have  seen  Mr.  De  Morgan's  views  as  to  Terms,  and  his 
enumeration  of  Fundamental  Propositions.  Before  proceeding 
to  view  his  enlargements  of  the  Syllogism,  we  shall  advert  to 
his  remarks  on  the  Copula. 

He  complains  that  the  *  is '  of  logicians  is  not  confined  to 
one  strict  meaning.  It  professes  to  be  a  word  of  the  highest 
abstraction,  a  formal  mode  of  joining  two  terms,  caiTying  no 
meaning,  and  obeying  no  law,  except  such  as  is  barely  neces- 
sary to  make  the  forms  of  inference  hold  good.  *  X  is  Y  *  com- 
mits us  to  nothing  specific.  Yet,  at  times,  logicians  employ  it 
in  the  sense  of  identity.     The  best  description  of  its  employ- 


COPULAR  RELATIONS. 


183 


ment,  he  considers  to  be — *  agreement  in  some  understood,  and, 
for  the  occasion,  unvarying  particular.' 

He  supposes  that  a  copular  symbol  had  been  used,  instead 
of  *is;*  the  effect  of  which  would  have  been  to  stamp  upon 
the  copula  the  character  of  an  abstraction,  as  is  done  by  the 
use  of  symbols,  X,  Y,  Z,  for  terms.  Had  such  a  symbol  been 
used,  the  copular  conditions  would  have  been  stated.  These 
are  two  in  number.  The  first  is  trarisitiveness  ;  meaning  that 
if  X  stands  in  a  certain  relation  to  Y,  and  Y  in  the  same  re- 
lation to  Z,  X  stands  in  the  given  relation  to  Z.  Very  many 
copulas  show  this  transitive  relation  ; — is, — rules, — lifts, — 
draws, — leads  to, — is  superior  to,  — is  ancestor  to, — is  brother 
of, — .joins, — depends  on, — is  greater  than, — is  equal  to, — is 
less  than, — agrees  with  (in  a  given  particular),  &c.      •* 

The  second  condition  is  convertibility,  in  which  the  relation 
is  its  own  correlation  ;  whatever  X  is  to  Y,  Y  is  to  X.  In  a 
certain  number  of  the  foregoing  examples,  there  occur  con- 
vertible relations;  is, — is  brother  of, — joins  (if  a  middle 
verb), — is  equal  to, — agrees  with.  There  are  cases  of  con- 
vertibility without  the  transitive  character  ;  converses  with, — 
is  in  the  habit  of  meeting, — is  cousin  of, — is  in  controversy 
with,  &c. 

Again,  there  are  copula  not  convertible,  bat  correlative;  A 
gives  to  B  ;  B  receives  from  A.  These  forms  also  are  duly 
reasoned  upon ;  and  syllogisms  might  be  constructed  accord- 
ingly. Every  X  gives  to  a  Y ;  Some  Xs  srive  to  no  Ys  ;  No 
X  gives  to  a  Y ;  Every  X  receives  from  a  Y  ;  Some  Xs  receive 
from  no  Ys, — are  examples  of  the  prepositional  forms.  They 
are  all  capable  of  conversion,  by  substituting  the  correlative 
copula. 

The  admission  of  Relation  in  general,  Mr.  De  Morgan  con- 
tends, and  of  the  composition  of  relation,  makes  logic  more 
in  alliance  with  ordinary  thinking.  The  reduction  of  all 
relations  by  *  is ' — *  mind  acts  on  matter,  mind  is  a  thing 
acting  on  matter,' — is  a  systematic  evasion,  hostile  to  the  pro- 
gress of  the  science. 

Logicians  are  aware  that  the  form  *  A  equals  B,  B  equals  C, 
therefore  A  equals  C '  is  not  reducible  to  the  syllogism.  So 
with  the  relation  of  *  greater  than,'  in  the  argument  a  fortiori 
Yet,  to  the  ordinary  mind,  these  inferences  are  as  natural,  as 
forcible,  and  as  prompt,  as  the  syllogistic  inference.  Mr.  De 
Morgan,  therefore,  would  propose  to  include  all  such  forms  in 
one  sweep  by  a  generalized  copula  of  relation,  which  would  be 
formally  embodied  and  symbolized  in  propositions.     Thus — 


184      DE  mokgan's  additions  to  the  syllogism. 


i|. 


Every  X  Las  a  relation  to  some  Y 
Every  Y  has  a  relation  to  some  Z 
from  which  the  interence  would  be  that  *  Every  X  has  a  com- 
pound relation  to  some  Z  ;'  the  compound  of  the  relations  X 
to  y,  and  Y  to  Z.  Under  this  form,  we  reason,  John  can 
control  Thomas ;  Thomas  can  control  William ;  John  can 
control  William.  Under  the  general  and  comprehensive 
copular  relation,  specific  modes  might  be  developed  for  specific 
purposes.  The  Logical  copula  in  common  use  is  the  equival- 
ent of  *  fastened  to,'  *  connected  with,'  *  co-exists  with,'  and 
may  be  considered  for  logical  purposes  the  most  important. 
The  copula  of  equality  and  inequality  is  developed  in  Mathe- 
matics, and  an  inference  according  to  it  would  probably  be 
called  a%iathematical  inference. 

The  converse  copular  relation,  *  causes,*  would  be  singled 
out  on  account  of  its  great  importance  : — A  causes  B,  B  is 
caused  by  A.  We  practically  construct  syllogisms  from  these 
propositions,  without  passing  through  our  minds  the  formal 
transformation  to — A  is  the  cause  of  C. 

These  remarks  of  Mr.  De  Morgan's  are  undoubtedly  just 
and  cogent ;  and  they  are  highly  valuable  in  the  way  of  eman- 
cipating the  student  from  the  Aristotelian  limits,  as  well  as 
for  pointing  out  the  vagueness  and  vacillation  of  the  ordinary 
copula.  Siill,  we  could  hardly  afford  the  labour  of  following 
out  the  technical  developments  of  half-a-dozen  distinct  forms 
of  copula.  It  is  well  to  see  that  such  developments  are  not 
merely  competent  in  themselves,  but  needed  to  formulate  the 
whole  compass  of  our  habitual  thinking  and  reasoning.  Being, 
however,  aware  of  this  fact,  we  must  be  content  with  con- 
structing one  scheme  adapted  to  the  most  useful  and  most 
frequently  recurring  relationship ;  which  scheme  we  should 
then  regard  as  an  example  of  the  rest,  one  out  of  many.  Any 
one  having  Mr.  De  Morgan's  genius  for  the  construction  of 
forms  might  do  well  to  develop  a  variety  of  copular  relations ; 
from  these  such  selections  might  be  made  as  would  extend 
the  inferential  grasp  of  the  ordinary  student. 

Mr.  De  Morgan's  Extensions  of  the  Syllogistic  foi'ms  are 
avowedly  based  upon  the  full  recognition  of  contraries,  as  laid 
out  in  his  scheme  of  eight  fundamental  propositions.  Also, 
by  providing  symbols  for  contraries  he  can  exhibit  all  denials 
as  assertions  ;  No  X  is  Y,  is  All  X  is  r  (U— Y).  Hence,  th© 
unit  syllogism  may  be  represented  in  an  affirmative  form^-*  If 
Bn  X  be  a  Y,  if  that  same  Y  be  a  2J,  then  the  X  is  a  Z.* 


SYLLOGISTIC   FORMS. 


185 


All  syllogisms  are  derivable  from  the  following  combinations 
of  Premises  : — 

(1)  All  Xs  are  Ys,  and  all  Ys  are  Zs.  Tho  conclusion  is 
All  Xs  are  Zs ;  the  unit  syllogism.  This  is  the  inversion  of 
the  Aristotelian  order  of  premises,  but  it  is  in  the  author's 
view  the  proper  and  the  natural  order. 

(2)  Some  Xs  are  Ys,  all  Ys  are  Zs  ;  some  Xs  are  Zs.  The 
unit  syllogism  is  here,  as  it  were,  cut  down  to  the  form, — *  as 
often  as  there  are  Xs  in  the  first  premise,  there  are  in  the  con- 
clusion.' 

(3)  Some  Xsare  all  Ys,  some  Ys  are  Zs  ;  conclusion — some 
Xs  are  Zs.  In  point  of  form,  this  is  the  previous  case  inverted. 
The  universal  middle  term  (all  Ys)  is  transferred  from  the 
second  premise  to  the  first. 

(4.)  Some  Xs  are  all  Ys,  All  Ys  are  Zs ;  Some  Xs  are  Zs, 
Here,  although  there  is  an  additional  universal  middle,  all 
Ys,  occurring  in  both  premises,  there  is  no  stronger  conclusion 
than  in  the  two  preceding  cases,  where  the  middle  term  is 
universal  (or  distributed)  only  once. 

These  are  all  the  possible  couples  of  affirmative  premises 
apart  from  any  cognisance  of  contrary  terms.  Now,  all 
negations  may  be  rendered  as  affirmations  about  contraries  ; 
and  therefore  the  application  of  these  cases  to  all  combinations 
of  propositions,  direct  or  contrary,  will  give  all  possible  valid 
sj'llogisms. 

Taking  X,  Y,  Z,  and  their  contraries  x,  y,  z,  there  are  eight 
combinations  of  threes  :— X  Y  Z,  x  Y  Z,  x  y  Z,  x  y  z,  X  Y  z, 
X  y  Z,  X  y  z,  X  Y  z.  To  each  of  these  the  four  modes  of  inference 
can  be  applied  ;  and  when  x,  y,  z,  are  read  as  the  contraries  of 
X,  Y,  Z,  we  obtain  the  proper  expression  of  the  syllogism. 
Thus,  the  first  or  unit  syllogism,  applied  to  x  y  Z,  gives  Every 
X  is  y,  Every  y  is  Z  ;  therefore.  Every  x  is  Z.  This  unfolded, 
by  giving  the  equivalents  of  the  contrary  terms  x,  y,  in  the 
forms  X,  Y,  the  whole  syllogism  may  be  read  thus : — 

Every  x  is  y  (All  not-X  is  not-Y)  is  the  same  as  No  Y  is 
not  X,  or  Every  Y  is  X,  or  Some  Xs  are  all  Ys. 

Every  y  is  Z  (Every  not-Y  is  Z)  is  the  same  as  Everything 
IS  either  Y  or  Z  (one  of  De  Morgan's  new  prepositional  forms). 

In  like  manner,  the  conclusion  Every  x  is  Z,  (Every  not-X 
is  Z)  is  Everything  is  either  X  or  Z.     The  syllogism  then  is  :— 
Some  Xs  are  all  Ys  (Every  Y  is  X). 
Everything  is  either  Y  or  Z. 
Everything  is  either  X  or  Z. 

A  syllogism  not  in  the  Aristotelian  figures.     From  the  very 


m 

m 


I 


186      BE  morgan's  additions  to  the  syllogism. 

wide  compass  of  the  form,  Everything  is  either  Y  or  Z,  there 
can  be  few  applications  of  such  a  syllogism. 

Some  extended  things  are  all  material  things. 
Everything  is  either  material  or  pertaining  to  mind. 
Everything  is  either  extended  or  pertaining  to  mind. 

The  remaining  seven  forms  being  expressed  and  nnfolded  in 
like  manner,  there  would  arise  the  eight  forms  of  universal 
svllogism,  that  is  universal  premises  vrith  universal  conclu- 
sion. 

Again,  apply  case  second  to  the  same  eight  forms — Some 
Xs  are  Ys,  all  Ys  are  Zs ;  some  Xs  are  Zs  ;  and  there  emerge 
eight  miiwr-particular  syllogisms,  particular  conclusion  with  the 
minor  (or  first)  premise  particular. 

Apply  case  third — Some  Xs  are  all  Ys,  some  Ys  are  Zs ; 
some  Xs  are  Zs — and  we  have  eight  major-particular  syllogisms, 
'particular  conclusion  with  the  major  (or  %Qcon6)  premise  par' 
ticular. 

Apply  case  fourth — Some  Xs  are  all  Ys,  All  Ys  are  Zs, 
Some  Xs  are  Zs — and  we  have  eight  strengthened  particular 
syllogisms,  universal  premises  with  particular  conclusion  By  a 
strengthened  syllogism,  the  author  means  one  whose  premises 
are  stronger  than  they  need  be  to  bear  out  the  conclusion. 

The  above  32  forms  are  those  that  give  inference,  out  of  64 
possible  combinations  of  the  premises.  The  remaining  32 
forms  could  be  drawn  out  by  representing  the  eight  proposi- 
ti onal  arrangements,  X  Y  Z,  x  Y  Z,  &c.,  in  four  varieties  of 
premises,  which  the  author  states.  Thus  :  (1)  Some  Xs  are 
some  Ys,  Some  Xs  are  all  Ys;  (2)  All  Xs  are  some  Ys,  Some 
Xs  are  some  Ys ;  (3)  Some  Xs  are  some  Ys,  Some  things  are 
neither  Xs  nor  Ys ;  (4)  Some  Xs  are  Ys ;  All  Xs  are  not  some 
Ys.  From  none  of  these  combinations  of  premises  could  any 
inference  be  drawn. 

The  test  of  validity,  and  the  rule  of  inference,  the  author 
expresses  thus : — 

There  is  inference  (1)  When  both  the  premises  are  uni- 
versnl.  (2)  When,  one  premise  only  being  particular,  the 
middle  term  has  different  quantities  in  the  two  premises. 
Either  of  these  cases  happening,  the  conclusion  is  found  by 
erasing  the  middle  term  and  its  quantities.  Premises  of  like 
quality  give  an  affirmative  conclusion ;  of  different  quality,  a 
negative.  A  universal  conclusion  follows  only  from  universals 
with  the  middle  term  differently  quantified  in  the  two.  From 
two  particular  premises  nothing  follows. 

A  particular  premise  having  the  concluding  term  strengthened 


RULES   OF  INFERENCE. 


187 


(that  is,  made  universal),  the  conclusion  is  also  strengthened, 
and  the  syllogism  becomes  universal ;  for  example,  JDariiy  by 
this  process,  would  become  Barbara,  With  the  middle  term 
strengthened,  the  conclusion  is  not  strengthened,  and  there 
being,  therefore,  a  surplus  of  affirmation  in  the  premises,  the 
syllogism  forms  what  the  author  calls  a  strengthened  particular 
sijllogisiii.     Thus,  Daraptij  in  the  third  figure — 

All  Y  is  Z 

All  Y  is  X 

Some  X  is  Z — 
has  the  middle  term  universal  in  both  premises,  when  once  is 
enough  ,  there  would  be  inference  with  *  Some  Y  is  X  *  in  the 
minor.     Felapton  and  Fesapo  are  other  examples. 

A  different  case  is  exemplified  in  Bramantip.  The  two 
universals — 'All  Z  is  Y,  All  Y  is  X,'  yield  the  universal  *all 
Z  is  X,'  which,  for  the  sake  of  a  different  order  of  the  terms 
in  the  conclusion,  is  converted  and  weakened  into  the  particular 
*  Some  X  is  Z.'  This  is  termed  by  the  author  a  weakened 
universal. 

Each  form  of  proposition  has  corresponding  to  it  certain 
opponetit  forms.  Thus,  if  the  propositions  A,  B,  gives  C,  they 
cannot  give  c  (the  contrary  of  C).  Hence  A  and  c  being  true, 
B  is  false  or  b  true  ;  that  is  A,  c,  give  B  j  that  is  to  say,  either 
premise  joined  with  the  contrary  of  the  conclusion  gives  the  con- 
trary of  the  other  premise.  Thus,  there  are  two  opponent  forms 
to  every  syllogism.  And  the  syllogisms  may  be  so  grouped  in 
threes,  that  each  one  of  any  three  may  have  the  two  others 
for  opponents.  Barbara  has,  for  opponent  forms,  Baroho  and 
Bohardo. 

Mr.  De  Morgan  considers  it  of  importance  to  remark  that 
the  adjective  for  expressing  universal  quantity— *  Air  means 
two  things,  which  should  be  kept  distinct.  It  may  be  *  All  * 
collectively,  the  entire  collection  or  aggregate  of  individuals ; 
this  he  calls  the  cumular  form  ;  and  it  may  be  *  all '  distribu- 
tively,  in  the  sense  of  'every  one,' or  *any  one,'  however 
taken,  which  he  calls  the  exemplar  mode.  He  holds  that  the 
language  of  Aristotle,  and  of  his  immediate  followers,  was 
exemplar  and  not  cumular ;  wa?  uvGpwiro^^  he  contends,  is  each 
or  every  man,  not  all  man.  *  All  man,*  as  a  comprehensive 
genus,  has  parts, — for  example,  the  several  species  or  varieties 
of  men  ;  *  every  man  '  has  no  parts,  but  makes  assertions  about 
every  individual  of  the  genus  man. 

The  exemplar  mode  is  that  used  in  geometrical  proof.     A 
proposition  in  Euclid  assumes  some  one  case,  and  the  demon- 


188     DE  morgan's  additions  to    thr  syllogism. 

Btration  is  such  that  nothing  prevents  the  one  chosen  from 
being  any  one.  It  would  be  useful  in  geometry,  to  admit  the 
form  *  any  one  X  is  any  one  Y.' 

In  negation,  the  exemplar  form  is  needed.  *  All  men  are 
not  fishes,'  does  not  deny  the  proposition,  '  All  men  are  fishes.* 
The  denial  would,  however,  bo  given  in    *  Every  man  is  not 

any  fish.'* 

Properly  speaking,  the  cumular  proposition  can  be  found 
proved  only  through  exemplars ;  hence  the  exemplar  precedes 
in  the  order  of  thought ;  a  circumstance  justifying  its  adoption 
as  the  basis  of  a  logical  system.  According  to  it,  quantity  is 
mode  of  selection  hy  example ;  universal  is  replaced  by  wholly 
indefinite;  particular  by  not  wholly  indefinite.  The  forms  of 
the  propositions  would  be  modified  thus  : — 

Any  one  X  is  any  one  T.     X  and  Y  singular  and  identical. 

Some  one  X  is  not  some  one  Y.  Either  X  not  singular,  or 
Y  not  singular  ;  or  if  both  singular,  not  identical. 

Any  one  X  is  some  one  Y.  All  Xs  are  some  Ys. 

Some  one  X  is  not  any  one  Y.     Some  Xs  are  not  (all)  Ys. 

Some  one  X  is  any  one  Y.  Some  Xs  are  all  Ys. 

Any  one  X  is  not  some  one  Y.   .All  Xs  are  not  some  Ys. 

Any  one  X  is  not  any  one  Y.       All  Xs  are  not  (all)  Ys. 

Some  one  X  is  not  some  one  Y.     Some  Xs  are  some  Ys. 

The  *  Numerically  Definite  Syllogism  *  is  a  scheme  of  infer- 
ence which  supposes  exact  numbers  to  be  given. 

If  in  100  instances  of  any  thing,  70  are  Xs,  and  30,  Ys, 
then  at  least  20  Xs  must  be  Ys.  The  author  develops  at  great 
length  a  symbolical  scheme  founded  on  this  assumption. 

Syllogisms  with  numerically  definite  quantity  occur  rarely, 
if  ever,  in  common  thought.  But  it  is  not  unfrequent  to  find 
forms  where  the  number  of  instances  of  one  term  is  the  whole 
number  of  instances  of  the  other  term  j — '  For  every  Z  there 

*  Mr.  Mill,  in  a  controversial  note  to  his  chapter  on  the  Functions 
of  the  Syllogism,  mtikcfl  the  following  remark:— The  language  of 
ratiocination  would,  I  think,  be  brought  into  closer  agreement  with 
the  real  nature  of  the  process,  if  the  general  propositions  employed 
in  reasoning,  instead  of  being  in  the  form  All  men  are  mortal,  or 
Ever}'  man  is  mortal,  were  expressed  in  the  form  Ani/  man  m  mortal. 
This  mode  of  expression,  exhibiting  as  the  type  of  all  reasoning  from 
experience  "  The  men  A.  B,  C,  &c.  are  so  and  so,  therefore  cwy  man  is  so 
and  so,"  would  much  better  manifest  the  true  idea—  that  inductive  reason- 
ing is  always,  at  the  bottom,  inference  from  particulars  to  particulars,  and 
that  the  whole  function  of  general  propositions  in  reasoning,  is  to  vouch 
for  the  legitimacy  of  such  inferences. 


THE   A.KISTOTELL^   SYSTEM  COAIPARED. 


189 


is  an  X  that  is  Y ;  some  Zs  are  not  Ys  ;'  *  For  every  man  m 
the  house  there  is  a  person  that  is  aged  ;  some  of  the  men  are 
not  aged ;'  from  which  it  follows,  but  not  by  any  common  form 
of  syllogism,  that  *  some  persons  in  the  house  are  not  men.* 

To  this  case  the  author  applies  the  designation  *  syllogism 
of  transposed  quantity.*  Of  terms  in  common  use  the  only 
one  that  gives  syllogisms  of  this  character  is  *  most  :* — *  Most 
Ys  are  Xs  ;  most  Ys  are  Zs ;  therefore  some  Xs  are  Zs.* 

Adverting  to  the  distinction  of  Figure,  he  styles  the  First 
the  figure  of  direct  transition ;  the  Fourth,  which  is  nothing 
but  the  first  with  a  converted  conclusion,  the  fio-ure  of  inverted 
transition ;  the  Second,  the  figure  of  reference  to  (the  middle 
term)  ;  the  Third,  the  figure  of  reference  form  (the  middle 
term).  Apart  from  the  conversion  of  the  conclusion,  the 
Fourth  Figure  is  the  most  natural  order,  as  it  takes  up  what 
was  left  ofi*  with— '  X  is  in  Y,  Y  is  in  Z,  therefore  X  is  in  Z  :'  this 
is  the  first  figure,  according  to  the  simplest  arrangement  of 
the  premises. 

In  the  author's  system,  however,  Figure  attains  importance 
only  through  a  wider  yiqw  of  the  copular  relation, 

Mr.  De  Morgan  compares  his  system  with  the  Aristotelian, 
of  which  he  regards  it  as  an  extension,  through  the  single  de- 
vice of  adding  contraries  to  the  matters  of  predication.  (Hamil- 
ton also  claims  to  extend  Aristotle,  but  on  a  different  principle). 
Accordingly  the  Aristotelian  syllogisms  may  bo  all  collected 
from  the  preceding  system,  by  the  following  modifications. 
1.  The  exclusion  of  all  idea  of  a  limited  universe,  of  contrary 
names,  and  of  the  propositions,  *  Every  thing  is  either  X  or  Y,* 
*  Some  things  are  neither  Xs  nor  Ys.*  2.  The  exclusion  of  the 
form  of  conversion,  *  Some  Xs  are  all  Ys.*  3.  The  exclusion  of 
every  copula  except  the  transitive  and  convertible  copula.  4. 
The  regarding  of  the  identical  pairs—No  X  is  Y,  No  Y  is  X, 
and  Some  X  is  Y,  Some  Y  is  X— as  distinct  propositions  of 
themselves  determining  distinction  of  figure  and  mood;  as 
Celarent  and  Cesare,  Ferio  and  Ferison,  &c.  5.  The  introduc- 
ing of  the  distinction  of  figure.  6.  The  writing  of  the  major 
and  minor  propositions  first  and  second,  instead  of  second  and 
first. 

Farther,  in  the  Aristotelian  scheme,  there  are  four  funda- 
mental syllogisms  in  the  first  figure,  each  of  which  has  an 
opponent  in  the  second,  and  an  opponent  in  the  third.  The 
opponents  of  Barbara  are  BaroJco  and  ftokardo.  There  are 
three  fundamental  syllogisms  in  the  fourth  figure  (Dimaris, 


SB 


190 


BOOLE  S  ADDITIONS   TO  THE   SYLLOGISM. 


Camenes,  Fresison),  each  of  which  has  the  two  others  for  op- 
ponents. AltofTfether  there  are  fifteen  fundamental  syllogisms. 
The  remaining  four  are — three  strengthened  particular  syllo- 
gisms, Darapti  (III),  Felapt&ti  (III),  Fesapo  (IV),  and  one 
weakened  universal;  Bramantip  (IV). 

The  Aristotelian  rule  that  the  middle  term  must  be  distri- 
buted once  fails  with  the  introduction  of  contraries.  The  rule 
to  be  substituted  is — All  pairs  of  universals  are  conclusive, 
but  a  universal  and  a  particular  require  that  the  middle  term 
should  also  be  a  universal  and  a  particular, — universal  in  one 
premise  and  particular  in  the  other. 

The  rule  that  when  both  premises  are  negative,  there  is  no 
syllogism,  also  fails.  In  the  system  completed  by  contraries, 
there  are  eight  such  syllogisms  ;  as  many,  in  fact,  as  with  pre- 
mises both  affirmative.  But  in  these  cases,  as  before  re- 
marked, the  premises  are  not  both  negative  in  reality. 

Again,  on  the  rule  *  that  two  particular  premises  can  give 
no  conclusion,*  the  author  brings  forward  as  a  legitimate 
inference,  *  Most  Ys  are  Xs,  most  Ys  are  Zs,  therefore  some 
Xs  are  Zs ;  most  men  wear  coats,  most  men  wear  waistcoats, 
therefore  some  men  wear  both  coats  and  waistcoats.*  He 
develops  this  form  at  length  into  a  symbolical  scheme,  under 
tlie  name  of  *  The  numerically  definite  syllogism.* 

Mr.  De  Morgan's  system,  on  the  whole,  is  characterized  by 
an  immense  multiplication,  not  only  of  symbolical  forms,  but 
of  verbal  designations  for  the  relationships  growing  out  of  the 
syllogism. 

Boole's  additions. 

The  late  Professor  Boole,  of  Cork,  published  two  works 
on  Formal  Logic.  The  first  and  smaller,  entitled — *  The 
Mathematical  Analysis  of  Logic,'  compi-ised  an  Algebraic 
rendering  of  the  syllogism,  showing  how  all  the  moods  might 
be  symbolically  deduced.  The  second  and  larger  work,  en- 
titled—  *  An  Investigation  of  the  Laws  of  Thought,  on  which 
are  founded  the  Mathematical  Theories  of  Logic  and  Proba- 
bilities,' takes  a  much  wider  sweep,  and  is  an  entirely  new 
application  of  the  symbolical  methods  of  Algebra,  to  Inference, 
both  Immediate  and  Mediate  ;  the  largest  share  of  attention 
being  given  to  the  first,  or  the  so-called  Immediate  Inference, 
The  author  also  extends  the  same  nomenclature  and  handling 
to  Probabilities. 

Besides  the  novel  employment  of  symbolical  processes  of  the 
Algebrdc  kind,  the  work  is  intended  to  bear  fruit  in  other 


CONNEXION  OF  LOOIC   AND  MATHEMATlCa 


191 


ways.      la  using  the  title  *  Laws  of  Thought,*  the  author  in- 
dicates that  one  purpose  of  his  theory  of  Reasoning  is  to  throw 
light  upon  the  workings  of  the  Intellect.     He  considers  that 
our  views  of  the  Science  of  Logic  must  materially  influence, 
perhaps  mainly  determine,  our  opinions  upon  the  nature  of  the 
intellectua    faculties.     For  example,  whether  reasoning  con- 
sists merely  in   the  application  of  certain  first  or  necessary 
truths,  originally  imprinted  on  the  mind,  whether  the  mitid  is 
itselt  a  seat  of  law  [whatever  that  may  mean],  or  whether  all 
reasoning  is  of  particulars,  concerns  not  Logic  merely,  but  also 
the  theory  of  the  intellectual  faculties.     It  cannot  be  said,  how- 
ever, that  the  author  has  been  able  to  decide  which  alternative 
IS  the  correct  one. 

He  farther  proposes  to  elucidate  the  subtle  connexion  be- 
tween Logic  and  Mathematics ;  how  far  a  common  theory  is 
applicable  to  both  kinds  of  reasoning,  and  how  far  the  likeness 
tails.  He  holds  that  the  ultimate  laws  of  Logic  are  mathe- 
matical  m  their  form,  that  they  are,  except  in  a  single  point, 
identical  with  the  general  laws  of  Number.  The  exhibition 
of  Logic  m  the  form  of  a  Calculus  is  not  arbitrary :  the  ultimate 
laws  of  thought  render  that  mode  possible,  and  forbid  the 
perfect  manifestation  of  the  science  in  any  other  form.  It  is 
not  of  the  essence  of  Mathematics  to  be  conversant  with  the 
ideas  of  number  and  quantity.  The  author  does  not  design  to 
supersede,  by  symbolic  processes,  the  common  forms  of  reason- 
ing ;  nevertheless,  cases  may  arise  where  the  value  of  scientific 
procedure,  even  in  things  confessedly  within  the  scope  of 
ordinary  reasoning,  may  be  felt  aud  acknowledged. 

The  author's  scheme  starts  with  the  consideration  of  Lan- 
guage  as  an  instrument,  not  of  communication  merely,  but  of 
Reasoning;  it  being  his  intention  to  substitute,  for  ordinary 
language,  a  set  of  symbols  adapted  to  perform  this  function  in 
a  more  efiective  manner. 

The  signs  composing  Language,  with  a  view  to  Reasoning 

especially,  are  characterized  in  the  following  definition  : *  A 

sign  is  an  arbitrary  mark,  having  a  fixed  interpretation,  and 
susceptible  of  combination  with  other  signs  in  subjection  to 
fixed  laws  dependent  upon  their  mutual  interpret^ion.*  The 
first  part  is  obvious  ;  a  sign,  in  its  primary  invention  is  purely 
arbitrary  ;  *  house  '  and  *  domus  *  are  equally  good  for  the 
purposes  of  language.  It  is  also  obvious  that  each  sign  should 
possess  a  fixed  interpretation,  that  there  should  never  be  any 
ambiguity  of  meaning.     Ordinary  language  is  greatly  liable  to 


192 


Boole's  additions  to  the  syllogism. 


I 


, 


this  infirmity ;  hence,  one  of  its  defects  as  an  instrument  of 
reasoning.  Lastly,  signs  must  be  susceptible  of  combination 
with  other  signs,  which  combinations  must  have  fixed  laws 
depending  upon  their  mutual  interpretation. 

The  author  proceeds  to  explain  his  artificial  symbols  for 
superseding,  by  a  higher  mechanism,  the  vocables  of  our  ordi- 
nary speech.  The  symbols,  and  their  connecting  signs  of 
operation,  are  borrowed  from  Algebra,  and  are  manipulated  by 
the  algebraic  processes,  after  allowances  are  made  for  the 
difference  between  the  material  of  Logic,  and  the  material  of 
Mathematics  (Number  and  Quantity). 

All  the  operations  of  Language,  as  an  instrument  of  Reason- 
ing, may  be  conducted  by  a  system  of  signs  composed  of  the 
following  elements : — 

First,  Literal  symbols,  as  x,  y,  z,  &c.j  representing  things  as 
subjects  of  our  conceptions.  For  the  object  *  man'  we  may  use 
a,  for  a  '  brute,'  y,  for  the  quality  *  living,'  z^  and  so  on. 

Second.  Signs  of  operation,  as  +,  — ,  X,  standing  for  the 
operations  whereby  conceptions  are  combined,  or,  when  com- 
bined are  resolved  into  their  elements  ;  *  men  and  brutes'  may 
be  represented  hy  x  -\-  y. 

Third.  The  sign  of  identity  == . 

These  symbols  of  Logic  are  used  according  to  definite  laws, 
partly  agreeing  with,  and  partly  differing  from,  the  laws  of 
the  corresponding  symbols  in  the  science  of  Algebra. 

The  first  class  of  symbols  above  given  are  the  appellative  or 
desciiptive  signs,  expressing  either  concrete  things,  or  the 
qualities  of  things  ;  that  is  to  say,  they  are  the  equivalents  of 
the  two  appellative  parts  of  speech,  the  Noun  and  the  Adjec- 
tive. Thus,  let  X  denote  *  men,'  or  all  men  ;  and  let  y  denote 
the  adjective  good ;  then  all  good  men  would  be  expressed  by 
some  suitable  combination  of  x  and  y.  Now  the  suitable  com- 
bination, for  the  case  of  a  thing  qualified  by  an  attribute,  or  of 
two  or  more  co-inhering  attributes  is  a  product  x  X  y,  or 
X  y.  Why  this,  and  not  the  sum  x  -\-  y,is  the  proper  symbol, 
the  auth(  r  does  not  specifically  explain  ;  the  means,  as  in 
other  symbolical  sciences,  are  left  to  be  justified  by  the  end, 
namely,  arriving  at  true  results.  So  if  x  stands  for  *  white  ' 
or  *  white  things,'  y  for  sheep,  x  t/  stands  for  *  white  sheep  ;' 
and  if  2  stands  for  *  horned,'  z  x  y  will  represent  *  horned 
white  sheep.'  In  this  symbolism,  the  order  of  the  symbols  is 
unimportant,  just  as  the  order  of  the  adjective  and  the  sub- 
stantive is  indifferent  as  regards  the  meaning ;  *  good  man,* 
*  vir  bonus '  are  equally  accepted  by  the  mind  to  suggest  that 


-''^'^wm'mmm'-mmr'mi^^'^^yW^^im*^ 


^^m^^ssssBSsmaprawsm 


symbols  for  parts  and  whole. 


193 


the  conception  *man'  is  to  be  limited  by  the  conception 
'good.'  Hence  we  may  use  at  pleasure  x  y^  and  y  xi  x  y  9 
and  zy  X,  &c,  ' 

It  is  a  law  of  speech  that  an  appellative  gains  nothing  (ex- 
cept perhaps  rhetorically)  by  repetition  or  duplication  ;  *  good, 
good,'  is  the  same  as  good ;  *  horse,  horse,'  is  the  same  as  horse! 
To  adapt  this  to  symbols,  x  x  would  amount  to  no  more  than 
<B ;  that  is,  using  =  (as  in  Algebra)  for  equivalence,  or  iden- 
tity, XX  z=  X,  Here  Logic  and  Algebra  are  at  variance,  and 
the  methods  of  manipulating  logical  symbols  must  vary  ac- 
cordingly. The  author  shows  that  the  form  x  x  z=z  x,  or  a^  = 
«,  has  still  deeper  meanings. 

Next  as  to  signs  for  collecting  parts  into  a  whole  (quantity  in 
extension)  or  for  separating  a  whole  into  parts.  These  cor- 
respond to  the  conjunctions  *  and,'  *  or,'  in  common  speech — 

*  trees  and  minerals  ; '  *  barren  mountains,  or  fertile  vales.' 
The  sign  of  addition  is  now  used;    let  x  be  *  trees*  and  y 

*  minerals  ;  '  the  conjoined  expression  is  «  -|-  y.  This  employ- 
naent  of  the  sign  is  so  closely  allied  to  addition  in  arithmetic, 
that  it  may  be  worked  upon  the  same  principle.  Again,  let 
a;    stand  for  men,  y  for  women,  and    z  for  European ;    then 

*  European  men  and  (European)  women '  would  be  represented 
oj  z  (x  +  y)  =zx  -{-  zy. 

Addition  implies  subtraction .  *  All  men  except  Europeans  * 
will  be  expressed  by  x—y.  *  White  men  except  white  Asiatics ' 
(«  men,  i/  Asiatics,  z  white), 

z^x  —  y)  =  zx  —  zy 

With  a  view  to  Propositions,  it  is  necessary  to  consider  the 
rendering  of  the  copula.  For  this  purpose  all  propositions  have 
to  be  reduced  to  the  form  *  is  '  or  *  are  ; '  *  Csesar  conquered  the 
Grauls,^  must  be  resolved  into  *  Caesar  is  he  that  conquered  the 
Gauls.'  This  is  the  copula  of  identity,  the  most  generalized 
form  of  relationship  of  subject  and  predicate.  It  may  be  ex- 
pressed by  the  symbol  =  ;  and  the  meaning  so  far  coincides 
Mviih  the  Algebraic  meaning,  that  the  Logical  equation  is  Httle 
different  from  the  Algebraic  equation. 

Take  the  Proposition,  'The  stars   are  the   suns   and  the 
planets.'      Let  stars    be  represented   by  x    suns,  by   y,  and 
planets,  by  2;  then, 
X  =  y-\~  z 

Whence  we  can  deduce, 

*  —  y  =  «  (The  stars,  except  the  suns,  are  planets), 

or,  a;  --  z  ==  7/  (The  stars,  except  the  planets,  are  suns). 

Thus,  in  the  Logical  equation,  we  may  apply  the  mathe- 


n 


M 


194 


Boole's  additions  to  the  syu/)gisxM. 


matical   axioms  'equals  added  to  equals   give  equal  sums;* 
*  equals  taken  from  equals  give  equal  differences.' 

If  two  classes  of  things,  «  and  y,  be  identical,  that  is,  if 
all  members  of  the  one  are  members  of  the  other,  then  such 
members  of  the  one  class  as  possess  a  given  property,  z,  will 
be  identical  with  the  members  of  the  other  that  possess  the 
same  property.     Hence,  if  we  have  the  equation 

a;  =  7/: 
then,  whatever  class  or  property  «  may  represent,  we  have  also 

z  X  =  zy, 

Tn  point  of  form,  this  coincides  with  the  algebraic  law — if 
both  members  of  an  equation  be  multiplied  by  the  same 
quantity,  the  products  are  equal. 

The  analogy,  however,  does  not  extend  to  division.  For, 
supposing  the  members  of  a  class  x,  possessing  the  property 
«,  are  identical  with  the  members  of  a  class  y,  possessing  the 
same  property,  it  does  not  follow  that  the  members  of  the  class 
X  universally  are  identical  with  the  members  of  the  class  y. 
Hence,  it  cannot  bo  inferred  from  the  equatioa 

«  a;  =  2  y, 
that  the  equation 

x  =  y 

is  also  true.  Thus,  the  process  of  division,  as  applied  to 
equations  in  Algebra,  has  no  formal  equivalent  in  Logic. 
Multiplication  sufl&ciently  represents  the  combination  or  com- 
position of  conceptions,  but  division  does  not  appear  to  repre- 
sent their  decomposition  or  abstraction.  The  want  of  analogy 
on  this  point,  however,  is  not  total.  Even  in  Algebra,  the 
rule  of  division  does  not  hold  throughout ;  for  example,  it  does 
not  apply  when  the  divisor  is  2  =  0.  Through  this  one 
loophole,  the  author  is  able  to  restore  the  consistency  of  the 
algebraical  and  the  logical  processes. 
Reverting  to  the  equation 

x^  =  X 
he  remarks  that  only  two  values  of  x  will  comply  with  it ; 
namely,  0  and  1.  For  0^  =  0,  and  I''  =  1  ;  and  of  no  other 
numbers  is  the  relation  true.  Hence,  in  an  Algebra,  whose 
symbols  x,  y,  z,  &c.,  never  knew  any  values  but  0  and  1,  the 
laws  of  operation  would  coincide  with  the  laws  of  operation  in 
Logic.  The  two  sciences  are  divided  bj  no  other  difference 
than  the  manner  of  interpretation. 

In  chapter  III.,  Boole  professes  to  derive  the  laws  of  the 
symbols  of  Logic,  above  assumed,  from  the  laws  of  the  opera- 


SYMBOLS  FOB  COMPLEX  SUBJECTS. 


195 


tion  of  the  mind.     He  proceeds  thus  :— In  every  discourse, 
there  is  a  limit  to  the  subjects  considered  ;  in  other  words, 
a  universe,    [He  is  here  at  one  with  De  Morgan].     Thus  the 
term  '  men '  is  used  with  reference  to  a  certain  implied  exten- 
Bion,  on  the  part  of  the  speaker ;  it  may  be  all  men  whatsoever ; 
or  It  may  be  a  more  limited  universe,  as  civilized  men,  men  in 
the  vigour  of  life,  and  so  on.     The  term  *  men  '  raises  in  the 
nimd  of  the  hearer  the  beings  so  intended  to  be  comprised. 
Let  us  next  consider  the  employment  of  an  adjective  in  addition, 
buppose  '  men  '  to  be  spoken   of  in  the  widest  sense,  the  uni- 
verse *all  men ; '  then  the  application  of  the  adjective  *  good ' 
prescribes  the  operation  of  selecting  from  the   universe  all 
objects  possessing  the  further  quality  *  good  ; '  such  selection 
corresponds  to  the  combination — ^good  men.    Thus,  the  office  of 
an  adjective  is  not  to  add  the  quality,  *  good '  for  instance,  to 
all  the  universe,  men,  but  to  select,  from  the  universe,  individuals 
according  to  the  idea  prescribed  in  the  word.    The  intellectual 
faculties  employed  in  these  successive  operations  may  be  sup- 
posed to  be  those  denominated  Conception  or  Imagination,  and 
Attention;  or  perhaps  the  entire  act  maybe  summed  up  in 
one  function  of  Conception.     Each  step  in  the  process  may  be 
characterized  as  a  definite  act  of  conception. 

Now,  the  syllogism  above  adopted  exactly  corresponds  to 
this  operation.  The  symbol  x  directs  attention  upon  a  certain 
universe,  men  for  example  ;  the  symbol  y,  good  or  white,  di- 
rects us  to  search  that  universe  for  individuals  owning  the  pro- 
perty named  ;  and  the  combination  ?/ a:,  or  x  y,  expresses  the 
selection— good  men  or  white  men.  This  symbol  will  not  fall 
under  the  relations  expressed  by  a  sum  ;  its  meaning  is  a  group 
qualified  by  the  conjoined  conceptions  x  and  y,  not  an  aggreo^te 
made  up  by  adding  the  universe  x  to  the  universe  y.  °\\ith\s 
way  does  Boole  consider  that  he  has  established  his  positions:  (1) 
that  the  operations  of  the  mind  are  subject  to  general  laws,  and 
(2)  that  these  laws  are  mathematical  in  their  form ;  whence 
the  laws  of  the  symbols  of  Logic  are  deducible  from  the  opera- 
tions of  the  mind  in  reasoning. 

He  then  proceeds  to  determine  the  logical  value  and  signifi- 
cance of  the  symbols  0  and  1,  to  which  quantities  Algebra  has 
to  be  cut  down,  in  order  to  become  Formal  Logic.  The  sjnoi- 
bol  0  corresponds  to  Nothing ;  the  symbol  1  corresponds  to 
the  universe  of  discourse.  Nothing  and  Universe  are  the  two 
limits  of  extension — none  and  all.  Whatever  the  class  y  may 
be,  the  individuals  common  to  it  and  to  the  class  0,  or  Nothing, 
are  Nothing  or  none.     That  is, 

0  X  ?/  =  0,  or  0  y  =  0 


1 


196 


BOOLES  ADDITIONS    TO  THE    SYLLOGISM. 


Again,  the  symbol  1,  satisfies  the  law  of  equation, 

I   X  y  =  ?/,  orly  =  2j 
whatever  y  may  represent.     The  class  represented  by  1,  there- 
fore must  be  *the  Universe,'  the  only  class  containing  all  the 
individuals  that  exist  in  any  class. 

Now  as  to  contraries.  If  x  represent  any  class  of  objects, 
1 — X  will  represent  the  contrary,  or  supplementary  class,  what 
remains  when  x  is  withdrawn  from  the  Universe  of  discourse 
1.  If  a;  be  *  men '  in  the  universe  *  animals,'  1  —  x  {b  the  not- 
men,  the  remaining  members,  or  the  brutes.  This  coincides 
with  De  Morgan's  symbolism,  U — x  for  the  contrary  of  x. 

The  author  next  offers  from  his  fundamental  logical  equa- 
tion, a^  =  Xy  or  a:  —  a:^  =  0,  a  formal  proof  of  the  Law  of  Con- 
tiadiction,  thus: — The  equation  admits  of  the  form 

a(l— a:)  =  0 
which,  being  interpreted  according   to  the    meaning  of  the 
symbols,  is  that  a  class  determined  at  once  by  x,  and  by  its 
contrary  1  —  x,  is  the  same  as  0  or  Nothing  ;  that  is,  does  not 
exist. 

Advancing  farther  into  the  consideration  of  Propositions 
(chap.  IV.),  the  author  divides  these  into  'primary*  or 
simple,  and  *  secondary  *  or  complex ;  the  one  relating  to 
things,  the  other  to  propositions.  Under  the  last  named  class 
are  included  hypotheticals,  &c.  He  begins  by  propounding  a 
general  method  for  expressing  any  *  term  '  that  may  enter 
into  a  primary  proposition.  The  method  is  merely  the  appli- 
cation of  his  symbols  as  already  explained.  Thus,  let  x  repre- 
sent opaque  substances,  y  polished  substances,  z  stones  ;    then 

X  y  z  =  opaque  polished  jtones. 

Now  as  1  —  z  represents  substances  that  are  the  contrary  of 
stones,  or  are  not  stones, 

xy  (1  —  2)  =  opaque  polished  substances  that  are  not  stones ; 
So 

X  (I  —  y)  (1 — 2)  =  o]>aquo  substances,  not  polished,  and 
not  stones. 

Again,  for  the  case  of  collections  of  things, — or  objects  con- 
joined by  'and,'  'or,' — the  sign  of  addition  must  be  added,  as 
above  explained.  The  sign  '  or  '  gives  a  disjunctive  form  ;  all 
x&  are  either  y's  or  z's ;  and  this  has  two  meanings  not  dis- 
criminated by  the  use  of  '  or,'  but  differently  rendered  in  the 
formula.  It  is  a  question  whether  x  may,  or  may  not  be  both 
y  and  z.  *  He  is  either  a  rogue  or  fool ;  '  he  may  or  may  not 
be   both,    so   far  as   this   expression   goes,  nlthongh  the  more 


iBanamnMMWTOtiiwuajii 


COMPLEX  TERMS. 


197 


usual  rendering  would  be  *  not  both.'  The  two  ways  of  sym- 
bolic expression  are  the  following.  (1)  Things  that  are  either 
x'b  or  2/'s,  are  things  that  if  a;'s  are  not  //'s,  and  if  ?/'s  are  not 
a;'s ;   that  is 

35  (1  —  2/)  +  2/  (1  —  2;). 
(2)  Things  that  are  either  a;'s,  or  if  not  aj's,  then  y's. 

x  +  y(l^x), 
^  This  admits  the  supposition  of  being  both  x  and  y,  a  suppo- 
sition more  explicitly  given  in  the  enlarged  equivalent  form. 

xy+x{l—y)  +  y  (I—a;), 
where  we  have  all  three  alternatives  ;  x  y  expressing  the  concur, 
rence  of  both  x  and  y.      If  he  is  not  a  rogue  he  is  a   fool,  x 
fool,  y  rogue,  a;  (1  —  y)  ;    if  he  is  not  a  fool  he  is  a  rogue, 
y  (I  —  x)  ;  he  is  a  fool  and  a  rogue  together,  x  y. 

To  take  a  more  complex  example,  exhibiting  the  full  power 
of  the  method ;  let 

X  =  hard,  y  =  elastic,  z  =  metals ; 
and  we  shall  have  the  following  results : 

non-elastic  metals  =  z  [1  —  y). 
Elastic  substances,  together  with  non-elastic  metals,  y  4-  z 

(^  —  y)' 

Hard  substances  except  metals,  x  —  z. 

Metallic  substances,  except  those  neither  hard  nor  elastic, 
z-z(l-x)  (1-7/)  or^l  1  -  (1  _  x)  (1  -  y). 

To  take  a  still  more  complicated  examples:  '  Hard  substance, 
except  such  (hard  substances)  as  are  metallic  and  non-elastic, 
and  such  (hard  substances)  as  are  elastic  and  non-metallic' 
Hard  substances  being  represented  by  x  ;  substances  hard, 
metallic,  and  non-elastic,  are  x  z  (1— y);  substances  hard, 
elastic,  and  non-metallic,  are  x  y  (I— 2),  and  the  whole  expres- 
sion is 

a:— -j  a;»(l  — y)+a;y  (1  — 2)  >  oraj  — a;  z(l  — ?/)— a;2/(l— z). 

Such  is  the  expression  of  Terms.  To  form  Propositions, 
the  sign  =  is  used  for  the  copula  of  identity.  Thus,  to  ex- 
press identity  between  *  Fixed  Stars'  and  '  Suns,'  or  to  express 
that  *A11  fixed  stars  are  suns,'  and  'All  suns  are  fixed  stars,' 
[Hamilton's  universal  with  universal  predicate], 

X  •=zy. 

This  is  the  form  applicable  to  the  verbal  proposition  or  de- 
finition ;  and  the  author  exemplifies  it  by  such.  For  example. 
Senior's  definition  of  wealth,  as  consisting  in  things  trans- 
ferable, limited  in  supply,  and  either  productive  of  pleasuro 


'M 


198 


BOOLE'S  ADDITIONS  TO   THE   SYLLOGISM. 


m^ 


I- 


or  preventive  of  paia,  is  symbolized  thus.  Let  w  =  wealth  ; 
i  =  things  transferable  ;  8  -^  limited  in  supply  ;  p  =  pro- 
ductive of  pleasure  ;  r  =  preventive  of  pain.  Now  it  is  to  be 
remarked  that  the  conjunction  *  and'  is  not  necessary  and 
might  be  misleading;  *  and'  conjoining  two  adjectives  *  great 
and  good  men,'  is  very  different  from  *  and '  coupling  two 
groups  *  great  men  and  good  men ;'  the  first  is  x  y  z,  the 
second  x  z  +  y  z.  We  farther  remark  that  the  disjunctive 
*  or'  in  *  productive  of  pleasure  or  preventive  of  pain,'  means 
things  that  *  if  not  productive  of  pleasure  are  preventive  of 
pain  ;'  and  that,  *if  not  preventive  of  pain  are  productive  of 
pleasure  ;'  and  does  not  suppose  any  class  of  things  to  be  both 
at  once.  With  these  explanations,  the  definition  is  embodied 
in  the  formula, 

w  =  st  <p  {I  —  r)  +  r  (1  — p)   > 

Passing  now  to  Real  Propositions,  as — *  men  are  mortal,*  we 
need  a  mode  of  rendering  particular  terms  ;  *  All  men  are 
some  mortal  beings.'  Let  v  represent  an  indefinite  class,  some 
of  whose  members  are  mortal  beings  ;  and  let  x  stand  for  the 
the  entire  class  *  mortal  beings ;'  tben  v  x  will  represent  *  some 
mortal  beings.*  Hence  if  y  stand  for  men,  the  equation  sought 
is — 

2/  =  raj 
The  qualifying  symbol  v  is  thus  the  mark  of  particularity  in 
every  case.    In  the  proposition,  *  the  planets  are  either  primary 
or  secondary  '  (some  primary  bodies  or  else   some  secondary 
bodies), 

Let  X  represent  planets  (the  subject) ; 
y  =  primary  bodies ; 
z  =  secondary  bodies  ; 
then,  assuming  that  the  planets  cannot  be  both  primary  and 
secondary,  the  equation  of  the  proposition  is 

2;  =  v|2/(l  — z)  +2(1— 2/).  I 

A  more  simple  form,  stating  the  same  proposition,  is 

X  =z  V  (y  +  z). 

For,  the  meaning  obviously  is,  that  the  planets  fall  exhaust- 
ively under  the  two  heads,  primary  and  secondary ;  that  is,  are 
made  up  of  some  primary  and  some  secondary  bodies. 

Such  is  the  symbolism  applicable  to  affirmative  real  proposi- 
tions, where  the  predicate,  as  a  rule,  must  be  supposed  to 
surpass  the  subject.  The  author  next  shows  how  to  express 
megative  propositions. 


-'H;.  ■?5*«''W^*^W^««l!e«"«■^^'^'!W^^1E^^  -.rantW 


EXPRESSION  OF  PROPOSITIONS. 


199 


Suppose  the  case,  *  No  men  are  perfect  beings,'  a  universal 
negative.  Here,  we  make  an  assertion  to  the  effect  that  '  all 
men  are  *  not  perfect  beings.'  The  meaning  may  then  be 
expressed  thus  :-^ZZ  7nen  (subject)  are  (copula)  not  any  part 
ofperject  (preaicate).  Let  y  represent  '  men,'  and  x  *  perfect 
beings.      *  Not  perfect  beings  *  are  represented  by  the  negative 

fi  i\  Ti^ '  ^""^  *  ^""""^  ""^^  P^^^^^^  t^'^gs,'  by  this  form,  quali- 
ted  by  the  sign  of  particularity,  v.     Hence,  the  equation  is 

m,        ^  y  =  v{\~x). 

'  /  .  f',,  ^^P^^ss  the  form  No  ars  are  ys,  we  have  to  convert  it 
into    All  xs  are  not  (any  part  of)  ys.' 

^  A  particular  negative  proposition,  *some  men  are  not  wise,* 
is  resolvable  into  '  some  men '  (subject)  'are'  (copula)  *  not 
wise  (predicate).  Putting,  then,  y  for  '  men,*  x  for  '  wise  ' 
and  V  for  an  indefinite  containing  some  individuals  of  the  class 
quaiifaed  by  it,  we  have  for  *some  men,'  vy,iov  *not  any 
part  of  the  wise,'  v  (1  —  x),  or  the  equation 

vy  =zv(l—x). 
fco  much  for  the  symbolical  expression  of  primary  or  simple 
propositions.  It  is  next  to  be  seen  how  these  forms  are  turned 
to  account  in  furnishing  immediate  inferences,  or  in  exhaust- 
ing all  the  equivalent  propositional  forms  of  each ;  in  which 
operation  the  author  principally  expends  the  force  of  his 
method. 

With  this  view,  permission  must  be  given  to  work  the  several 
equations  after  the  algebraical  model,  with  the  restrictions 
a  ready  stated.  The  reader  must  be  satisfied  from  the  ex- 
planations afforded  that  the  signs  used  have  the  same  force  in 
Logic  as  in  Algebra.  The  conditions  of  valid  reasoning  are 
then  those  three  :-First,  that  a  fixed  interpretation  be  as- 
signed  to  the  symbols  ;  secondly,  that  ihe  formal  processes  of 
solution  or  demonstration  be  conducted  in  obedience  to  the 

r^i  !':'!?  ''l^''}^^  meanings  of  the  signs  of  operation; 
thirdly,  that  the  final  result  be  interpreted  in  the  same  way  ai 
the  original  data.  Having  once  clothed  the  logical  meaning 
in  the  algebraic  dress,  the  author  claims  to  proceed  exactly  as 
il  he  had  to  deal  with  an  algebraic  equation  wherein  the  symbols 
liave  only  the  two  meanings  0  and  1. 

The  exhaustive  renderings  of  each  proposition  are  to  be 
gamed  by  a  process  of  *  development,'  which  is  explained  at 
length,  and  is  strictly  after  the  manner  of  Algebra,  with  the 
conditions  of  value  specified.  The  skeleton  of  the  form  of 
development  is  furnished  from  these  considerations  :— Suppose 
we  arc  considering  a  class  of  things  with  reference  to  the  point 


ti 


200 


Boole's  additions  to  the  syllogism. 


whether  its  members  possess  or  do  Dot  possess  a  property  x ; 
as  auimals,  with  reference  to  humanity.  Suppose  next  that 
the  members  possessing  the  property  d:,  possess  also  a  property 
u  ;  and  that  the  members  not  possessing  the  property  x  are 
subject  to  a  condition  v.  On  these  suppositions  the  class  in  ita 
totality  is  represented  by 

U  X  '\'  V  {\  —  x). 
Any  function  of  x,  f  (t),  wherein  a:  is  a  logical  symbol, 
susceptible  onlv  of  the  values  0  and  1,  is  said  to  be  developed, 
when  it  is  reduced  to  the  form  a  x  +  6  (1  —  a;),  a  and  &  being 
so  determined  as  to  make  the  result  equivalent  to  the  function 
whence  it  is  derived.  The  following  out  of  this  development 
is  purely  algebraical,  and  occupies  a  good  many  pages  of  the 
work.  To  a  student  versed  in  ordinary  Algebraical  equations, 
the  whole  is  sufficiently  intelligible.  We  shall  here  indicate 
merely  the  results  and  applications.  The  following  is  given 
as  an  example.  It  is  a  definition  with  two  defining  marks. 
*  Clean  beasts  are  such  as  both  divide  the  hoof  and  chew  the 

cud.* 

Let  X  =  clean  beasts, 

y  =  beasts  dividing  the  hoof, 

z  ==  beasts  chewing  the  cud. 
The  definition  will  then  be  represented  by  the  equation 

a;  =  2/2, 
which  may  be  reduced  to  the  form 

X  —  y  z  =  0, 
Here  a  function  of  x,  y,  and  2,  namely  x  —  y  z  has  to  be 
developed  according  to  the  methods  laid  down.     As  a  speci- 
men, we  may  transcribe  the  development ; 
Oxyz^xy(Y'-z)  +  x(l'—y)z-\-x(\  —y)  (1  —  2)  —  ( 1  --x)  yz  + 
O(l--x)y(l—z)+0{l^x){l'-y)z  +  0{i—x){l—y){l—z). 
Now  all  those  terms  that  are  multiplied  by  0  necessarily 
vanish  and  the  remaining  terras  are 

xt/{l—z)=0,xz{l—y)=0,x(l-y){\-^z)=0,{l—x)yz=zO. 
Which  equations  all  express  the  denial,  or  nothingness,  of 
the  combinations  given  in  the  left  side  of  each.  Thus  x  y 
(1  —  z)  =  0  means  that  there  cannot  be  beasts  that  are  clean 
(x)  and  that  divide  the  hoof  (y),  and  that  do  not  chew  the 
cud  (1  —  2).  So  the  last  of  the  four,  (1  —  a?)  2/  «  =  0,  indi- 
cates that  there  are  no  beasts  unclean  (1  —  x)  and  yet  divid- 
ing the  hoof  (2/),  and  chewing  the  cud  (2). 

These  equivalent  forms  are  somewhat  obvious  in  themselves 
without  the  aid  of  analysis;  but  the  author  evolves  more 
complicated  equivalents,  such  as  these : — *  Unclean  beasts  are 


EQUIVALENT  FOKMS. 


201 


all  that  divide  the  hoof  without  chewing  the  cud,  all  that  chew 
thQ  cud  witliout  dividing  the  hoof,  and  all  that  neither  divide 
the  hoof  nor  chew  the  cud.'  The  reader  may  be  curious  to 
Bee  the  corresponding  equation  : — 

1  -  ^  =  2/ (1  -  ^)  +  2  (1  -  2/) +(  1  -  2^)  (1  ^  .). 
It  IS  obvious,  from  this  mstance,  that,  out  of  a  definition 
containing  three  or  four  defining  marks  (Senior's  definition  of 
wealth,  for  example),  a  great  many  equivalent  forms  are  deriv- 
able. Whether  there  be  any  important  form  that  the  unassisted 
mmd  might  not  evolve,  is  not  quite  apparent.  It  is  possible, 
however,  that  cases  might  arise  where  the  symbolical  method 
would  yield  equivalents  too  recondite  for  an  intellect  with 
only  the  ordinary  logical  training. 

The  author  extends  his  analysis  so  as  to  comprise  a  more 
difficult  order  of  examples,  typified  thus.  Suppose  the  analysis 
of  a  particular  class  of  substances  has  conducted  us  to  the 
following  general  conclusions,  namely  : — 

First.  Wherever  the  properties  A  and  B  are  combined, 
either  the  property  C  or  the  property  D  is  present  also ;  but 
they  are  not  present  jointly. 

Secondly.  Wherever  B  and  C  are  combined,  A  and  D  are 
either  both  present  or  both  absent. 

Thirdly.  Wherever  A  and  B  are  both  absent,  C  and  D  are 
both  absent  also ;  and  vice  versa,  where  C  and  D  are  both 
absent,  A  and  D  are  both  absent  also. 

Let  it  then  be  required  from  these  conditions  to  determine 
what  may  be  concluded  in  any  particular  instance  from  the 
presence  of  the  property  A,  with  respect  to  the  presence  or 
absence  of  the  properties  B  and  C,  paying  no  regard  to  the 
property  D.  The  working  of  the  corresponding  equations 
leads  to  this  answer  .-—Wherever  A  is  present,  there  either  0 
IS  present  and  B  absent^  or  C  is  absent.  And,  inversely, 
wherever  C  is  present  and  A  is  absent,  there  A  is  present. 

Several  other  curious  combinations  might  be  quoted,  still 
growing  out  of  the  equivalence  of  simple  propositions.  We 
are  next  led  t-o  the  consideration  of  Secondary  Propositions 
(hypotheticals,  &c.),  which  the  author  symbolizes  by  introduc- 
mg  the  idea  of  Time  as  their  peculiarity.  A  simple,  unqualified 
proposition  (affirmative)  holds  through  all  time  ;  a  negative, 
through  no  time ;  a  qualified  proposition  holds  only  throuo^h 
a  certain  limited  time.  The  symbol  1  may  represent  an 
unqualified  truth,  as  being  true  through  the  whole  universe  of 
time  ;  0  will  stand  for  an  unqualified  negation,  something  true 
for  no  time.     Let  X  represent  a  certain  proposition,  and  let  » 


n 


t 
I 


\ 


i 


i 


i 


202 


BOOLE'S  ADDITONS  TO  THE  SYLLOGISM. 


represent  the  time  of  its  being  trne.  So,  if  Y  represent 
another  proposition,  y  may  be  taken  for  the  time  of  its  being 
trne.  Taking  both  propositions  together,  x+y  will  denote  the 
aggregate  of  the  times  when  both  X  and  Y  are  respectively 
true,  those  times  being  separated  from  each  other.     Again, 

jp \j  may  denote  a  remainder  of  time  left  when  the  time  y  is 

taken  from  the  time  so,  it  being  supposed  that  x  includes  y. 
Q^^^^^y  ^iii  indicate  that  X  and  Y  are  true  for  identical 
times.     Further,  x  y  indicates  the  portion  of  time  when  X  and 

Y  are  both  true. 

Now,  as  X  denotes  the  time  of  X's  being  true,  I  —x  will 
denote  the  time  that  X  is  false.  So  a;  (1  —  ij)  will  denote  the 
time  when  X  is  true  and  Y  is  false :  and  so  on.  The  same 
system  is  to  be  applied  to  any  number  of  symbols. 

To  express  the  proposition  *  X  is  true  *  (there  being  no  limit 

or  qualification),  we  have 

X  =  1. 

To  express  the  dtoposition  *  X  is  false — .' 

a;  =  0. 

To  express — *  Either  the  proposition  X  is  true  or  the  propo- 
sition Y  is  true  (not  both).'  First,  *  When  X  is  true  Y  is 
false,'  is  signified  by  a:  (1  —  y)  ;  *  when  Y  is  true  X  is  false,' 
is  signified  hj  y  (I  —  x) :  the  equation  then  is 

a;  (1  — 2/)  +  2/{l— ^)  =  1- 
Next  to  express  the  conditional  Proposition,  *  If  the  proposi- 
tion Y  is  true,  the  proposition  X  is  true.'  This  implies  that 
whenever  Y  is  true,  X  is  true  ;  or  that  the  time  of  the  truth  of 
X  covers  the  whole  time  of  the  truth  of  Y,  and  possibly  more. 
Hence  X  is  at  least  equal  to,  if  not  larger  than  Y.  Conse- 
quently some  form  must  be  given,  implying  that  Y  is  contained 
in  X  :  a  form  analogous  to  that  required  for  a  universal  affir- 
mative proposition.  Let  v  represent  an  indefinite  portion  of 
time,  such  as  to  express  the  unknown  part  of  a  whole,  '  some, 
it  may  be — all,'  and  the  equation  required  is 

y  z=z  V  X. 
It  is  unnecessary  to  exemplify  the  symbolism  for  the  more 
complicated  cases.  The  author  is  so  far  carried  away  by  the 
success  of  his  expedient  for  expressing  compound  or  secondary 
propositions  by  a  reference  to  time,  that  he  speculates  on  an 
analogous  mode  of  expressing  the  primary  propositions  by  a 
reference  to  space  ;  and  thinks  that  he  thus  lends  some  coun- 
tenance to  the  doctrine  that  Space  and  Time  are  *  forms  of  the 
human  understanding.' 
A  chapter  is  devoted  to  the  treatment  of  the  secondary  pro- 


ENUMEKATION  OF  PROPOSITIONa 


203 


positions,  by  way  of  exhausting  their  whole  implication,  in  the 
^ffp^K  P^'^T'^'^y  shewn  for  the  primary  propositions;  the 
effect  bemg,  however,  merely  to  deduce  the  usual  consequences 
of  disj'inctive  and  of  conditional  assumptions.  It  is  to  be 
remarked  that  the  process  is  still  one  of  immediate  inference, 
confirming  the  view  that  iu  hypothetical  syllogisms  so-called 
there  is  no  real  or  mediate  inference. 

In  order  to  exhibit  the  value  of  the  symbolical  evolution  of 

rntt^^r''  ^^:g^,^«"tf  t^««»  sufficiently  perplexing  to  test  the 
powers  of  a  logical  method.  They  are  (1)  a  portion  of  Samuel 
^nd  r9^%  I>emonstration  of  the  Being  and  Attributes  of  God!' 
and  ( j;  bpinoza  s  argument  to  prove  the  identity  of  God  and 
the  Universe.  He  confessed  that  one  main  difficulty  in  dealing 
with  those  arguments  is  to  extricate  the  real  premises  of  th! 

fn.,^  fi  '  -^  "^'/^^  ^?^^  ^^^^^  ^^^  ^^^^b^'*  difficulty  of  assign, 
mg  definite  and  consistent  meanings  to  the  ^ry  abstract  terms 
made  use  of  by  them-necessity,  existence,  eternity,  cause,  &c. 
But  the  premises  once  obtained,  it  is  possible  to  embody  them 
m  symbols,  and  then  to  extract  all  their  equivalents  by  solving 
as  anTnf '^"""f  ^"^  equations.     The  method  may  be  commended 

follow^H  r  T  '^T^'  T^^"^  '^"^  corroborating  the  method 
lollowed  by  a  logical  and  acute  mind  working  upon  the  ipsa 
corpora  of  the  premises,  without  symbolism.  ^  ^ 

We  have  now  reviewed  the  larger  half  of  Boole's  work,  and 

k  an  fw -'"r  r  "'^"^^^'^  °^  *^"  syllogism.  A  short  chapter 
IS  all  that  IS  bestowed  upon  mediate  inference ;  which  how- 
ever is  a  mere  carrying  out  of  the  algebraic  method,  with  the 
modifications  demanded  by  the  nature  of  the  case. 
i^^l  r'""^  by  accepting  De  Morgan's  additions  to  the  four 
types  of  propositions  m  the  common  Logic.  He  lays  out  the 
eight  forms  with  his  equations  for  them  :  expressing  the  four 
forls  Th^  supplying  a  contrary  subject  to  each  of  the  old 
lorms.      Ihe  parallelism  is  shown  thus 


A  — 

(A) 
E 

(E) 

=   I  All  Xs  are  Ys 

I  Some  Ys  are  Xs 

(I)  Some  not-Ys  are  Xs 


All  Ys  are  Xs 
All  not-Ys  are  Xs 
No  Ys  are  Xs 
No  not-Ys  are  Xs 


y  -=2  V  X 
\  —  y  •=.  V  X 

y  =  V  (1  —  x) 


1  — y  =  ^(l 

a;  =  -y  7/  I 
V  y  =i  V  X 


vx 


O) 

(2) 
(3) 

(4) 


(5) 

(6) 


\\ 


I 


204 


BOOLE'S   ADDITIONS  TO   THE   SYLLOGISM. 


I 


=  4  Some  Xs  are  not  Ys  v  7/  =  v  (1  —  J/)  j 

O  Some  Ys  are  not  Xs  vy  =  v  (I  ^  x)  (7) 

(O)        Some  not-Ys  are  not-Xs      v(\ —y)  =  v  (l  — x)  (8) 

The  second  form  of  E  coincides  with  A  by  mere  transposition 
of  letters.  The  second  form  of  I  is  O,  in  like  manner.  The 
second  form  of  O  (0)  is  the  only  new  form— Some  not-Ys  are 
not-Xs,  some  things  are  neither  Ys  nor  Xs.  This  is  one  of 
De  Morgan's  two  disjunctives;  his  other  disjunctive— no 
not-X  is  not  Y,  every  thing  is  either  X  or  Y— does  not  appear 
in  the  above  list. 

The  laws  of  Conversion  follow  from  the  symbolical  forms. 
The  proposition  *  All  Ys  are  Xs  *  being  represented  by 
y  =z  V  X,  we  have  only  to  read  v  x  =  y,  Some  Xs  are  Ys.  To 
convert  the  same  proposition  by  negation  (obversion  and  con- 
version), we  deduce,  by  eliminating  v, 

2,(l-*)  =  0 
which  gives  by  solution  with  reference  to  1  —  ar, 

1  —  a;  =  ^  (1  —  y), 

whose  interpretation  is  *  All  not-Xs  are  not-Ys.  [This  opera- 
tion contains  methods  and  symbols  not  explained  in  the  fore- 
going abstract]. 

So  far  as  Conversion  goes,  the  author  merely  continues  his 
former  methods  of  reducing  and  interpreting  equations  ;  as  we 
might  expect  from  considering  that  conversion  is  merely  one 
variety  of  Immediate  or  Equivalent  Inference.  The  syllogism 
demands  a  step  in  advance.  The  two  premises  must  be  em- 
bodied in  two  equations,  with  a  common  middle  term,  and  that 
term  must  be  made  to  disappear  in  a  third  formed  out  of  these 
two.     Thus, 

All  Xs  are  Ys  x  =z  v  1/ 

All  Ys  are  Zs  y  =  v'  z. 

Whence,  by  substituting  for  2/>  in  the  first  equation,  its 
value  in  the  tecond,  we  have 

All  Xs  are  Zs  ar  =  v  v'  r. 

The  form  v  vz  shows  that  a;  is  a  part  of  a  part  of  2.  So  with 
all  other  cases  ;  it  is  requisite  merely  to  eliminate  the  middle 
term  y.  The  method  might  be  easily  carried  through  the 
whole  of  the  ordinary  syllogisms  ;  as  well  as  applied  to  the  uu- 
figured  and  fallacious  forms.  But  the  author  proceeds  to 
deduce  the  general  rules  of  the  syllogism  by  an  equation  com- 
prehending all  the  forms  of  valid  reasoning.  He  gives  as  the 
results  of  the  analysis  these  rules  :  *  when  one  middle  term,  at 


RULES   OF  THE   SYLLOGISM. 


205 


least  is  universal,  equate  the  extremes.*  *In  case  of  unlike 
middle  terms  (one  positive  and  the  other  negative),  with  one 
universal  extreme,  change  the  quantity  and  quality  of  that 
extreme,  and  equate  the  result  to  the  other  extreme  :  and  with 
two  universal  middle  terms,  change  the  quantity  and  the 
quality  of  either  extreme,  and  equate  the  result  to  the  other 
extreme  unchanged.* 

Suppose  the  case — 

All  Ys  are  Xs 
All  Zs  are  Ys. 

This  belongs  to  the  first  rule.  *  All  Ys  *  is  the  universal 
middle  term  ;  the  extremes  being  equated  give  as  the  conclu- 
sion, 

All  Zs  are  Xs. 

Suppose  next — 

All  Xs  are  Ys 
No  Z3  are  Ys. 
The  proper  expression  of  these  premises  is — 

All  Xs  are  Ys 
All  Zs  are  not-Ys. 
They  belong  to  the  case  of  unlike  middle  terms,  and  have 
one  universal  extreme.      Whence,  by  application  of  the  rule, 
we  change  the  quality  and  the  quantity  of  that  extreme,  and 
equate  it  with  the  other  extreme — 

AH  Xs  are  not  Zs,      or  No  Xs  are  Zs. 
Commencing  from  the  other  universal  extreme,  we  obtain 
the  equivalent  result — 

No  Zs  are  Xs. 
A  third  case — 

All  Ys  are  Xs 

All  not-Ys  are  Zs. 
Here  the  terms  are  of  unlike  quality.      There  are  two  uni- 
versal middle  terms,  and,  by  the  rule,  we  change  the  qu^  ^tity 
and  the  quality  of  either  extreme  (Some  Xs  into  All  -.ot-Xs), 
and  equate  with  the  other  extreme  (Some  Zs). 

All  not-Xs  are  Zs. 
The  two  last  examples  are  selected  by  the  author  as  present- 
ing syllogisms  that  would  not  be  regarded  as  valid  in. the 
Scholastic  Logic,  which  virtually  requires  that  the  subject  of  a 
proposition  should  be  positive.  [As  often  remarked  already, 
the  want  of  a  thorough-going  recognition  of  contraries  is  the 
defect  of  the  Aristotelian  scheme].  The  cases  are,  however, 
perfectly  legitimate  in  themselves,  and  the  rules  for  determin- 
ing them  are  undoubtedly  the  most  general  canons  of  sylhijlstie 


i  F 


I 


% 


I 


206 


BOOLE'S  ADDITIONS  TO  THE  SYLLOGISM. 


inferevce.  The  analysis  employed,  the  anihor  contends,  is  not 
properly  of  the  syllogism,  but  of  a  much  more  general  mode 
of  combining  propositions  to  yield  results ;  and  he  gives  an 
imaginary  case  to  illustrate  this  wider  import. 

Without  pursuing  the  syllogism  farther,  Boole  now  dis- 
cusses the  vexed  question  as  to  the  fundamental  type  of  de- 
ductive reasoning,  and  takes  issue  with  Whately  and  with 
Mill,  who  agree  in  this  that  all  valid  ratiocination  is  ultimately 
the  inferring  of  propositions  from  others  of  a  more  general 
kind ;  the  syllogism  being  a  full  and  adequate  formal  repre- 
sentation of  the  process.  Now,  as  the  Syllogism  is  a  species 
of  elimination,  the  question  resolves  itself  into  these  two  deter- 
minations, namely,  first,  whether  all  elimination  is  reducible 
to  Syllogism ;  and,  secondly,  whether  deductive  reasoning 
consists  only  of  elimination. 

To  the  first  question,  he  replies,  that  it  is  always  theoreti- 
cally possible  so  to  resolve  and  to  combine  propositions  that 
elimination  may  subsequently  be  effected  by  the  syllogistic 
canons,  but  that  the  process  of  reduction  would,  in  many  cases, 
be  constrained  and  unnatural,  and  would  involve  operations 
that  are  not  syllogistic. 

To  the  second  question,  he  replies  that  reasoning  cannot,  ex- 
cept by  arbitrary  restriction,  be  confined  to  elimination.  It 
cannot  be  less  than  the  aggregate  of  the  methods  founded  on 
the  Laws  of  Thought,  and  the  process  of  elimination,  import- 
ant as  it  is,  is  only  one  process  among  others. 

He  farther  remarks  that,  of  all  the  Laws  of  Thought,  the 
one  of  fundamental  importance  in  Logic,  is  the  Law  of  Con- 
tradiction, to  which  Leibnitz  also  assigned  the  same  position. 

All  persons  that  have  attained  a  just  notion  of  the  Rela- 
tivity of  Knowledge,  would  agree  with  Boole  in  the  prime  im- 
portance thus  given  to  Contrariety  or  Contradiction  ;  but  this 
merely  goes  the  length  of  Equivalence  or  Immediate  Inference. 
It  prepares  the  way  for  Syllogism,  and  is  the  main  key  to  the 
useful  enlargements  of  the  syllogism  ;  but  it  does  not  touch 
what  is  essential  to  deduction.  The  axiom,  or  '  law  of  thought,' 
at  the  foundation  of  mediate  inference  must  be  something  else, 
and  if  it  is  not  the  axiom  assigned  in  the  previous  chapter  of 
this  work,  it  is  an  axiom  yet  to  be  sought.  Passing  from  Boole's 
somewhat  vague  generalities  to  his  actual  method,  which  con- 
sists in  combining  two  equations  standing  for  the  premises  of 
the  syllogism,  into  a  third  standing  for  the  conclusion  ;  and 
adverting  to  the  maxim  that  justifies  the  process  of  reduction, 


AXIOM   OF  THE  SYLLOGISM. 


207 


we  seem  to  see  that  it  is  the  same  maxim  as  enters  into  a  pro- 
blem of  equations  with  two  or  more  unknown  quantities  ;  as 
for  example,  given  a;  -f.  y  =  a,  «  —  y  =  6,  to  find  x  and  y. 
Orrant  that  the  conditions  of  a  logical  syllogism  are  fairly  ex- 
pressed by  Boole's  symbols,  and  that  the  algebraic  reduction  is 
suitable  and  relevant  to  the  case,  then  the  logical  axiom  is  the 
algebraic  axiom  that  permits  the  substituting   for  y  in  one 
equation,  of  its  equivalent  in  the  other ;  as  when  we  obtain  from 
*. "~  y  ==  ^»  y  =  »  —  ^,  and  insert  this  value  of  y  in  the  equa- 
tion  X  +  y  =  a.     The  axiom  of  direct  application  to   the 
case  would  be  that,  for  any  quantity,  its  equivalent  may  be 
substituted  m  an  equation ;  in   other  words,  the  substitution, 
for  any  quantity,  of  its  equivalent,  does  not  change  the  value 
of  the  equation.     This  is  a  various  reading  of  the  axiom    of 
mediate  equality— things  equal  to  the  same  thing  are  equal  to 
one  another ;  an  axiom  to  which  Mr.  Mill  compares,  in  point 
of  form,  the  axiom  of  the  syllogism.     If  one  thing  is  equal  to 
a  second,  and  the  second  equal  to  a  third,  the  first  is  also  equal 
to  the  third.     In  a  combination  containing  A  and  B,  we  may 
mtroduce  in  room  of  B  its  equivalent  C. 

A  large  portion  of  the  work  is  devoted  to  Probabilities,  in 
handlmg  which,  the  author  continues  the  symbolism  employed 
m  the  previous  portion  of  the  work.  It  is  generally  admitted 
that  he  has  made  important  additions  to  the  theory  of  this 
subject,  the  common  ground  of  Mathematics  and  of  Logia 


CHAPTER  m. 
FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 

1.  It  is  the  peculiarity  of  the  Syllogism,  that  the  conclu- 
sion does  not  advance  beyond  the  premises.  This  circum- 
stance has  been  viewed  in  two  lights. 

On  the  one  hand,  it  is  regarded  as  the  characteristic 
excellence  of  the  Syllogism. 

On  the  other  hand,  it  is  represented  as  constitutiug  a 
petitio  principiL 

In  the  syllogism  *  men  are  mortal,  kings  are  men,  kings  are 
mortal.'  the  conclusion  seems  already  affirmed  in  the  premises. 


I 


[ 


V   i 


I 


9 


208 


FUNCTIONS   AND   VALUE  OF  THii:  SYLLOGISM. 


By  virtue  of  the  nniversal  major,  coupled  with  the  interpreting 
minor,  there  is  distinctly  involved  in  the  premises  the  fact  that 

*  kings  are  mortal/  .         j   ii  r 

(1)  To  this  circumstance  Las  been  attributed  the  peculiar 
excellence,  dignity,  and  certainty  of  syllogistic  mference. 
When  the  two  premises  are  supplied,  the  conclusion  cannot  be 
refused  without  self-contradiction.  There  is  nothing  precarious 
in  the  leap  from  the  premises  to  the  conclusion. 

The  same  circumstance  has  been  represented  in  a  more  dis- 
advantageous light.  The  allegation  is  made  that  mere  repeti- 
tion is  not  inference  :  that  to  reproduce  in  a  new  form  what  is 
already  given  may  be  highly  convenient  (as  in  the  various 
kinds  of  Immediate  Inference),  but  is  no  march,  no  progress 
from  the  known  to  the  unknown. 

(2)  There  remains  a  far  more  serious  charge,  and  one  that 
takes  us  direct  to  the  root  of  Formal  Reasoning.  Supposing 
there  were  any  doubt  as  to  the  conclusion  that  kings  are  mortal, 
by  what  right  do  we  proclaim,  in  the  major,  that  all  men  are 
mortal,  kings  included  ? 

It  would  be  requisite,  seemingly,  to  establish  the  conclusion 
before  we  can  establish  the  major.  In  order  to  say,  *  All  men 
are  mortal,'  we  must  have  found,  in  some  other  way,  that  all 
kings,  and  all  peoples  are  mortal.  So  that  the  conclusion  first 
contributes  its  quota  to  the  major  premise,  and  then  takes  it 

back  again.  , 

This  is  the  deadlock  of  the  syllogism,  the  circumstance  that 
has  brought  down  upon  it  the  charge  of  *  reasoning  in  a  circle 
(petitio  pnncipii).     In  point  of  fact,  we  can  hardly  produce  a 
more  glaring  case  of  that  fallacy.  t  i.    oi.     ^ 

The  extrication  from  the  puzzle  is  due  to  Mr.  John  Stuart 
Mill,  and  the  consequence  has  been  a  total  revolution  in  Logic. 

2.  The  major  premise  of  a  syllogism  (in  the  regular 
figure)  may,  so  far  as  the  evidence  is  concerned,  be  divided 
into  two  parts  ;  the  one  part  containing  the  instances 
observed,  and  the  other  part  containing  the  instances  not 
observed,  but  inferred. 

The  major  premise,  *  All  men  are  mortal,'  consists  of  two 
very  difi'erent  statements.  The  first  is,  that  a  certain  number 
of  men  have  actually  died.  The  evidence  for  these  is  actual 
observation,  the  highest  of  all  evidence.  The  second  statement 
is,  that  the  men  now  living,  and  the  men  yet  to  be  born,  will 
die  ;  for  which  there  is  not  the  evidence  of  observation. 

In  the  same  manner  may  we  analyze  any   other   general 


EEASONING  IS  FROM  PARTICULARS  TO  PARTICULARS.    209 

affirmation  or  negation.  The  proposition  *  transparent  bodies 
bend  light '  is  made  up  of  the  bodies  that  have  been  actually 
experimented  on,  and  of  bodies  that  have  not  been  experi- 
mented on ;  in  the  one  case,  the  predicate  is  affirmed  on  the 
evidence  of  fact ;  in  the  other  case,  the  predicate  is  affirmed  by 
virtue  of  the  inductive  leap  from  the  known  to  the  unknown. 

Thus,  the  ordinary  form  of  the  general  proposition  confounds 
together  the  observed  with  the  unobserved ;  the  indiscriminate 
fusion  of  the  two  is  what  has  perplexed  the  theory  of  the 
syllogism. 

3.  In  affirming  a  general  proposition,  real  Inference  is 
exhausted. 

When  we  have  said  *  All  men  are  mortal,'  we  have  made 
the  greatest  possible  stretch  of  inference.  We  have  affirmed 
mortality  of  all  men,  of  every  class,  in  every  age,  past  and 
future.  We  have  incurred  the  utmost  peril  of  the  inductive 
hazard.  Whatever  justification  needs  to  be  offered  for  the 
inference  in  hand,  must  be  advanced  as  a  security  for  the 
major  premise. 

4.  The  type  of  reasoning  that  best  discloses  the  real 
process  is  reasoning  from  Particulars  to  Particulars. 

The  basis  of  fact  in  every  argument  may  be  stated  to  be 
the  particulars  actually  known  from  experience ;  as  the  mor- 
tality of  the  men  that  have  died.  The  inference  is  usually  to 
some  other  particulars  unobserved,  as  *  the  present  inhabitants 
of  London  will  dia'  The  real  evidence  for  the  mortality  of 
the  men  now  living  is  the  death  of  their  predecessors.  A,  B, 
and  C,  have  died  ;  D,  now  living,  will  die. 

The  practice  of  reasoning  at  once  from  certain  particulars 
experienced,  to  some  other  particular  as  yet  unexperienced, 
(there  being  a  similarity  in  the  cases)  is  not  only  the  usual, 
but  the  most  obvious  and  ready  method.  We  feel  that  the 
real  force  of  every  reasoning  lies  not  in  the  general  statement, 
but  in  the  actual  facts ;  and  we  are  as  much  moved  by  the 
facts  in  their  particularity,  as  when  they  are  given  in  a  gene- 
rality. That  boiling  water  will  scald  the  hand,  is  sufficiently 
proved  by  its  having  done  so  in  innumerable  past  instances ; 
the  deterring  force  Hes  in  these  a<;tual  instances.  We  are  in- 
fluenced by  individual  precedents,  as  strongly  as  by  rules. 

This  is  seen  extensively  in  all  professions.     The  experience 
of  a  professional  man  consists  of  the  cases  he  has  actually  ob- 


>  if 


iiii 


!!, 


-J 

I 


I  m 


$ 


210  FUNCTIONS  AND   VALUE  OF  THE  SYLLOGISM. 

served  ;  these  he  remembers  as  particulars,  and  when  a  new 
example  is  presented,  he  at  once  assimilates  that  with  the  pre- 
vious particulars,  and  infers  accordingly.  When  Dr.  Mead 
was  called  in  to  the  last  illness  of  Qaeen  Mary,  he  pronounced 
the  disease  to  be  small  pox  ;  his  knowledge  of  that  ailment 
was  the  remembrance  of  a  series  of  patients  previously  wit- 
nessed by  him  ;  the  queen's  symptoms  resembled  those,  and  he 
drew  the  inference. 

5.  Wherever  we  may  infer  from  a  certain  number  of 
particulars  given,  to  one  other  particular,  we  may  infer  to 
a  whole  class,  or  make  the  inference  general. 

If  we  can  infer,  from  the  men  that  have  died,  that  the  pre- 
sent Pope  will  die,  it  is  by  virtue  of  a  sufficient  amount  of  re- 
semblance between  them  and  him ;  and  we  must  be  prepared 
to  make  the  same  inference  in  all  other  cases  where  the  re- 
semblance holds.  We  may,  therefore,  say  once  for  all,  whoever 
resembles  past  generations  of  human  beings,  in  the  points 
wherein  the  pope  resembles  them,  will  die.  The  justification 
of  one  is  the  justification  of  the  whole.  The  inference  to  an 
individual  case  must  not  be  arbitrary  ;  it  must  be  grounded  on 
a  resemblance,  and  be  applicable  wherever  the  resemblance  is 

found. 

In  a  general  proposition,  therefore,  we  state  the  points  of 
resemhlance  that  entitle  us  to  infer  from  past  particulars  to  a 
new  particular ;  and  in  stating  these  points  we  render  the  in- 
ference at  once  general,  and  formally  exhaustive.  We  mingle 
up  in  one  statement  the  observed  known,  and  the  inferred 
unknown,  the  evidence  and  the  conclusions.  The  use  of 
general  language  enables  us  thus  to  rise  beyond  particular 
inferences. 

6.  Deductive  Inference  may  be  described  as  a  process  of 

Interpretation. 

Although  the  major  premise  covers  the  conclusion,  it  does 
not  point  to  it  by  name,  but  only  by  character.  The  premise 
*  men  are  mortal '  does  not  specify  kings,  nor  the  living  pope  ; 
it  indicates  certain  marks  by  which  we  are  to  judge  whether 
kings  and  popes  are  to  be  pronounced  mortal,  namely,  the 
marks  of  *  men  or  humanity.'  Something,  therefore,  is  want- 
ing in  addition  to  the  major  premise,  in  order  to  the  conclu- 
sion, the  pope  is  mortal ;  we  have  to  be  assured  that  he  is  a 
man,  that  he  conforms  to  the  defining  marks  of  human  beings. 
To  supply  this  requisite  is  the  purpose  of  the  minor  premise, 


DEDUCTIVE  INFERENCE   IS  INTERPRETATION 


211 


i ' 


which  declares  that  the  pope  possesses  the  attributes  of  men, 
or  identifies  him  with  the  subject  of  the  major  premise.  The 
necessity  for  such  an  affirmation  rescues  the  syllogism  from 
Immediate  Inference  or  tautology.  *  All  men  are  mortal  *  in- 
cludes *  the  pope  is  mortal,'  on  the  supposition  that  the  pope  is 
a  man  ;  and  if  this  supposition  is  explicitly  given  in  a  distinct 
proposition,  the  pope  is  then  brought  within  the  sweep  of  the 
major  premise  :  and  the  conclusion  is  established. 

After  affirming  a  general  proposition  (or  making  a  general 
denial)  connecting  or  disconnecting  a  certain  subject  with  a 
certain  predicate — men  and  mortality —  we  have  still  to  hunt 
out  the  particular  cases  of  the  subject,  the  things  that  possess 
its  attributes.  This  is  the  real  deduction,  and  it  is  a  material 
and  not  a  formal  process.  It  is  an  operation  of  comparing  the 
actual  individuals  already  pointed  out  by  the  generalized  subject 
— actual  and  known  men — with  all  future  individuals  as  they 
occur,  and  of  pronouncing  agreement  of  the  new  with  the  old. 
The  deductive  inference  that  *  the  pope  is  mortal,'  presupposes 
an  examination  (direct  or  indirect)  of  the  pope's  personality. 
If  this  resembles  the  usual  type  of  humanity,  judged  from  the 
instances  actually  known  to  us,  we  identify  him  with  the 
subject,  *  men,'  in  our  general  proposition.  The  identity  being 
considered  satisfactory,  we  complete  the  syllogistic  formula, 
and  declare  him  to  be  mortal. 

The  proposition  *men  are  mortal,*  by  its  form  of  universality, 
imposes  upon  us,  and  leads  us  to  suppose  that  we  have  in  our 
grasp  the  whole  human  race.  The  correcter  view  is  to  regard 
it  as  an  allegation  respecting  a  certain  number,  with  a  power 
of  including  others  as  they  come  on  the  stage.  The  proposition 
assigns  marks  for  the  future  identification  of  the  beings  that 
are  to  be  declared  mortal ;  and,  as  the  identification  proceeds, 
the  minor  premise  is  replenished  with  appropriate  cases,  and 
so  brings  forth  the  conclusion. 

The  interpretation  of  a  law  or  a  command  illustrates  the 
purely  deductive  part  of  the  operation  of  reasoning — the  sup- 
plying of  the  minor.  The  law  is  given  in  general  terms ;  cer- 
tain characters  are  assigned  as  belonging  to  the  subject  of  the 
proposition.  The  administrator  or  judge  ascertains  whether 
any  particular  case  has  or  has  not  the  characters  specified.  If 
it  has,  a  minor  proposition  is  afforded,  and  a  conclusion  is 
drawn. 

This  case  also  shows  that  the  syllogism  is  the  mere  formal 
completing  of  an  operation,  not  at  all  formal,  but  in  the  strict 
sense  material.     The  operation  consists  in  comparing  one  par- 


mmimmmpm 


212       FUNcrnoNS  and  value  of  the  syllogism. 

ticular  fact  with  other  particnlar  facts,  throtlgh  the  medium  of 
•a  general  description.  The  wording  of  a  law,  however  gene- 
ral be  the  terras,  mnst  be  snch  as  to  suggest  definite  individual 
cases.  When  the  law  mentions  heritable  property,  or  person- 
alty, it  must  either  state  or  suggest  the  particular  things  in- 
tended ;  and  the  question  of  the  application  to  a  given  case 
turns  upon  the  comparison  of  the  case  with  the  cases  cited 
or  suggested  by  the  general  term  or  definition.  Hence,  the 
business  of  the  reasoner,  in  actual  practice,  is  concrete  com- 
parison, from  which,  in  the  last  resort,  he  can  never  be  ex- 
empted.  This  is  material  deduction,  which,  in  its  essence,  is  the 
same  as  material  induction,  being  the  carrying  out  of  the  in- 
ductive operation,  or  the  in-gathering  of  the  details  shadowed 
forth,  but  not  actually  seen,  in  the  general  proposition. 

Legal  decisions  are  founded  sometimes  on  statutes,  some- 
times^'on  precedents  or  previous  decisions.  There  is  no  generic 
distinction  between  the  two  modes.  A  statute  has  no  meaning 
except  the  particular  cases  specified  or  suggested  ;  and  a  pre- 
cedent must  involve  a  principle  or  rule.  In  both,  the  judge 
refers  back  to  concrete  particulars,  which  are  viewed  under  a 
certain  point  of  likeness  or  community. 

Another  case  is  the  application  of  general  theorems  furnished 
by  the  observations  of  others,  such  as  the  principles  of  science 
established  by  foregone  researches.  We  may  have  had  no 
share  in  arriving  at  the  induction  known  as  the  atomic  theory  ; 
we  have  not  even  seen  the  facts,  we  receive  them  embodied 
and  registered  in  the  general  statement  of  the  law.  We  must 
understand  the  meaning  of  that  statement ;  we  must  realize 
the  kind  of  facts  intended  by  it.  When  a  case  is  started,  a 
given  compound  of  two  substances,  we  must  say,  by  concrete 
comparison,  whether  this  compound  has  the  characters  of  the 
compounds  expressed  as  chemical  compounds.  For  example, 
is  the  atmosphere  a  chemical  compound  P  Does  it  agree  with 
the  general  characters  of  chemical  compounds,  or  with  those 
typical  instances  that  the  general  characters  can  do  nothing 
but  refer  us  to.  '  This  is  a  truly  material  deduction  ;  it  is  that 
process  of  comparing  instances  that  is  the  essence  of  the 
generalizing  operation,  as  seen  in  induction.  It  exactly 
resembles  generalization  with  a  view  to  definition. 

7.  Although  the  deductive  stage  of  induction  is  still  an 
inference  from  particulars  to  particulars,  which  nothing 
can  supersede,  there  are  certain  advantages  in  embodying 
the  possible  inferences  in  ft  formal  generality. 


UTILITY   OF  THE   SYLLOGISM. 


213 


Mr.  Mill  remarks  that  the  syllogistic  form  of  inference,  from 
generals  to  particulars,  which  supposes  that  each  induction 
is  made  general,  is  *  a  collateral  security  for  the  correctness  of 
the  generalization  itself.*     It  is  so  in  two  ways. 

First.  It  increases  the  sense  of  responsibility  on  the  part  of 
the  reasoner,  by  letting  him  know  that  his  inference  to  one 
individual  must  equally  apply  to  a  large  host  of  individuals. 
A  common  device  for  checking  a  rash  inference  is  to  point  out 
the  extent  of  the  consequences  involved.  The  legal  decision 
against  John  Hampden,  in  the  matter  of  thirty  shillings  of 
ship  money,  was  portentous  as  affirming  tlie  king's  power  to 
tax  the  nation  without  a  parliament. 

Secondly.  If  an  induction  is  unsound,  the  making  it 
general  is  likely  to  suggest  contradictory  instances.  This  is 
merely  a  modification  of  the  same  consequence.  Any  person 
attempting  to  justify  a  particular  despotism  must  be  prepared 
to  say  that,  in  all  similar  circumstances,  despotism  would  be 
desirable.  The  remark  is  sometimes  made,  in  the  controversy 
as  to  the  inspiration  of  the  Bible,  that  even  Milton  was 
inspired ;  but,  if  so,  then  all  great  poets — Homer,  Virgil, 
Dante,  Chaucer,  Shakespeare,  Dry  den,  Byron,  Shelley — must 
also  own  the  gift  of  inspiration, 

Mr.  Grote,  in  defending  the  received  canon  of  the  Platonic 
writings  from  the  critics  that  would  reject  many  of  the  Dia- 
logues, on  the  ground  of  their  style  being  unworthy  of  Plato, 
points  out  the  numerous  Dialogues  that  would  have  to  be 
sacrificed  to  this  criterion,  if  each  critic  were  allowed  to  reject 
for  himself,  and  all  rejections  were  admitted. 

8.  One  great  use  of  the  syllogistic  form  is  to  analyze, 
bring  to  light,  and  present  for  separate  consideration,  the 
parts  of  a  step  or  a  chain  of  reasoning. 

This  has  been  already  exemplified  in  the  applications  of  the 
syllogism  to  confused  reasonings.  It  is  advantageous  to  know 
that  the  truth  of  a  conclusion  by  inference  supposes  the  truth 
of  two  separate  allegations,  both  alike  necessary  to  the  conclu- 
sion. To  prove  that  A  is  C,  by  a  mediate  inference  (B  is  C, 
A  is  B),  two  propositions  have  to  be  verified ;  and  the  mind  is 
aided  in  disentangling  a  perplexed  argumentation,  by  knowing 
what  to  look  out  for. 

In  stating  the  distinction  between  the  two  modes  of  reasoning, 
used  both  in  Law  and  in  Politics — reasoning  from  Precedents  or 
Examples,  and  reasoning  from  Eules  or  Principles — Sir  G.  C. 
Lewis  adverts  to  the  great  superiority  of  the  last,  the  reasoning 


if 


f:. 


'" 


214    TRAINS  OF   REASONING  AND  DEDUCTIVE  SCIENCES. 

from  Rules.  The  reason  of  the  comparative  obscurity  of  the 
argument  from  example  or  precedent,  is  that  the  principle  involved 
is  usually  suppressed.  '  The  reasoning  is  much  more  perspicuous 
when  the  general  principle  is  stated  first,  the  particular  case  is 
placed  under  it,  and  the  conclusion  is  then  drawn.  In  order  to 
argue  from  one  case  to  another,  it  is  necessary  to  reject  from  each 
the  circumstances  immaterial  to  the  matter  in  hand,  and  to 
compare  those  in  which  they  agree.  In  complex  cases,  this  process 
is  often  extremely  difficult.  Much  sagacity  and  knowledge  of  the 
subject  are  required,  in  order  to  discriminate  between  material 
and  immaterial  facts — to  reject  enough,  but  not  more  than 
enough.  For  if  immaterial  facts  are  retained,  the  comparison 
becomes  obscure  and  uncertain;  if  material  facts  are  rejected,  it 
becomes  fallacious.  This  process,  which,  in  the  argument  from 
precedent,  must  often  be  performed  mentally,  though  it  may  be 
easy  and  sure  to  the  experienced  practician,  perplexes  the  tiro. 
Hence,  students  of  the  law  have  great  difficulty  in  collecting  legal 
rules  from  cases,  though  they  are  soon  able  to  apply  a  rule  of  law, 
laid  down  in  general  terms,  to  a  particular  case  of  practice.' 


CHAPTER  IV. 
TRAINS  OF  REASONING  AND  DEDUCTIVE  SCIENCES. 

1.  A  series  of  syllogisms  may  be  connected  in  a  chain. 

Logicians  have  always  recognized  compound  reasonings. 
The  Sorites  is  a  connected  chain  of  syllogisms.  The  conclusion 
of  one  syllogism  may  be  the  major  premise  to  a  second,  and  so  on. 

The  /Soi'ites  is  usually  stated  in  this  form  : — 

A  is  B,  B  is  C,  0  is  D,  &c.,  therefore  A  is  D. 

The  regular  form  of  proof  (by  the  First  Figure  of  the  Syllo- 
gism') is — 

B  is  C,  A  is  B,  therefore  A  is  C. 
C  is  D,  A  is  C,  therefore  A  is  D,  &c. 

It  can  scarcely  ever  happen  that  a  proper  deduction  in  this 
simple  form  can  be  protracted  over  two  or  three  syllogisms. 
The  application  of  a  universal  proposition  to  a  particular  case 
seldom  needs  to  descend  by  three  or  more  distinct  steps : 
indeed,  in  by  far  the  greater  number  of  instances,  the  descent 
is  made  at  once. 

No  new  logical  principle,  or  modification  of  principle,  is 
involved  in  these  consecutive  reasonings.     Their  lucid  state* 


EXAMPLE  OF  A  CHAIN. 


215 


ment  is  a  matter  of  consideration  for  the  expositor,  but  they 
present  no  speciality  to  the  logician.  Still,  they  are  usually 
discussed  in  treatises  on  logic ;  and  we  may,  following  the 
example  of  Mr.  Mill,  take  occasion  from  them  to  discuss  two 
themes — the  compatibility  of  the  foregoing  theory  of  the  syllo- 
gism with  such  trains,  and  the  nature  of  the  Deductive 
Sciences. 

^  2.  A  chain  of  Reasoning  is  reducible  to  a  series  of  syllo- 
gisms, the  major  in  each  being  an  induction  from  par- 
ticulars, or  a  truth  ultimately  based  in  particulars. 

Thus,  if  we  were  to  prove  that  intelligent  beings,  although 
they  may  be  interrogated,  are  not  to  be  experimented  on  like 
brute  matter,  we  should  have  the  following  chain  : — wherever 
there  is  intelligence,  there  is  sensibility,  in  other  words,  suscepti- 
bility to  pleasure  and  pain  ;  we  are  not  at  liberty  to  inflict  pain  ; 
now,  most  experiments  that  could  be  tried  upon  sentient  crea- 
tures would  be  painful ;  hence,  intelligent  beings  are  not  fit 
subjects  for  experimental  enquiry.  Three  syllogisms  are  con- 
cerned in  this  chain  of  reasoning.     The  majors  are — 

( 1 )  Society  prohibits  the  infliction  of  pain. 

(2)  All  intelligent  beings  have  sensibility  to  pain. 

(3)  Experiments  for  ascertaining  function  in  sentient  beings 
lead  to  pain. 

Each  of  these  majors  may  be  resolved,  according  to  the 
method  of  the  previous  chapter,  into  particulars  observed  and 
particulars  inferred,  or  left  to  be  inferred,  by  virtue  of  identity. 
The  first  major  (Society  prohibits)  is  in  the  form  of  a  command, 
the  case  where  we  may  be  supposed  to  be  least  concerned  with 
the  particulars,  and  most  concerned  with  the  general  descrip- 
tion serving  to  identify  the  particulars.  Still  it  must  not  be 
forgotten  that  the  real  force  even  of  a  command  is  embodied 
in  the  instances  where  it  is  enforced ;  the  general  state- 
ment means  nothing,  is  nothing,  except  as  referring  us  to 
these ;  the  application  of  the  rule  is  an  inductive  extension 
of  these  instances.  The  second  major  (intelligent  beings  have 
sensibility)  takes  in  the  observed  coincidences  of  intelligence 
and  sensibility,  together  with  the  future  extensions  of  these  by 
identification  with  the  presence  of  intelligence — the  first  term 
of  the  couple,  The  third  major  is  likewise  an  inductive  gene- 
ralization, containing  the  observed  particulars  where  experi- 
menting has  ended  in  pain,  together  with  the  resembling 
inferred  particulars. 

We  may  arrange  the  train  of  reasoning  in  syllogisms.  Thus, 
— taking  a  difierent  order — 


216   TKAINS   OF  REASONING  AND   DEDUCTIVE   SCIENCES. 

First  Syllogism, 

Experiments  for  ascertaining  function  in  sentient  creatures 

lead  to  pain. 
The  present  proposal  is   an   experiment  for  ascertaining 

function. 
The  present  proposal  will  lead  to  pain  (Barbara). 

Second  Syllogism. 

Society  prohibits  the  infliction  of  pain. 
The  present  proposal  will  lead  to  pain. 
Society  prohibits  the  proposal  to  experiment  on  sentient 
beings  (Cesare), 

Tliird  Syllogism, 

Society  prohibits  experiments  on  sentient  beings. 

All  intelligent  beings  are  sentient  beings. 

Society  prohibits  experiments  on  intelligent  beings.  (Cesare), 
The  form  (Society  prohibits,  &c.),  has  the  force  of  a  nega- 
tive ;  were  it  not  so,  the  last  syllogism  would  not  be  valid. 

The  language  of  inference  from  particulars  to  particulars 
might  be  used  in  each  of  these  syllogisms.  Thus  in  the  first : 
Experiments  for  ascertaining  function  in  sensitive  beings  have 
been  observed  to  lead  to  pain  ;  the  present  case  is  an  experi- 
ment for  ascertaining  function  :  the  present  case  will  lead  to 
pain  (as  the  observed  cases  have  done).  Similarly  for  the 
others. 

Tlie  Deductive  Sciences. 

3.  The  Deductive  Sciences  are  those  where  the  labour 
niiiinly  lies  in  applying  or  carrying  out  ascertained  induc- 
tions, that  is,  in  the  discovery  of  minors  to  given  majors. 

From  the  foregoing  theory  of  the  syllogism,  it  is  apparent 
that  every  deduction  supposes  a  previous  induction.  The 
Deductive  Sciences,  therefore,  do  not  dispense  with  induction. 
Whereas,  in  the  Inductive  Sciences,  such  as  Chemistry  and 
Physiology,  the  chief  labour  consists  in  arriving  at  inductions  ; 
in  the  Deductive  Sciences,  as  Mathematics,  the  inductions  are 
few  and  easily  gained  (being  in  fact  sometimes  called  intui- 
tions) and  the  labour  consists  in  carrying  them  out  into  their 
various  applications,  by  bringing  cases  under  them.  We  soon 
arrive  at  the  inductions  *  things  equal  to  the  same  thing  are 
equal,*  or  *  the  sums  of  equals  are  equal ; '  *  the  diflferences  of 


f^  .'^°A^^m»|«|^|^ 


GEOMETfilCAL  DEDUCTION. 


217 


equals  are  equal : '  but  it  was  not  easy  to  bring  under  the  sweep 
of  these  inductions  the  proposition  *  a  sphere  is  equal  to  two- 
thirds  of  the  circumscribed  cylinder.'  This  is  arrived  at  only 
after  a  long  and  circuitous  process  of  successive  deductions, 
based  upon  the  invention  of  numerous  diagrams. 

K  we  take  a  comparatively  simple  case  of  geometric  deduc- 
tion, the  47th  of  the  First  Book  of  Euclid,  *  the  square  des- 
cribed on  the  hypothenuse  of  a  right-angled  triangle  is  equal  to 
the  sum  of  the  squares  described  on  the  two  sides,*  we  shall  find 

that  the  proof  can  be  accomplished  by  two  main  leaps two 

syllogisms  having  axiomatic  majors,  and  a  preparatory  syllo- 
gism having  as  its  major  a  previously  established  derivative 
proposition.  The  rest  of  the  process  is  not  syllogistic.  We 
first,  by  an  ingeniously  devised  construction,  establish  two 
minors  under  the  proposition — *  A  parallelogram  and  a  triangle 
being  on  the  same  base  and  between  the  same  parallels,  the 
parallelogram  is  double  of  the  triangle  ;  *  and  then  proceed  to 
the  main  steps,  the  application  of  the  axioms.  We  first  apply 
the  axiom — |  The  doubles  of  equals  are  equal,'  (a  derivative 
from  the  axiom — *The  sums  of  equals  are  equal,')  to  prove 
that  the  square  described  on  one  of  the  sides  is  equal  to  a  part 
of  the  hypothenuse  square,  and  that  the  square  described  on 
the  other  side  is  equal  to  the  remaining  part  of  the  hypothen- 
use square.  This  being  done,  it  needs  but  an  easy  application 
of  the  axiom—*  The  sums  of  equals  are  equal,'  to  complete  the 
proof. 

The  deductive  sciences  circumvent  their  problems  ;  they 
accomplish  indirectly  what  there  is  no  means  of  accomplishing 
directly.  The  science  of  mathematics  instead  of  resting  satis- 
fied with  announcing  its  axioms  and  definitions,  and  leaving 
people  to  apply  them  at  once,  evolves  a  vast  scheme  of  deductive 
properties,  to  any  one  of  which  we  may  repair  in  an  emergency, 
mstead  of  making  a  connexion  at  once  with  the  fountain  head! 
We  measure  a  height  by  bringing  the  case  under  some  theorem 
of  Plane  Trigonometry  that  chances  to  be  adapted  to  the 
means  at  our  command. 

The  length  and  the  complicacy  of  mathematical  or  other 
reasonings  may  be  ascribed  to  these  two  circumstances. 

(1)  There  are  many  steps  of  mere  Immediate  Inference,  as 
m  applymg  Definitions.  Thus,  when  Euclid  shows  that  two 
figures  coincide,  he  makes  a  formal  appeal  to  the  Definition  of 
Equality  (namely.  Coincidence),  and,  by  virtue  of  that  declares 
them  to  be  equal.  This  is  seemingly  a  step  in  the  reasoning ; 
It  involves  a  distinct  act  of  attention  on  the  part  of  the  stu- 


'■'it 


218  TRAINS  OF  REASONING  AND  DEDUCTIVE   SCIENCES. 

dent,  but  it  is  not  a  deduction  or  syllogism.  So,  there  may  be 
steps  involving  other  transitions  to  Equivalent  Forms,  as  Ob- 
version,  Conversion,  &c. 

(2)  Not  only  is  a  great  deal  of  preparatory  construction  or 
scaffolding  often  required  in  order  to  bring  the  case  under  the 
sweep  of  a  previous  generality,  but,  when  the  construction  is 
made,  there  jut  out  from  every  part  of  it  separate  inferences, 
and  all  these  have  to  be  made  convergent  to  the  pui-pose  in 
hand.  Moreover,  many  propositions  start  at  once  with  a  com- 
plicated hypothesis — *  If  a  point  be  taken  without  a  circle  (1), 
and  straight  lines  be  drawn  from  it  to  the  circumference  (2), 
whereof  one  passes  through  the  centre  (3),*  &c. ;  the  proof  in 
these  cases  is  a  convergent  series  of  steps,  each  starting  from 
a  distinct  member  of  the  hypothesis. 

The  process  of  Identification  to  supply  a  minor  is  difficult 
according  to  the  complicacy  of  the  subject  of  the  major  ;  as  in 
Diseases,  in  Law,  in  Politics,  &c.  A  disease  being  character- 
ized by  three,  four,  or  five  distinctive  symptoms,  must  be 
identified  on  all  these  symptoms  ;  a  failure  in  any  one  leaves 
the  disease  unidentified.  Hence,  deduction  may  be  a  work  of 
labour  even  in  the  sciences  of  Induction,  as  Medicine  must  be 
pronounced  to  be. 

So,  in  Politics,  Sir  G.  C.  Lewis  remarks  that  the  difficulty 
may  lie  in  bringing  the  Premises  of  the  syllogism  together, 
that  is,  in  finding  the  major  to  a  given  minor,  or  the  minor  to 
a  given  major.  '  It  is  the  subsumption  of  the  minor  under  the 
major  premise  that  really  constitutes  the  originality,  or  inven- 
tion, of  the  argument.*     The  following  is  an  example  : — 

General  Maxim^  or  Major — When  a  customs  duty  is  so  high 
as  to  produce  extensive  smuggling,  it  ought  to  be  reduced. 

Farticular  case^  or  Minor — The  existing  customs  duty,  in 
country  A,  upon  tobacco,  or  brandy,  or  hardware,  &c.,  leads 
to  extensive  smuggling. 

Now,  the  minor  is  obviously  a  matter  of  fact  (determined 
partly  by  reasonings  from  facts),  and  may  take  much  trouble 
to  establish. 

4.  The  special  aim  of  Deduction  is  to  ascertain  every 
fact  implied  in  facts  already  known.  A  Deductive  deter- 
mination is  opposed  to  an  Experimental  determination. 

When,  by  the  application  of  ascertained  inductions,  we  can 
discover  new  truths,  we  save  the  appeal  to  direct  experiment. 
By  the  parallelogram  of  forces,  we  can  find  the  exact  course 
of  any  moving  body  urged  in  difierent  directions  by  given 


PUSHING  OF  DEDUCTIONS. 


219 


forces.  A  process  of  computation  is  substituted  for  a  process 
of  observation ;  the  consequence  is,  in  most  instances,  a  great 
economy. 

The  pushing  of  truths  of  induction  to  all  their  deductive 
applications  is  one  great  department  of  scientific  rese^irch. 
The  aptitude  for  the  operation  is  almost  purely  intellectual. 
When  a  great  law,  such  as  Gravitation,  has  been  established, 
the  following  out  of  all  its  deductive  consequences  supplies 
work  to  several  generations  of  men.  The  generalization  of 
the  present  day,  called  the  Persistence  of  Force,  will  give  pro- 
bably an  equal  amount  of  occupation  to  the  more  purely  de- 
ductive or  speculative  aptitudes  of  the  scientific  mind.  The 
inductive  laws  that  connect  Mind  with  Body,  when  ascertained 
with  precision,  will  admit  of  being  deductively  pushed  in 
numerous  ways,  and  will  yield  many  facts  at  present  discover- 
Able  only  by  separate  observations.  The  doctrine  of  the 
Relativity  of  all  Feeling  and  Thought  has  not  as  yet  been 
completely  followed  out  to  its  consequences. 


CHAPTER  V. 
DEMONSTEATIOK— AXIOMS.— NECESSARY  TRUTH. 

1.  The  kind  of  evidence  named  '  Demonstration'  has  its 
sources  in  Induction,  . 

Demonstrative  proof  is  only  another  name  for  Deductive 
proof,  which,  in  the  last  resort,  is  Induction.  The  propositions 
of  Euclid  are  said  to  be  demonstrated ;  and,  as  above  seen,  this 
means  that  the  conclusions  are  proved  by  bringing  each  case 
under  the  sweep  of  the  fundamental  principles  of  the  science. 

To  make  out  Mathematical  Demonstration  inductive,  it  is 
requisite  to  show — (1)  that  the  foundations  of  the  Science 
(the  axioms)  are  inductive  ;  and  (2)  that  the  axiofh  of  the 
Syllogism  is  inductive.  The  axioms  of  mathematics  supply 
the  principles,  and  the  axiom  of  the  syllogism  justifies  their 
application. 

In  the  question  respecting  the  ultimate  foundations  of  the 
so-called  axioms,  these  are  the  chief  examples  in  dispute.  It 
is  maintained,  on  one  side,  that  the  axioms  of  Mathematics, 


F 


220     DEMONSTRATION.— AXIOMS.— NECESSAUY   TRUTH. 

the  axiom  of  the  Syllogism,  together  with  the  axiom  of  Causa- 
tion, —are  inductions  from  particular  facts  of  experience  ;  and 
on  the  other  side,  that  they  are  of  intuitive  origin,  and,  in  this 
origin,  possess  a  higher  certainty  than  can  be  given  by  experi- 
ence. * 

2.  The  chief  argument  against  the  Inductive  origin  of 
these  principles  is  that  they  are  necessary,  and  no  experi- 
ence can  give  the  character  of  necessity. 

The  idea  of  *  necessity,*  as  attaching  to  such  truths  as  the 
mathematical  axioms,  dates  from  Leibnitz;  it  was  re-stated, 
in  a  qualified  form,  by  Kant,  and  persists  in  the  minds  of  many 
to  the  present  day.     The  term,  however,  is  ambiguous. 

Meanings  of  Nccessily. 

3.  T.  In  common  speech,  '  necessity '  is  a  synonym  of 
certainty  ;  and  would  apply  to  inductive  truths. 

When  speaking  of  anything  that  is  certain  to  happen,  we  use 
among  other  words,  the  term  *  necessary.*  We  should  call  the 
freezing  of  water,  at  32°,  a  necessity,  meaning  that  we  are 
perfectly  sure  of  its  happening.  We  even  say  that  vice  is  a 
necessary  consequence  of  bad  training. 

The  necessity  in  such  cases  has  admittedly  nothing  to  do 
with  intuitive  perception.  Experience  is  competent,  in  every 
instance,  to  give  the  strong  assurance  that  the  word  signifies. 
So,  we  have  only  experience  to  rely  upon  in  believing  that  the 
sun  must  rise  to-morrow. 

There  could  be  nothing  incompatible  with  this  usage  in 
terming  all  the  inductive  laws  of  nature  *  necessary  ' — the  law 
of  gravity,  the  laws  of  motion,  the  fundamental  laws  of  organi- 
zation, and  so  on.  But  metaphysicians  are  accustomed  to  call 
these  principles  *  contingent,'  as  opposed  to  necessary ;  for  al- 
though they  are  true,  as  the  universe  is  now  constituted,  they 
might  have  been  otherwise.  The  law  of  gravity  might  have 
been  wanting  ;  the  laws  of  organized  beings  might  have  been 
different.  But,  in  no  circumstance  (it  is  said)  could  *  two 
straight  lines  enclose  a  space  ; '  this,  therefore,  is  necessary  iu 
a  more  peculiar  sense  of  the  word,  as  will  be  next  stated. 

•  On  the  subject  of  Mathematical  Evidence,  other  questions  have  heen 
raised,  namely,  the  place  of  the  Definitions  in  the  Science,  and  the  sup- 
posed hypothetical  character  of  definicions.  These  questions  will  b«  vA* 
verted  to  afterwards  (Logic  op  the  Scie>ce8,  Math  etna  licsj. 


NECESSITY  AS  IMPLICATION. 


221 


4.  II.    'Necessity'  more  properly  means  implication; 

*  necessary  truths  '  in  this  sense  are  the  truths  demanded 
by  Consistency.     Their  denial  is  a  contradiction  in  terms. 

These  truths  have  already  been  fully  exemplified.  (See 
Introduction,  and  also  Equivalent  Propositional  Forms).  That 
the  less  cannot  contain  the  greater,  is  necessary ;  it  follows 
from  the  very  meaning  of  less  and  greater ;  it  could  not  be 
contradicted  without  declaring  the  greater  not  to  be  the 
greater.  *  The  same  thing  cannot  be  in  two  places  at  once  * 
is  necessary  ;  the  meaning  of  a  *  place  *  is  some  definite  spot 
the  negative  of  all  other  places;  to  say  that  a  thing  is  in  a 
particular  place  is  to  deny  that  it  is  in  a  second,  or  a  third, 
or  any  other  place.  *  Time  is  an  eternal  now  !'  must  be  set 
down  as  self-contradictory. 

Some  of  the  axioms  of  Euclid  are  necessary  in  this  sense. 

•  A  whole  is  greater  than  its  part '  is  implicated  in  the  defini- 
tion  of  whole  and  part ;  it  could  not  be  contradicted  without 
contradicting  the  definition.  A  whole  is  summed  up  by  its 
parts ;  omit  any  of  these,  and  the  whole  is  not  made  up ;  the 
result  is  something  less  than  the  whola 

*  Things  that  coincide  are  equal '  is  not  an  axiom  but  a  de- 
finition ;  it  is  the  mark  or  test  of  equality,  the  only  mark  that 
can  be  propounded  in  the  last  resort. 

Of  all  the  alleged  necessary  truths,  the  one  most  frequently 
cited  in  the  present  controversy  is — '  Two  straight  lines  can- 
not enclose  a  space.'  This  was  held  by  Kant  to  be  a  real  pro- 
position, a  sy7ithetic  judgment ;  in  other  words,  the  subject  is 
not  implied  in  the  predicate  ;  to  it  the  criterion  of  *  implica- 
tion' would,  therefore,  not  apply. 

On  the  other  hand,  mathematicians  are  now  probably  unani- 
mous in  regarding  this  as  a  corollary  from  the  definition  of 
the  straight  line,  or  as  implicated  in  the  very  essence  of 
straightness  ;  so  that  to  deny  it  would  be  a  contradiction  in 
tei-ms.  They  would  characterize  it,  in  Kant's  own  language, 
as  an  *  analytic '  judgment.  A  very  little  reflection  on  the 
case  proves  that  the  mathematicians  are  right.  Starting  from 
the  definition  of  the  straight  line — *  when  two  lines  are  such 
that  they  cannot  coincide  in  two  points  without  coinciding  alto- 
gether, they  are  called  straight  lines,'  we  see  that  the  very 
terms  forbid  the  enclosing  of  a  space ;  what  meaning  can  we 
attach  to  *  coinciding  altogether,'  but  the  exclusion  of  non- 
coincidence,  or  of  an  intermediate  space  ?  Total  coincidence, 
and  an  intervening  space,  are  wholly  incompatible  ;  if  the  one 


222      DEMONSTRATION. — AXIOMS. — NECESSARY  TRUTH. 

is  true  the  other  is  false.  The  proposition  is  therefore  neces- 
eary  in  the  sense  of  implication,  as  nwich  so  as  a  *  straight 
line  is  not  a  bent  line,'  *  a  whole  is  greater  than  its  part.* 

The  axiom  *  Things  eqaal  to  the  same  thing  are  equal  to 
one  another  '  is  not  a  truth  of  implication,  and  therefore  is  not 
a  necessary  truth  in  the  present  sense.  The  subject  and  the 
predicate  express  distinct  properties,  and  the  one  does  not  in- 
volve the  other.  The  axiom  declares  that  mediate  coincidence 
is  to  be  held  as  carrying  with  it,  or  as  making,  immediate 
coincidence ;  but  the  two  modes  of  coincidence  are  not  iden- 
tical. It  is  immediate  coincidence  that  makes  equality,  accord* 
ing  to  the  definition  of  equality ;  the  axiom  extends  this  very 
narrow,  and  often  inapplicable  test,  and  declares  that  coin- 
cidence through  some  third  thing,  a  go-between,  will  be  found 
in  the  end  to  be  the  same  as  actual  coincidence,  and  is  conse- 
quently to  be  accepted  in  all  cases  as  a  test  of  equality.  If, 
therefore,  this  axiom  is  to  be  held  as  a  necessary  truth,  some 
other  meaning  than  the  present  must  be  assigned  to  necessity. 

5.  Necessary  truths,  in  the  foregoing  signification,  are  so 
far  independent  of  experience,  that  they  are  perceived  to  be 
true  when  the  language  is  understood.  They  do  not,  how- 
ever, require  any  powers  of  intuitive  perception. 

As  soon  as  we  fully  comprehend  the  notion  of  whole  and 
part,  we  perceive  that  the  whole  is  greater  than  the  part ; 
wo  do  not  need  to  make  observations  and  experiments  to  prove 
it.  We  required  concrete  experience,  in  the  first  instance,  to 
attain  to  the  notion  of  whole  and  part ;  but  the  notion  once 
arrived  at  implies  that  the  whole  is  greater.  In  fact,  we  could 
not  have  the  notion  without  an  experience  tantamount  to  this 
conclusion.  When  we  know  a  fact,  we  know  it,  even  when 
called  bv  another  name,  which  is  all  that  is  meant,  at  present, 
by  necessary  truth.  When  we  have  mastered  the  notion  of 
straightness,  we  have  also  mastered  that  aspect  of  it  expressed 
by   the    affirmation,    *  two   straight    lines   cannot  enclose   a 

space.* 

Ko  intuitive  or  innate  powers  or  perceptions  are  needed  for 
such  cases.  Our  ordinary  intellectual  powers  enable  us  to 
pronounce,  in  more  than  one  form,  that  an  object  is  everything 
or  anything  that  we  have  found  it  to  be.  We  cannot  have  the 
full  meaniug  of  *  straightness  '  without  going  throagh  a  com 
parison  of  straight  objects  among  themselves,  and  with  their 
opposites,  bent  or  crooked  objects.  The  result  of  this  com- 
parison is,  inter  alia,  that  straightness  in  two  lines  is  seen  to 


INCONCEIVABILITY  OF  THE   OPPOSITE. 


223 


be  incompatible  with  enclosing  a  space ;  the  enclosure  of  space 
involves  crookedness  in  at  least  one  of  the  lines. 

6.  III.  A  third  meaning  and  criterion  of  Necessity,  is 
inconceivability  of  the  opposite. 

It  is  maintained  that  *  things  equal  to  the  same  thing  are 
equal  to  one  another,'  because  the  mind  is  unable  to  conceive 
things  agreeing  with  a  common  standard,  and  yet  not  agree- 
ing when  directly  compared.  It  is  also  maintained  that  we 
are  unable  to  conceive  *  effects  arising  without  a  cause  ;*  whence 
such  propositions  are  declared  to  be  true  necessarily.  The 
test  of  inconceivability  of  the  opposite  (strongly  urged  by 
Whewell,  and  held  with  modifications  by  Spencer),  is  liable  to 
serious  objections.  What  we  can,  or  cannot  conceive,  is  mani- 
festly dependent,  in  a  very  large  measure,  on  our  education  : 
the  proof  of  which  is  that  many  truths  inconceivable  in  one 
age  and  country  are  not  only  conceivable  under  a  different 
state  of  edication,  but  are  so  thoroughly  engrained  that  their 
opposites  are  inconceivable.  The  Greeks  held  matter  to  be 
eternal  and  self-existent ;  many  moderns  hold  that  the  self- 
existence  of  matter  is  inconceivable.  Some  maintain  that 
mind  is  the  only  conceivable  source  of  moving  power  or  force ; 
others,  regarding  the  action  of  mind  upon  matter  as  incon- 
ceivable, have  contrived  special  hypotheses  to  get  over  the 
difficulty, — we  may  instance  Malebranche's  doctrine  of  Divine 
Interference,  and  Leibnitz's  Pre-established  Harmony.  New- 
ton could  not  conceive  gravity  without  a  medium. 

With  regard  to  truths  of  Implication,  the  difficulty  of  con- 
ceiving the  opposite  must  be  at  its  maximum.  Yet  self-con- 
tradiction is  not  an  impossible  operation,  for  it  is  often  done. 
In  Theology,  people  have  even  boasted  of  holding  contradic- 
tory propositions.  But  where  the  subject  does  not  imply  the 
predicate,  there  is  no  self-contradiction,  and  the  opposite  of 
any  such  proposition  may  be  conceived.  That  things  medi- 
ately coinciding,  should  not  immediately  coincide,  is  conceiv- 
able  ;  for  the  facts  are  different ;  the  difficulty  that  we  feel  is 
in  contradicting  our  habitual  experience  on  a  matter  so  very 
familiar  and  tangible. 

Propositions  of  avowedly  inductive  origin  may  be  so  strongly 
associated  that  their  opposites  are  all  but  impossible  to  con- 
ceive. ^  It  is  scarcely  in  our  power  to  conceive  colour  without 
extension  ;  and  yet  the  two  are  united  solely  by  our  experi- 
ence ;  they  strike  the  mind  through  different  avenues,  and  their 
incessant   conjunction    constitutes   a  practically    indissoluble 


224      DEMONSTRATION.— AXIOMS. — NECESSARY   TRUTH. 

bond.  We  should  have  some  difficulty  in  conceiving  soot 
flakes,  particles  of  dust,  and  small  pieces  of  paper,  falling  to 
the  ground  plamb  and  swift  like  a  stone.  The  Greek  proverb 
for  the  impossible  was  water  flowing  back  to  its  source. 

The  Nature  of  Axioiois. 

7.  The  fundamental  principles  of  the  Deductive  Sciences 
are  called  Axioms. 

Every  Deductive  Science  must  begin  with  certain  funda- 
mental assumptions.  In  Mathematics,  and  in  Logic,  these  are 
deemed  so  self-evident,  that  no  express  effort  is  made  to 
establish  them.  In  Mechanics,  the  statement  of  the  Laws  of 
Motion  is  accompanied  with  a  few  examples  to  make  them  at 
once  intelligible  and  evident.  In  Chemistry,  the  Atomic 
Theory  is  somewhat  too  far  removed  from  ordinary  compre- 
hension to  be  called  a  self-evident  axiom,  albeit  the  most  fun- 
damental assumption  contained  in  the  science. 

The  requisites  of  an  axiom  are,  first,  that  it  should  be  a  real 
proposition,  and  not  a  definition  ;  and,  secondly,  that  it  should 
be  independent  of  any  other  principle  within  the  science. 

On  the  first  of  these  two  requirements,  we  should  have  to 
reject  Euclid's  axioms—*  Magnitude^  that  coincide  are  equal,' 
and  *  The  whole  is  greater  than  its  part.' 

On  the  second  requirement,  we  must  reject, — 

The  differences  of  equals  are  equal ; 

If  equals  be  added  to  unequals,  the  wholes  are  unequal ; 

If  equals   be    taken   from    unequals,   the    remainders    are 
unequal ; 

Doubles  of  equals  or  of  the  same  are  equal ; 

Halves  of  equals  or  of  the  same  are  equal ; 

Two  straight  lines  cannot  be  drawn  through  the  same  point, 
and  parallel  to  the  same  straight  line,  without  coinciding. 

It  may  be  useful  to  give  an  explicit  statement  of  these 
truths,  but  as  they  are  all  derivable  from  other  axioms 
(together  with  Definitions),  they  should  be  appended  to  these 
others,  as  corollaries  or  inferences.  If,  in  any  instance,  we  set 
up  a  derivative  proposition  as  an  axiom,  we  break  down  the 
sole  boundary  between  axioms  and  the  propositions  or  theorems 
constituting  the  body  of  a  science. 

8.  The  only  two  Axioms  of  Mathematics,  properly  so 
called,  are,  the  axiom  of  'mediate  coincidence,*  and  the 
axiom  of  the  '  equality  of  the  sums  of  equals.*  These  are 
Inductive  truths. 


AXIOMS  OF  MATHEMATICS. 


225 


The  excision  of  Definitions  with  their  corollaries,  and  of 
Derivative  Propositions,  leaves  only  the  two  axioms  now  men- 
tioned— *  Things  equal  to  the  same  thing  are  equal,'  and  *  The 
sums  of  equals  are  equal.'  These  are  real,  and  not  essential  or 
analytic,  propositions:  and  they  are  ultimate  within  the 
science.  They  are  two  distinct  tests  of  equality,  over  and 
above  the  defining  test,  immediate  coincidence.  From  them, 
together  with  the  definition,  all  other  tests  of  equality  are 
deducible. 

To  say  that  they  are  Inductive  truths,  generalizations  from 
our  experience  of  the  particular  facts,  is  to  say  that  they  have 
the  same  origin  as  the  great  mass  of  our  knowledge  (not 
deductive).  That  day  and  night  alternate,  that  water  flows 
downward,  that  smoke  ascends,  that  plants  grow  from  seed, 
that  animals  die,  that  men  seek  pleasure  and  eschew  pain, — ^are 
all  obtained  by  a  comparison  of  observed  facts  ;  and  this  is  the 
regular,  the  usual  source  of  scientific  generalities.  The  burden 
of  proof  lies  upon  those  that  would  assign  any  other  source  to 
the  two  axioms  named  ;  some  reasons  must  be  given  to  show 
that  they  are  exceptions  to  the  prevailing  rule. 

The  chief  reasons  actually  assigned  are  those  already  ex- 
amined, their  Necessity,  and  the  Inconceivability  of  their  Op- 
posites.  As  corroborating  these,  or  rather  as  putting  in  a 
different  shape  the  supposed  difficulty  of  referring  the  axioms 
to  experience,  it  is  said  that  the  intensity  of  our  conviction  that 
*  things  equal  to  the  same  thing  are  equal  *  is  greater  than  could 
arise  from  the  accumulated  comparisons  that  we  have  instituted 
on  actual  things.  The  considerations  that  serve  to  obviate 
what  force  there  is  in  this  objection  are  the  following. 

First,  by  the  law  of  Belief  already  explained,  every  uncon^ 
tradicled  experience  has,  on  its  side,  all  the  force  of  our  primi- 
tive credulity.  The  initial  believing  impetus  of  the  mind  errs 
on  the  side  of  excess  ;  and  if  nothing  has  happened  to  check 
it  in  a  particular  case,  it  will  be  found  strong  enough  for 
anything. 

Secondly,  our  opportunities  of  comparing  magnitudes  are 
numerous  and  incessant ;  they  require  only  the  very  simplest 
and  most  accessible  instruments.  The  child,  havinsr  at  com- 
mand,  three  equal  chips  of  wood,  cannot  avoid  making,  in  the 
course  of  an  hour,  scores  of  comparisons  that  exemplify  the 
axiom  of  mediate  equality. 

Thirdly,  it  is  usual  to  remark,  on  the  mathematical  axioms 
generally,  that  the  subjects  of  them — namely,  magnitudes  and 
forms — are  with  the  greatest  possible  ease  represented  in  ima- 


226      DEMONSTRATION. — ^AXIOMS. — NECtiSSAliY  TRUTH. 

gination,  so  that  we  can  make  numerous  ideal  experiments,  in 
addition  to  our  comparison  of  actual  things  in  the  concrete. 

9.  The  Axioms  of  the  Syllogism  repose  upon  experience. 

In  the  form — *  Attributes  co-existing  with  the  same  attri- 
bute, co-exist,*  we  have  a  principle  closely  resembling  Euclid's 
first  axiom  of  Equality  ;  the  character  of  the  evidence  for  both 
must  be  the  same.  Now,  so  far  is  this  axiom  from  being  an 
absolute  and  intuitive  certainty,  that  it  is  erroneous.  We  may 
illustrate  it  by  a  parallel  form,  *  Things  in  contact  with  the 
same  thing  are  in  contact  with  one  another  ;*  which  is  plausible 
but  fallacious. 

The  dictum  de  omni  et  nullo  cannot  be  exempted  from  the 
criterion  of  experience.  It  is  not  intelligible  without  much 
familiarity  with  examples  of  the  generalizing  process  ;  and,  as, 
in  the  case  of  all  other  first  principles,  the  same  knowledge 
that  makes  it  understood,  suffices  to  verify  it. 

However  expressed,  the  Axioms  of  the  Syllogism  are,  in  the 
first  place,  Real  Propositions,  and  not  identical  statements  under 
the  so-called  Law  of  Identity,  or  Self- Consistency.  And,  in 
the  second  place,  as  Heal  Propositions,  they  are  not  intuitively 
suggested  to  the  mind  ;  they  grow  up  with  our  experience,  and 
if  our  belief  in  them  seems  to  outrun  experience,  the  same 
thing  happens  to  all  our  beliefs. 

10.  As  regards  the  Law  of  Causation,  usually  included 
among  the  so-called  a  ^Wo/*t  elements  of  our  knowledge,  there 
is  a  strong  primitive  tendency  to  believe  it  in  a  crude  form, 
while  experience  must  adapt  this  belief  to  the  actual  facts. 

We  have  already  seen  that  the  primitive  tendency  of  the 
mind  is  to  believe,  until  checked,  that  what  is  now  will  continue, 
that  what  is  here  is  the  same  everywhere.  Neither  experience 
nor  any  intellectual  faculty  creates  this  impetus  ;  but  experi- 
ence arrests  and  modifies  it,  till  by  degrees  it  adapts  itself  to 
the  real  occurrences.  The  headlong  impulse  is  curbed  in  such 
matters  as  the  surrounding  temperature,  luminosity,  and  visi- 
ble appearances  ;  it  is  left  in  possession  of  other  matters,  as  the 
force  of  gravity.  The  instinct  is  important  as  giving  the  active 
element  of  belief ;  it  is  perfectly  worthless  as  a  guide  to  the 
things  proper  to  be  believed.  So  far  as  concerns  the  authority 
or  evidence,  for  causation,  experience  is  paramount  over 
instinct ;  apart  from  experience,  the  infant  would  for  life  be- 
lieve that  all  the  water  of  the  globe  is  of  the  temperature  of  its 
first  bath. 


THE  UNIFORMITY  OF  NATURE. 


227 


The  crude  impulse  to  believe  that  what  is  will  continue, 
after  the  shock  of  many  contradictions,  is  transformed  into  a 
belief  in  the  uniformity  of  nature,  as  represented  by  the  law  of 
Causation. 

11.  The  axiom  underlying  the  axioms  of  Mathematics, 
and  the  axiom  of  the  syllogism,  is  the  axiom  of  the  Uni- 
formity of  Nature. 

The  consideration  of  cause  and  effect  brings  us  face  to  face 
with  the  most  fundamental  assumption  of  all  human  know- 
ledge, expressed  by  such  language  as  'Nature  is  Uniform' 
*  the  Future  will  resemble  the  Past*,  *  Nature  has  fixed  Laws.* 
This  axiom  is  the  common  ground  of  all  inference,  whether 
avowedly  inductive,  or  induction  disguised  under  the  forms  of 
deduction.  Without  this  assumption,  experience  can  prove 
nothing.  We  may  have  found,  in  ten  thousand  instances,  that 
magnitudes  coinciding  with  the  same  magnitude  also  coincide 
when  applied  to  one  another ;  so  far  as  these  instances  go,  the 
fact  is  not  to  be  disputed  ;  the  evidence  of  actual  trial  is  the 
highest  we  have.  But  they  do  not  prove  that  it  will  happen 
in  any  untried  instance.  This  must  be  received  without  proof; 
it  can  repose  on  nothing  more  fundamental  than  itself.  If  we 
seena  to  offer  any  proof  for  it,  we  merely  beg  it  in  another 
shape.     (See  Appendix  D.) 


i    \ 


I 


BOOK   IIL 

INDUCTION. 


I 


CHAPTER  I. 

MEANING  AND  SCOPE  OF  INDUCTION. 

1.  Induction  is  the  arriving  at  General  Propositions,  by 
means  of  Observation  or  Fact. 

In  an  Induction,  there  are  three  essentials:— (1)  the  result 
must  be  a  proposition — an  affirmation  of  concurrence  or  non- 
concurrence— as   opposed  to  a  Notion:    (2)    the  Proposition 
must  be  gerieraly  or  applicable  to  all  cases  of  a  given  kind :  (3) 
^he  mechod  must  be  an  appeal  to  observation  or  Fact. 

(1)  By  Induction,  we  arrive  at  Propositiofis, — Affirmations 
of  coincidence  or  non -coincidence  of  distinct  properties ;  we 
have  to  do,  not  with  verbal,  but  with  Real  Predication.  That 
*  The  boiling  temperature  destroys  animal  life,*  is  an  induction 
so  far  as  being  a  proposition,  affirmation,  or  real  predication  ; 
there  are  two  distinct  facts — boiling  heat,  and  destruction  of 
animal  life — and  these  two  facts  are  coupled  in  an  affirmation 
of  coincidence. 

To  this  essential  of  Induction,  are  opposed  the  cases  where 
what  we  arrive  at  is  a  Notion  or  Definition.  Sometimes  we 
are  liable  to  confound  the  two.  This  happens  when  we  are 
attending  too  exclusively  to  the  second  characteristic  of  Induc- 
tion—generality. In  the  process  of  defining,  wo  generalize  a 
number  of  individuals,  so  as  to  obtain  and  express  their  point 
or  points  of  community,  which  expressed  community  is  a  De- 
finition or  Notion ;  as  Heat,  Knowledge,  Justice.  If  such 
definitions,  or  expressed  general  notions,  are  absolutely  limited 
to  on^  indivisible  fact  or  attribute,  they  are  by  that  circum- 
stance decisively  contrasted  with  inductions,  which  always  join 

n 


232 


MEANING  AND   SCOPE   OF  INDUCTION. 


IMPKOPER  INDUCTIONS. 


233 


at  least  two  facts  or  attributes.  Thus,  the  generalized  notions 
of  length,  resistance,  whiteness,  heat,  could  not  be  confounded 
with  inductions  ;  there  is  clearly  absent  from  these  the  con- 
joining or  coupling  of  distinct  properties.  But  we  have  seen 
many  instances  where  a  definition  expresses  a  plurality  of 
attributes  concurring  in  the  same  subject,  as  in  all  the  natui*al 
kinds — minerals,  plants,  animals — and  in  various  other  things. 
' /There  is  no  small  delicacy  in  placing  the  boundary  between 
those  generalities  ending  in  plural  notions,  or  definitions,  and 
proper  inductive  generalizations.  We  have  to  ask  whether  or 
not  the  stress  is  laid  on  the  circumstance  of  conjunction^ 
whether  it  is  made  a  question — are  the  properties  conjoined 
or  not.  In  definition,  the  conjunction  is  tacitly  assumed  ;  in 
induction,  it  is  laid  open  to  question  ;  it  has  to  he  proved  or 
disproved.     (See  p.  292). 

(2)  The  Propositions  established  by  Induction  are  getieral. 
A  single  individual  concurrence,  as  *  the  wind  is  shaking  the 
tree,'  is  in  its  statement  a  proposition,  but  not  an  induction. 
On  such  individual  statements,  we  base  inductions,  but  one  is 
not  enough.  If  the  coincidence  recurs,  we  mark  the  recur- 
rence ;  we  are  affected  by  the  shock  or  flash  of  identity,  a  very 
important  step  in  our  knowledge.  If,  pursuing  the  sugges- 
tion, we  remark  that  as  often  as  the  wind  is  high,  the  trees 
are  shaken ;  that  the  two  things  have  concurred  within  the 
whole  course  of  our  observation  ;  that  the  same  concurrence 
has  been  uniform  in  the  observation  of  all  other  persons 
whose  experience  we  have  been  informed  of, — we  are  then 
entitled  to  take  a  still  wider  sweep,  and  to  say,  *  every  time 
that  a  high  wind  has  been  observed,  a  waving  of  the  trees  has 
aiso  been  observed.* 

Still,  with  all  this  multitude  and  uniformity  of  observations, 
there  is  no  proper  Induction.  What  then  remains  ?  The 
answer  is,  the  extension  of  the  concurrence  from  the  observed 
to  the  unobserved  cases — to  the  future  which  has  not  yet 
come  within  observation,  to  the  past  before  observation  began, 
to  the  remote  where  there  has  been  no  access  to  observe.  This 
is  the  leap,  the  hazard  of  Induction,  which  is  necessary  to 
complete  the  process.  Without  this  leap,  our  facts  are 
barren  ;  they  teach  us  what  has  been,  after  the  event ;  whereas, 
we  want  knowledge  that  shall  instruct  us  before  the  event, 
that  shall  impart  what  we  have  no  means  of  observing.  A 
complete  induction,  then,  is  a  generalization  that  shall  express 
what  is  conjoined  everywhere,  and  at  all  times,  superseding 
i\)v  ever  the  labour  of  fresh  observation. 


},' 


y 


'y 


y 


A       We  thus  contrast  Induction  with  that  species  of  *Induo- 
\   tions  improperly  so  called/  where  a  general  statement  merely 
Bums  up  the  observed  particulars. 

If,  after  observing  that  each  one  of  the  planets  shines  by  the 
suns  hght,  we  afiirm  that  *all  the  planets  shine  by  the  sun's 
light,  we  make  a  general  proposition  to  appearance,  but  it 
tails  short  of  an  induction  in  the  full  sense  of  the  term.  The 
general  statement  is  merely  another  way  of  expressing  the  par- 
ticulars ;  it  does  not  advance  beyond  them.  But  without  such 
an  advance  there  is  no  real  inference,  no  march  of  information, 
no  addition  to  our  knowledge.  Induction  is  the  instrument  of 
multiplying  and  extending  knowledge ;  it  teaches  us  how, 
trom  a  ie^f  facts  observed,  to  affirm  a  great  many  that  have 
not  been  observed.  If,  from  the  observation  of  the  planets 
now  discovered,  we  make  an  assertion  respecting  all"  that  have 
yet  to  be  discovered,  we  make  the  leap  implied  in  real  or 
mductive  inference.  If  the  assertion  had  been  made  when 
only  six  planets  were  known,  actual  observation  would  have 
been  the  guarantee  for  those  six,  induction  for  the  remaining 
hundred  or  upwards* 

So  the  proposition  *  all  animals  have  a  nervous  system '  is 
an  induction  only  when  affirmed  on  the  observation  of  a  part 
ot  the  animal  species.  If  the  representatives  of  every  species 
had  been  examined  before  the  statement  was  made,^the  pro- 
position would  be  proved  by  observation,  and  not  by  induction; 
the  generality  would  be  merely  a  literal  repetition  or  summarv 
ot  the  particulars.  ^ 

iiJ^u  M""?  ?f  improper  induction  is  assumed  in  the  attempt,  made 
i^st  by  Aristotle  and  repeated  by  others,  to  bring  Induction  imder 
the  syllogism  Induction  '  is  defined  by  Aristotle,  *' proving  the 
major  term  of  the  middle  by  means  of  the  minor;''  in  which 
defamtion,  the  expressions  major,  middle,  and  minor,  are  used 
relatively  to  their  extension,  to  designate  respectively  the  attribute 
proved,  the  constituted  species  of  which  it  is  proved,  and  the 
aggregate  of  indi^duals  by  which  the  species  is  constituted.' 
(Mansel's  Aldnch,  Note  G.).    Thus— 

^»  ^y  Z,  (minor)  are  B  (major), 

X,  Y,  Z,  are  all  A  (middle), 

All  A  is  B. 

;«  ^'^  ^-  *^«^^PPearance,  but  only  the  appearance  of  a  syllogism 
m  the  Third  Figure.  It  is  liable  to  the  criticism  already  ma(S 
upon  syUogisms  with  two  smgular  premises.  It  is  not  a  syWsm 
at  all,  m  any  correct  sense,  but  a  mere  process  of  equivalence.  The 
two  premises  can  be  summed  in  one,  by  verbal  or  grammatical 
condensation ;  and  when  that  has  been  done,  the  conclusion  is  a 
mere  repetition  of  part  of  the  meaning  of  the  combined  statement. 


^ 


m 


234 


MEANING  AND   SCOPE   OF  INDUCTION. 


\\ 


^ 


A  more  ambitious  form  of  the  Inductive  Syllogism  is  given  by 
Aldrich  and  Whately,  which  trenches  on  Induction  proper. 

The  magnets  that  I  have  observed,  together  with  those  thai  I 

have  not  observed,  attract  iron. 
These  magnets  are  all  magnets. 
All  magnets  attract  iron. 
The  major  here  obviously  assumes  the  very  point  to  be  estab- 
lished, and  makes  the  inductive  leap.    No  formal  logician  is  entitled 
to  lay  down  a  premise  of  this  nature.      The  process  altogether 
transcends  syllogism  or  formal  logic. 

In  no  sense  is  the  Inductive  Syllogism  an  admissible  logical 
form* 

A  truly  inductive  Proposition  may  be  but  a  narrow  genera- 
lity. That  *  the  breeze  always  spreads  the  royal  flag  hoisted 
at  Windsor  Castle '  is  a  proper  induction  ;  it  covers  the  unseen 
and  the  future  as  well  as  the  seen.  The  still  wider  induction, 
*  the  breeze  spreads  all  the  flags  of  all  nations,'  is  not  more 
essentially  inductive,  although  of  more  value  as  knowledge. 

(3)  An  Inductive  Proposition  is  based  on  the  observation 
of  facts.  Many  true  propositions,  instead  of  being  based  on 
a  direct  appeal  to  observation,  are  derived  from  other  propo- 
sitions ;  such  are,  with  a  few  exceptions,  the  propositions  ol 
Mathematics,  and  many  truths  in  all  the  other  sciences.  In 
this  view.  Induction  is  contrasted  with  Deduction.  Induction 
is  necessarily  the  prior  source  of  truths  ;  the  Deductive  pro- 
positions are  obtained  from  Inductions.  We  must  commence 
with  observation  of  fact,  and  thence  rise  to  Inductive  gene- 
ralities, before  we  can  proceed  downwards  in  the  way  of 
deduction. 

By  the  use  of  our  observing  faculties  for  the  object  world, 
and  of  self-consciousness  for  the  mind,  we  not  merely  obtain 
our  notions  of  things — stars,  mountains,  trees,  men,  pleasures 
— but  also  discern  the  conjunctions  or  connexions  of  things. 
A  single  conjunction  excites  little  notice,  but  an  iterated  con- 
junction awakens  our  feeling  of  identity ;  we  attend  to  the 
circumstance,  and  watch  for  the  recurrence.  If,  in  the  midst  of 
fluctuation,  some  one  couple  of  things  is  found  always  associ- 
ated, we  state  the  fact  to  ourselves  as  a  natural  conjunction,  a 
law  of  nature  ;  and  the  statement  is  an  inductive  proposition. 
A  meteor  flashing  along  the  sky  is  an  isolated  circumstance ; 
we  term  it  casual  or  accidental.  The  recurrence  of  a  stream 
of  meteors  year  after  year,  in  the  same  month,  is  a  coincidence, 
which  we  elevate  into  an  induction,  a^^ming  it  for  the  future 
as  well  as  for  the  past. 

The  semblance  of  Induction  is  put  on  by  certain  operations 


INDUCTION  AND   DEDUCTION   CONFOUNDED. 


235 


R 


\ 


\ 


\ 


purely  Deductive.     Of  these  Inductions  improperly  so  called, 
two  forms  mav  be  mentioned. 

First.  There  is  a  certain  likeness  to  Induction  in  the  demon- 
strations of  Euclid ;  which  are  each  made  upon  an  exemplary 
diagmm,  and  thence  extended  to  all  similar  instances,  by  what 
is  termed  parity  of  reasoning, 
V  When  Euclid  proves  that  the  angles  at  the  base  of  an  isos- 
celes triangle  are  equal,  he  proves  it  upon  a  single  diagram, 
and  rests  the  general  proposition  upon  the  circumstance  that 
the  same  result  would  be  arrived  at  in  every  other  case  of  the 
same  sort.  The  resemblance  to  Induction  lies  in  extending 
what  is  found  in  one  instance  to  all  other  instances.  Yet  the 
resemblance  fails  on  vital  points. 

In  reality,  such  truths  are  not  established  by  measuring  the 
particular  diagram,  and  recording  that  measure  as  an  observed 
fact,  to  be  taken  with  other  facts  similarly  observed,  in  mak- 
ing up  a  general  rule  ;  as  if  we  were,  by  means  of  an  induction 
from  the  pyramids,  to  lay  down  a  jjfeneral  law  of  pyramid ical 
structure.  The  only  use  mado  of  the  figure  is  to  provide  a 
concrete  reference  in  applying  the  general  language  of  the 
demonstration.  One  triangle  is  as  good  as  another  for  the 
purpose.  We  expressly  omit  from  the  reasoning  all  reference 
to  the  size  of  the  triangle,  to  its  material,  to  the  size  of  the 
angle  included  by  the  two  equal  sides ;  consequently,  our 
proof  is  independent  of  any  one  of  these  elements,  and  holds 
under  all  variations  of  each.  The  demonstration  is  to  the 
effect  that,  quoad  isosceles  triangle,  the  affirmation  is  true ;  it 
is  a  perfectly  general  truth.  The  expression,  *  the  same  might 
he  proved  of  any  other  isosceles  triangle,'  would  be  idle  and 
superfluous;  the  fact  is  already  proved  of  every  such  triangle. 
:::=ir^ Secondly.  The  term  Induction  has  been  improperly  applied 
to  discoveries  of  identification  to  establish  a  minor — a  purely 
deductive  operation. 

When  Kepler,  after  comparing  a  great  many  positions  of 
Mars,  came  to  the  conclusion  that  all  these  places  lay  in  an 
ellipse  of  certain  dimensions,  he  made  an  advance  from  the  // 
known  to  the  unknown,  which  is  one  criterion  of  induction,  u 
Without  any  farther  observations,  it  was  possible  to  assign 
the  place  of    the  planet  at    any  moment  of  time  throughout 
the   entire  circuit.      Yet,    notwithstanding   this  remarkable 
peculiarity,  the  case  is  not  J»n  induction.     It  is,  in  fact,  a 
deduction.     We  might  term  it  a  discovery  of  identification  to 
establish  a  minor. 

Supposing  that,  in  the  time  of  Kepler,  the  geometrical  pro- 


I 


ti 


-■I 


n* 


^( 


236 


MEANING  AND   SCOPE   01?  INDUCTION. 


FUNDAMENTAL   INDUCTIVE   METHOD. 


237 


positions  of  the  ellipse  had  been  still  nndiscovered,  he  could 
not  have  established  his  law,  nop  applied  it  to  fill  in  the  inter*  A 
mediate  places  of  the  planet.  What  he  really  discovered  was 
an  identity  between  the  series  of  observed  positions  of  Mars 
and  the  path  of  an  ellipse  with  the  sun  in  the  focus.  It  was 
by  the  help  of  the  known  properties  of  the  ellipse  that  he  made 
this  identity.  The  identity  once  established,  any  or  all  of  the 
propositions  of  the  ellipse  could  be  applied  to  the  orbit  of 
Mars,  and  by  these  the  orbit  could  be  as  it  were  drawn,  so  as 
to  show  the  successive  positions  of  Mars  as  he  described  his 
circuit.  There  could  have  been  no  inference  from  places 
observed,  to  places  unobserved,  except  through  the  applicatiou 
of  those  laws  respecting  the  ellipse,  which  had  been  dis- 
covered by  the  Greek  geometers.  The  propositions  of  the 
ellipse  supplied  the  major  premise  of  the  reasoning.  Kepler's 
observations  supplied  the  minor  premise  ;  they  showed  that 
the  places  of  Mars  coincided  with  the  places  in  an  ellipse ; 
whereupon  whatever  was  true  of  the  ellipse  was  true  of  the 
\.    orbit  of  Mars. 

Xy  Similar  instances  of  discoveries  of  Deduction  could  be  cited. 
When  after  the  inductive  establishment  of  the  laws  of 
magnetism  upon  Iron,  other  substances  were  discovered  to 
be  magnetic  as  Nickel,  Cobalt,  Manganese,  Chromium,  <fec., 
the  magnetic  laws  were  forthwith  transferred  deductively  to 
these  bodies.  Franklin's  great  discovery  of  the  identity  of 
lightning  and  electricity,  enabled  all  the  previously  ascertained 
facts  regarding  electricity  to  be  applied  to  the  atmospheric 
charge. 

In  contrast  to  the  law  of  the  elliptic  orbits,  we  may  quote 
Kepler's  third  law---thft  relation  of  the  periodic  times  to  the 
mean  distances,  an  induction  in  the  proper  sense  of  the  word. 
There  is  still  a  mathematical  element  present,  but  that  element 
is  not  the  major  proposition,  to  which  Kepler  supplied  a  minor. 
The  numerical  ratio  merely  expresses  the  point  of  concurrence 
of  the  particulars  observed,  it  being  the  nature  of  that  con- 
currence to  be  numerical.  The  basis  of  the  induction  was  the 
agreement  of  the  six  planets  in  the  numerical  ratio ;  and  the 
induction  was  brought  out  in  its  real  character  when  new 
planets  were  discovered  and  the  law  applied  to  them  at  once, 
and  before  there  was  time  to  observe  the  fact  in  each  indivi- 
dual case. 

^         Of  a  similar  nature  to  Kepler's  third  law  Is  the  law  of  the 
X  refraction  of  light,  a  proper  induction  set  in  mathematical  lan- 
guage.    From  a  number  of  positions  of  the  incident  and  re- 


1> 


Iracted  rays  of  light  in  various  substances,  Snell  found  that 
the  relation  of  the  two  could  be  expressed  by  a  definite 
numerical  proportion  of  the  sines  of  the  angles,  the  proportion 
being  constant  for  the  same  transparent  medium.  He  had 
observed  the  relation  in  a  number  of  cases,  and  he  inductively 
affirmed  it  in  all. 

In  like  manner  the  establishment  of  the  law  of  gravitation 
^^        was  an  induction  numerically  expressed. 

\  2.  The  sole  method  of  attaining  Inductive  truths  being 

the  observation  and  the  comparison  of  particulars,  the  sole 
evidence  for  such  truths  is  Universal  Agreement. 

A  permanent  or  uniform  concurrence  can  be  established,  in 
the  last  resort,  only  by  the  observation  of  its  uniformity.  That 
unsupported  bodies  fall  to  the  ground,  is  a  conjunction  sug- 
gested by  the  observation  of  mankind,  and  proved  by  the 
unanimity  of  all  observers  in  all  times  and  places.  What  is 
found  true,  wherever  we  have  been  able  to  carry  our  observa- 
tions, is  to  be  accepted  as  universally  true,  until  exceptions  are 
discovered.  This  is  to  apply  the  Universal  Postulate,  the 
primary  assumption  at  the  root  of  all  knowledge  beyond  the 
present — that  what  has  never  been  contradicted  (after  sufficient 
search)  is  to  be  received  as  true. 

Through  this  method  alone — of  Universal  Agreement  in  de- 
tail— can  our  most  general  and  fundamental  traths  be  dis- 
covered and  proved.  It  is  the  only  proper  Inductive  Metliod. 
By  it  are  established  the  Axioms  of  Mathematics,  the  Axioms 
of  the  Syllogism,  the  Law  of  Gravity,  the  Law  of  Causation  or 
of  Conservation.  Likewise  on  it  we  depend  for  the  proof  of 
all  uniformities  that,  although  not  ultimate,  are  for  the  time 
unresolved  into  higher  uniformities  j  or  what  are  termed  Empi- 
rical Lawfii 


CHAPTER  IL 

THE  GROmSTD  OF  INDUCTION- UlSTIFORMITY  OF 
NATURE-LAWS  OF  NATURE. 

i.  As  Induction  proper  infers  from  the  known  to  the 
unknown ;  it  assumes  that,  under  certain  circumstances 
(to  be  specified),  what  has  been  will  be.  The  same  thing 
is  otherwise  expressed  by  affirming  that  Nature  is  Uni- 
form ;  that  there  are  Laws  of  Nature. 

This  great  foundation  of  all  possible  infereDce  is  stated  iu 
many  forms  of  language.  *  Nature  repeats  itself,'  *  the  future 
will  resemble  the  past,'  *  the  absent  is  like  the  present,'  *  the 
Universe  is  governed  by  Laws.'  In  one  great  department,  it 
is  named  Causation,  or  the  Law  of  Cause  and  Effect. 

The  principle  is  put  in  another  light  by  the  remark  of  Mr. 
Mill  that  the  Uniformity  of  Nature  is  the  ultimate  major  premise 
of  every  inductive  inference.  To  prove  that  the  present 
generation  of  men  will  die,  we  may  construct  a  syllogism 
thus : — major — what  has  been  in  the  past  will  continue 
(under  given  circumstances)  ;  minor — men  have  died  in  the 
past ;  co7iclusion — men  will  continue  to  die. 

Nature  is  not  uniform  in  all  things.  One  day  agrees  with 
another  in  part,  and  differs  in  part.  Human  beings  are 
bom  with  a  certain  amount  of  uniformity,  and  also  with 
a  certain  amount  of  difference.  The  law  of  uniformity,  there- 
fore, needs  to  be  limited  and  qualified. 

2.  The  course  of  the  world  is  not  a  Uniformity,  but 
Uniformities.  There  are  departments  of  uniformity,  which 
are  radically  distinct. 

The  naost  pointed  illustration  of  this  statement  is  the 
Classification  of  the  Sciences.  Although,  in  early  ages,  men's 
minds  were  strongly  prepossessed  with  a  supposed  Unity  of 
Nature,  w«  now  recognize  a  plurality  of  distinct  kinds  of 
phenomena,  each  kind  having  its  own  separate  principles  or 
laws.  Thus,  the  facts  and  principles  of  Number  are  studied 
apart  from  the  facts  and  principles  of  Life. 


LAWS   OF  NATURE. 


239 


^ 


1"^ 


.- 


The  phrase  *  Laws  of  Nature '  may  be  understood  to  imply 
(1)  that  Nature  is  uniform,  and  (2)  that  this  uniformity  is  a 
plurality  and  not  a  unity.  There  are  separate  departments, 
each  with  its  own  uniformities  or  laws.  That  unsupported 
bodies  fall  to  the  ground,  that  fire  is  quenched  by  water,  that 
men  pursue  pleasure— are  said  to  be  laws  of  nature  ;  they  are, 
however  genencally  different  laws,  and  are  distributed  under 
distinct  branches  or  departments  of  Science  or  Knowledge. 

The  word  *  Law  *  is  a  metaphor  taken  from  human  society, 
where  it  supposes  the  relationship  named  authority  and  obedi- 
ence.  Seeing  that  in  all  well- constituted  societies,  the  decrees 
emanating  from  the  sovereign  authority  are  alike  binding  upon 
all  citizens,  in  all  times  and  places,  they  have  the  characteristic 
of  uniformity  ;  and  it  is  on  this  characteristic  alone,  that  *  law ' 
can  be  employed  to  signify  the  order  of  the  natural  world. 
The  full  definition  of  a  law  is  inapplicable  to  physical  sequences. 
The  likeness  fails  in  the  essential  point.  In  human  authority, 
a  certain  beneficial  result  is  aimed  at  by  rules  of  conduct  on 
the  part  of  the  subjects  of  the  state  ;  which  conduct  is  enforced 
by  a  penalty  or  punishment ;  and  the  penalty  is  directed  with 
precision  upnn  the  wrong  doer.  In  the  order  of  the  world, 
on  the  contrary,  a  man  conforming  to  the  physical  sequences 
IS  safe,  whatever  be  the  extent  of  his  violations  of  moral  law. 
Night  exposure  may  be  more  injurious  to  the  policeman  than 
to  the  thief;  immunity  is  purchased  not  by  virtuous  conduct 
as  regards  others,  but  by  prudential  care  as  regards  self. 

3.  The  term  *Law  of  Nature'  is  sometimes  used  in  a 
more  restricted  sense,  to  express  the  highest  generalities, 
or  ultimate  uniformities  of  nature.  ' 

There  being  a  constant  wish  to  discover,  not  merely  laws 
that  shall  be  true,  but  laws  of  the  highest  and  most  command- 
J'mi.  ^®^®^^^^^J»  such  laws  are  more  emphatically  termed 
TAe  Laws  of  Nature'— the  most  centralized  and  all-compre- 
hending expressions  of  the  order  of  nature.  This  more 
imposmg  character  appears  to  belong  to  the  law  of  Gravity, 
and  to  the  principle  named  *  The  Conservation  of  Force.' 

4.  As  regards  Logical  Method,  the  general  Uniformity 
of  nature  may  be  distributed  under  three  branches,  already 
expressed  in  the  ultimate  classification  of  Propositions— 
Co-existence  (as  Co-inherence  of  Attributes),  Causation 
and  Equaliit. 

The  three  great  relationships  found  capable  of  embracing 


/^ 


240 


THE   GROUND   OF  INDUCTION. 


all  propositions  were  stated  to  be  (I)  Co-existence,  (2) 
Sequence,  (3)  Equality  and  Inequality  (Number  and  Quan- 
tity). Under  Co-existence  was  included  Order  in  Place,  and 
Co-inhering  Attributes;  the  first — Order  in  PJace,  being 
resolvable  into  laws  of  Quantity.  Under  Sequence  or  Succes- 
sion was  included  Order  in  Time  and  Causation;  the  first-named 
being  also  a  purely  numerical  relationship.  The  third  rela- 
tionship, Equality  and  Inequality,  is  the  basis  of  Mathematics, 
the  science  of  Qu\ntity  and  NumlDer. 

Thus  the  three  distinct  heads  of  scientific  investigation, 
comprising  all  the  uniformities  or  laws  of  nature,  are  Unifor- 
mities of  Co-existence,  Uniformities  of  Succession  (Causation), 
Uniformities  of  Equaliiy  and  Inequalihj,  These  are  the  three 
cases  that  Induction  has  to  deal  with. 

In  the  actual  working  of  Induction,  we  find  it  to  be  almost 
entirely  absorbed  with  the  second  head — Causation. 

Besides  that  there  are  very  few  general  laws  of  pure  Co- 
existence, Causation  is  singular  in  providing  a  comprehensive 
Uniformity,  which  may  be  appealed  to  deductively,  for  all 
cases.  The  uniformities  of  Co-existence  (independent  of 
Causation)  can  be  proved  only  piece-meal ;  each  stands  on  its 
own  evidence  of  observation  in  the  detail ;  no  one  assists  us 
to  prove  another.  There  is  thus  a  blankness  of  resources 
in  regard  to  the  proper  laws  of  Co-existence  ;  their  Logic  is 
speedily  exhausted. 

The  same  defect,  strange  as  it  may  sound,  attaches  to  the 
uniformities  of  Quaniity — based  on  the  relations  of  Equality 
and  Inequality.  The  certainty  of  the  mathematical  axioms  is 
a  certainty  due  to  their  easy  and  thorough  verification  one  by 
one ;  not  to  their  falling  under  any  unitormity  more  compre- 
hensive than  themselves.  It  is  by  *  Agreement  through  all 
Nature  *  that  we  prove  that  *  Things  equal  to  the  same  thing 
are  equal ;  *  having  found  this  fact  always  true,  never  false, 
we  extend  it,  by  the  Inductive  hazard,  to  all  cases  whatsoever. 
We  repeat  the  operation  upon  the  other  great  axiom — *  The 
sums  of  equals  are  equal.*  We  must  proceed,  in  the  same 
method  of  detail,  to  all  other  axioms — as  the  dictum  of  the 
syllogism,  the  axiom  a  fortiori,  &r<Q. 

The  extended  machinery  of  Inductive  research,  constituting 
the  Logic  or  Method  of  Induction,  is  thus  nearly  confined  to 
Causation.  The  greatest  resources  for  eliminatmg  accidental 
accompaniments  and  for  seizing  the  real  concomitances  of 
facts — the  so-called  *  Experimental  Methods  * — have  their  full 
application  only  to  Cause  and  Effect. 


CHAPTER  in. 

INDUCTION  OF  CO-EXISTENCE. 

1.  Of  Uniformities  of  Co-existence,  a  very  large  num- 
ber may  be  traced  to  Causation.  It  remains  to  be  seen 
whether  there  be  any  not  so  traceable. 

The  numerous  Co-existences  of  Order  in  Place,  or  the  dis- 
tribution and  arrangements  of  material  objects  throughout  the 
Universe,  are  all  the  results  of  causation,  starting  from  some 
prior  arrangements.  The  distribution  of  sea  and  land,  the 
stratification  of  the  earth's  crust,  the  existence  of  an  atmos- 
phere, the  distribution  of  the  materials  of  the  globe  generally, 
— ^are  the  result  of  natural  agencies  or  forces,  operating  upon 
prior  arrangements.  Salt  is  found  in  the  ocean,  because  the 
water  has  dissolved  all  accessible  portions  of  it.  The  heavy 
metals  are  found  in  deep  rocks  in  consequence  of  their  weight ; 
the  corrosible  and  combining  metals  occur  in  combination  ; 
and  those  that  are  reluctant  to  combine,  occur  nearly  pure,  as 
Platinum  and  Gold. 

There  are  thus  no  independent  laws  of  co-existence  to  be 
found  among  uniformities  of  Order  in  Place.  We  must  seek 
for  them,  if  there  be  any  such,  among  Co-inhering  Attributes. 
It  is  possible  that  attributes  or  properties  not  connected  as  cause 
and  effect,  may  yet  be  conjoined  uniformly  through  all  nature. 

If  so,  they  are  likely  to  be  found  among  the  natural  kinds 

Minerals,  Plants,  Animals.  The  conj  auction  of  body  and 
mind  in  man,  and  in  the  animals,  is  to  all  appearance  such  a 
case  as  we  are  in  quest  of. 

2.  It  is  the  special  peculiarity  of  the  Natural  Kinds  to 
combine  many  attributes  in  unity  of  subject.  In  them  we 
have  the  chief  exemplification  of  co-inhering  attributes ; 
and  they  seem  to  furnish  uniformities  of  co-existence. 

Thus  Gold  unites  a  certain  specific  gravity  (19.3),  crvstal- 
lization  (cubical),  tenacity,  fusibility  (melting  point,  1200°  C), 
colour  and  lustre  (yellow),  electrical  conduction,  atomic  weight 
(196),  combining  properties  (acted  on  by  aqua  regia).  These 
are  eight  leading  attributes  that  concur  in  every  piece  of  gold ; 


242 


INDUCTION  OF  CO-EXISTENCB. 


and  unless  we  see  onr  way  to  deriving  some  of  them  from 
others,  we  must  pronounce  them  essenticBf  essential  or  defining 
attributes  of  gold.  There  is  a  co-existence,  or  co- inherence  of 
these  eight  facts,  with  others,  in  the  object  named  gold. 

To  appearance  there  is  here  a  uniformity  of  co- existence. 
No  specimen  of  gold  is  devoid  of  any  one  of  the  eight  proper- 
ties. Properly  speaking,  however,  this  is  merely  affirming  an 
identical  proposition.  Should  there  occur  a  specimen  wanting 
in  one,  two,  or  three  of  the  eight,  we  should  say  not  that  a  law 
of  co-existence  was  infringed,  but  that  a  difierent  substance 
was  produced.  If  these  be  the  essential  attributes  of  gold — the 
meaning  or  connotation  of  the  name,  then,  on  the  failure  of  any 
one  or  more,  the  name  would  cease  to  be  applied,  the  substance 
would  not  be  ranked  as  gold,  it  would  be  classed  as  a  new  and 
distinct  substance.  Gold  with  the  specific  gravity  of  9,  or 
with  a  silvery  colour,  or  with  a  liability  to  corrode,  would  not 
be  gold,  it  would  be  treated  as  a  difierent  material,  a  distinct 
grouping  or  aggregate  of  powers  and  properties.  If  there  be 
any  one  of  the  now  enumerated  properties  of  gold  that  we 
could  see  changed  and  yet  keep  up  the  designation  gold,  that 
property  is  declared  not  to  be  the  essence,  but  a  concomitant 
of  gold.     A  proper  inductive  enquiry  would  hold  in  such  a  case^ 

3.  For  a  Law  or  Uniformity  of  Co-existence,  properly 
so  called,  we  must  refer  to  examples,  if  such  there  be, 
where  two  or  more  independent  properties  are  conjoined 
through  all  nature,  or  in  all  substances  where  one  of  them 
occurs. 

We  must  search  among  the  properties  of  kinds — mineral, 
vegetable,  and  animal,  for  some  that  are  coupled  throughout 
every  species,  and  under  every  variety  of  aggregation.  For 
example,  could  we  find  a  certain  crystalline  form  regularly 
conjoined  with  certain  chemical  characters,  not  in  one  sub- 
stance only,  but  in  all  substances  possessing  that  crystal- 
lization,— this  would  be  a  proper  law  or  uniformity  of  co-exist- 
ence. There  would  still  remain  a  question,  often  difficult  to 
settle — whether,  on  the  one  hand,  the  two  are  mutually  im- 
plicated properties,  or,  on  the  other  hand,  whether  they  are 
connected  by  cause  and  effect. 

To  detect  such  uniformities  of  general  co-existence,  among 
the  essential  properties  of  mineral  bodies,  whether  simple  or 
compound,  is  a  proper  object  of  scientific  enquiry.  Nor  has 
it  been  neglected  by  physical  enquirers.  The  following  are 
the  leading  examples  obtained  up  to  the  present  time. 


LAWS   OF  CO-EXISTENCE. 


2  id 


(1)  A  law  has  been  discovered  connecting  Atomic  Weight 
and  Specific  Heat  by  an  inverse  proportion.  For  equal 
weights  of  the  simple  bodies,  the  atomic  weight,  multiplied  by 
a  number  expressing  the  specific  heat,  gives  a  nearly  uniform 
product  Thus,  for  sulphur,  the  atomic  weight  (32),  multi- 
plied by  the  specific  heat  (0.1776),  gives  5.U8  ;  the  atomic 
weight  of  platinum  (197),  multiplied  by  its  specific  heat, 
(0.0324),  gives  6,38.  The  products  for  all  the  elements  are 
near  the  constant  number  6. 

(2)  A  law  obtains  between  the  Specific  Gravity  of  substances 
in  the  gaseous  state  and  the  Atomic  Weights.  Thus,  the  specific 
gravity  of  oxygen  is  16,  its  atomic  weight  16  ;  hydrogen, 
specific  gravity  1,  atomic  weight  1 ;  phosphorus,  specific 
gravity  62,  atomic  weight  31  (the  relation  here  is  2  to  1) ; 
steam,  specific  gravity  9,  atomic  weight  18  (relation  of  1  to  2). 
The  relationship  of  the  two  numbers  is  thus,  in  some  instances, 
equality ;  in  other  instances,  the  one  is  a  multiple  of  the 
other.  .  The  law  is  one  of  importance  in  ascertaining  atomic 
weights. 

With  an  exception  to  be  noticed  presently,  these  are  perhaps 
the  two  most  widely-operating  laws,  as  yet  discovered,  whereby 
two  distinct  properties  are  conjoined  throughout  substances 
generally.  There  are  various  laws  of  narrower  range,  as,  for 
example,  Andrews's  laws  of  the  heat  of  combination  of  the 
metals. 

4.  A  peculiar  importance  belongs  to  the  law  of  universal 
co-existence  uniting  the  two  properties  — Inertia  and 
Gravity.  These  properties  are  co- existent  through  all 
matter  and  proportionate  in  their  amount. 

Inertia,  the  defining  attribute  of  matter,  means  both  resist- 
ance to  movement,  and  force  when  moved.  It  is  totally  dis- 
tinct from  gravity.  A  body  rolled  on  a  level  surface  shows  its 
inertia ;  so  also  do  two  weights  equipoised,  as  in  the  beautiful 
experiments  of  Attwood.  Now,  all  inert  matter  gravitates  ; 
and  the  force  of  gravitation  is  proportional  to  the  inertia. 
Equal  weights,  (which  are  the  estimate  of  gravity),  are  equally 
resisting  to  a  horizontal  impulse  (the  measure  of  inertia)  or  to 
a  vertical  impulse  in  the  balanced  condition. 

It  cannot  be  maintained  that  these  properties  are  mutually 
implicated.  We  can  easily  suppose  matter  (considered  as 
inert)  without  the  property  of  distant  mutual  attraction,  or 
gravitation  ;  this  last  property  may  be  fairly  viewed  as  added 
to,  or  superinduced  upon  mere  inertia.     Nor  can  we  call  the 


I 


244 


INDUCTION   OF  CO-EXISTENCE, 


CONCOMITANT  PKOPERTIES  OF  KINDS. 


245- 


two  either  cause  and  effect,  or  effects  of  a  common  cause ;  onr 
knowledge  does  not  entitle  us  to  make  either  supposition.  Wo 
can  prove  cause  and  effect  only  bj  exhibiting  first  a  cause, 
and  then  an  effect  flowing  from  it.  Here  the  two  facts  or 
properties  are  inseparable. 

There  is  no  other  equally  unambiguous  instance  of  a  law  of 
universal  co-existence.  The  examples  above  quoted  with 
reference  to  three  properties — specific  gravity  in  the  gaseous 
state,  atomic  weight,  and  specific  heat — may,  for  anything  we 
know,  be  mutually  implicated,  or  related  as  cause  and  effect. 
If  we  understood  more  thoroughly  the  ultimate  arrangement 
of  the  atoms  of  bodies,  and  their  intestine  motions,  we  might 
not  improbably  find  that  some  one  fundamental  property  was 
at  the  foundation  of  all  the  three ; — a  real  essence,  of  which 
these  are  but  propria.  As  regards  many  of  the  minor  laws, 
the  existence  of  either  implication  or  causation  is  more  than  a 
mGrQ  surmise. 

Under  such  circumstances  we  are  entitled  to  conclude  that 
nniformities  of  general  co-existence  are  very  rare.  The  pre- 
sumption or  probability  (although  not  the  certainty)  in  every 
new  case  of  uniformity  is  that  it  is  a  case  of  causation  and  not 
of  co-existence.  Thus,  the  conjunction  of  Mind  and  Body  may 
be  a  co-existence  independent  of  causation,  like  inertia  and 
gravity ;  but  it  may  also  follow  the  more  prevailing  type,  and 
be  a  case  of  cause  and  eflTect.  Which  is  cause  and  which 
effect,  or  whether  they  are  effects  of  a  common  cause,  may  bo 
open  to  dispute. 

5.  The  only  proof  of  Uniformities  of  Co-existence  not 
known  to  depend  on  causation,  is  uncontradicted  Agree- 
ment through  all  nature. 

This  is  the  proof  of  the  Law  of  Causation  itself.  Now  any 
uniformity  not  coming  under  causation  must  stand  on  its 
own  independent  evidence  ;  and  this  evidence  is  uniform 
agreement  throughout  the  whole  compass  of  observation. 
We  must  find  it  true  in  all  times,  all  places,  and  all  circum- 
stances ;  and  provided  our  search  has  been  so  extensive,  that  if 
there  were  any  exceptions  we  should  light  upon  them,  and  no 
exceptions  have  been  found,  we  are  entitled  to  declare  it  a  law 
of  all  nature. 

The  coincidence  of  gravity  with  inertia  has  been  proved  over 
the  entire  globe  ;  it  applies  undoubtedly  to  the  solar  system  ; 
and  by  very  strong  analogy  to  the  distant  stars.  This,  there- 
fore, may  be  held  to  be  an  established  uniformity  of  co-existence. 


The  alliance  of  mind  with  a  bodily  mechanism  extends 
throughout  the  whole  of  animal  life,  past  and  present 

The  co-existences  above  mentioned  regarding  the  properties 
of  gaseous  specific  gravity,  atomic  weight,  and  specific  heat, 
have  to  be  verified  by  the  method  of  Agreement  throughout  all 
bodies.  We  cannot,  as  in  cause  and  effect,  presume  from  a 
small  number  to  all  the  rest. 

6.  The  special  coincidences  making  up  the  Natural 
K^inds  must  also  be  verified  by  Agreement  over  the  whole 
field  of  instances. 

We  have  already  remarked  that  an  exception  to  a  kind, 
arising  from  the  failure  of  an  essential  property,  would  not  be 
the  infringement  of  a  uniformity,  but  the  setting  up  of  a  new 
kind.  The  only  case  for  proving  a  co-existence  would  be  the 
case  of  concoTuitant  properties,  or  those  not  adopted  into  the 
essence  or  connotation  of  the  kind.  Of  such  a  character  is  the 
blackness  of  the  crow,  the  whiteness  of  the  swan,  and  varia- 
tions of  colour  generally  ;  a  point  seldom  treated  as  essential, 
whether  in  minerals,  plants,  or  animals.  Now  the  sole  proof 
that  *  every  crow  is  black,'  is  observation  through  all  Nature ; 
so  long  as  no  other  colour  is  seen,  we  affirm  the  general  pro- 
position ;  the  occurrence  of  various  albinos  has  disproved  the 
generality,  and  reduced  it  to  an  approximate  generalization,  of 
A  very  high  order  of  probability. 


CHAPTER  rV. 

LAW  OF  CAUSATION. 

1 .  The  Uniformities  of  Succession  presented  in  nature 
are  subject  to  one  great  uniformity — the  law  of  Causation. 

The  law  may  be  expressed  thus  : — In  every  change,  there 
is  a  uniformity  of  connexion  between  the  antecedents  and  the 
consequents. 

No  single  expression  sums  up  all  that  is  implied  in  Cause 
and  Effect.  When  it  is  said,  *  Every  effect  has  a  cause,  and 
every  cause  an  effect,  and  that  the  sequence  is  regular,  the 
Kame  causes  being  always  followed  by  the  same  effects,*  the 


246 


LAW  OF  CAUSATION. 


proposihon  is  an  identical  statement;  the  word  '  Cause'  means 
what  brings  about  nn  effect ;  and  the  word  <  Eflect '  what 
follows  from  a  cause.  To  avoid  this  objection,  we  maV  state 
the  law  as  follows  :-<  Every  event  that  happens  is  definitely 
and  uniformly  connected  with  some  prior  event,  or  events. 

tK-  ^?P^"V"^'«'*  happens;  and  which  failing,  it  failj 
The  kindling  of  a  fire  follows  regularly  on  the  prior  events  of 
making  a  heap  of  combustibles  and  applying  a  li<rht 

A  law  IS  more  sharply  stated  by  help  of  its  denial^.    Causa- 
tion  denies  two  things.     First,  it  denies  pure  spontaneity  of 
commencement.     If  the  law  is  true,  no  cLnge  arises  out  of 
vacuity  or  stillness  ;  there  must  be  some  prior  event,  cbanee 
or  movement,  as  a  sine  qua  non  of  the  occuiTence  of  kny  nfw 

orr„tcf  •   T^'',''"'-st«  <»^t  without  some  commencing 

circumstance,  in  the  shape  of  movement,  change,  or  activity. 
.    Secondly.  The  law  denies  that  events  foUSw  one  anoth;r 
irregnlariy,  indiscriminately,  or  capriciously.      The  same  cir- 
cumstances that  make  a  fire  burst  out  to-day,  will  if  reoeated 
make  it  burst  out  to-morrow,  or  at  any  future 'timf    The 
T^^\  ''^'^'  \°  *'=^f  ">«  circumstances,  does  not  at  one  time 
repel,  and  at  another,  attract  and    allure  us.     In  short  the 
iaw  IS  the  statement  of  uniformity  in  the  Succession  of  events. 
2.  In  Causation,  the  same  cause  always  produces  the 
saine  effect;    but  the  converse  does  not  hold;    the  same 
ettect  IS  not  always  produced  by  the  same  cause.      There 
may  be  Plurality  of  Causes. 

hJ^Atltr-  ^'T  ?"  "  "'"''"  '"^'""^  *^'"  '^l^VS  cause  death  : 
but  death  IS  not  always  caused  by  a  blow  on  the  head  There 
are  many  causes  of  motion  ;  and  the  presence  of  any  one  1^ 
the  proper  circumstances,  will  always  be  followed  by  mot"on 

kept  in  view  in  the  investigation  of  causes.      If  a  chance  ha! 

LdentlW  W  '"?'*  ^"^  ^^"^  ^  P^^^^O"^  <=bange,  orW 
cedent  fact,  but  not  necessarily  one  particular  antecedent. 

3.  The  Plurality  of  Causes  is  subject  to  uniformity  in 
two  respec  s :  (1)  tlie  number  of  causes  is  fi.xed  ;  (2)  the 
character  of  each  ,s  as  definite  as  if  it  were  the  sole  ciuse 

fi.i  o  Tf°'  of  death  may  be  numerous,  but  they  are  all 
fixed  and  knowable ;  and,  when  known,  may  be  connt^  on 
with  certainty  and  precision.  The  fact  of  plurality  renders 
the  causation  of  an  event  ambigaons  j  there  m^y  berverll 
alternative  a:ita33i3..t3.     Tet,  these  antecedents  being,  once 


PRACTICAL  ASPECT  OF  CAUSATION. 


247 


for  all,  exhaustively  known,  we  are  sure  that  one  of  them  is 
the  operative  circumstance  in  the  case  before  us. 

It  will  bo  pointed  out  afterwards  that  plurality  of  causes  is 
more  an  incident  of  our  imperfect  knowledge  than  a  fact  in 
the  nature  of  things.  As  knowledge  extends,  we  find  less  of 
plurality.  The  numerous  apparent  causes  of  motion  are  differ- 
ent only  in  superficial  appearance  ;  they  are  all  one  at  bottom. 

4.  Causation  may  be  viewed  uuder  three  different  aspects. 

(1)  The  first  may  be  called  the  practical  and  popular  aspect 
—a  partial  view  suited  to  the  ordinary  emergencies  of  life. 
Under  this  aspect,  the  cause  is  some  one  circumstance  or 
condition  demanding  our  solicitude,  as  being  precarious. 
Thus,  when  the  soldier,  on  the  eve  of  an  engagement,  is  urged 
to  keep  his  powder  dry,  this  is  not  the  whole  cause  of  his 
bitting  the  enemy  ;  it  is  the  circumstance  that  happens  to  be 
in  peril  at  the  time. 

(2)  The  second  aspect  is  the  Scientific  or  complete  view  of 
Causation.  Under  this  view,  all  the  conditions  or  antecedent 
circumstances  are  fully  enumerated. 

(3)  A  third  aspect  is  Causation  viewed  as  embracing  the 
modern  generalization,  entitled  the  Conservation  or  Correlation 
of  Force. 

CAUSATION   PRACTICALLY   VIEWED. 

5.  In  common  language,  the  Cause  of  an  event  is  some 
one  circumstance  selected  from  the  assemblage  of  condi- 
tions, as  being  practically  the  turning  point  at  the  moment. 

A  man  slips  his  foot  on  a  ladder,  falls,  and  is  killed.  The 
cause  of  the  fatality  is  said  to  be  the  slipping  ;  for  if  this  one 
circumstance  had  been  prevented,  the  effect  would  not  have 
happened.  Yet,  in  order  to  the  result,  many  other  conditions 
were  necessary  :— the  weight  of  the  body  (gravity),  the  height 
of  the  position  (a  certain  collocation),  the  fragility  of  the  human 
frame.  Yet,  for  practical  purposes,  we  leave  out  of  sight  at 
the  moment  all  the  elements  that  are  independent  of  us  and 
secure,  taking  notice  only  of  what  is  in  our  power  and  needs  our 
attention.  By  a  common  ellipsis,  all  arrangements  that  are 
fixed  and  settled,  are  passed  over  in  silence.  We  presume 
on  the  forces  of  heat  and  gravity,  and  devote  our  care  to  the 
choice  and  shaping  of  the  materials  whereby  these  forces  may 
be  made  to  work  out  our  ends. 

When  we  speak  of  food  as  the  cause  of  animal  strength,  we 


248 


LAW  OF  CAUSATION. 


snppose  a  healthy  constitofclon,  able  to  digest  and  assimi- 
late it.  But,  in  this  particular  case,  mankind  long  en^ed  in 
ignorantly  suppressing  a  condition  no  less  essential  than 
tooa,  namely,  the  oxygen  of  the  atmosphere  —  the  aerial 
element  of  our  food.* 

Language  is  adapted  principally  to  this  mode  of  viewing 
causation.     In  the  distinction  of  agent  and  thing  acted  on 
which  pervades  the  whole  of  grammar,  and  gives  the  character 
to  the  active  verb,  there  is  an  arbitrary  selection  of  one  circum- 
stance as  cause,  other  equally  indispensable  circumstances  bein^ 
overlooked.      A  prize  ox  is  reared  in  a  breed  of  cattle  •    the 
breederis  by  courtesy  styled  the  cause  ora-ent;  but  his  activity 
IS  only  a  single,  although  indispensable  circumstance.  A  teacher 
mstructs  a  pupil,  and  is  credited  as  the  cau.e  or  author  of  the 
pnpil  s  knowledge      A  still  more  glaring  ellipsis  is  practised 
in  attributing  the  issue  of  a  war  to  the  commander-in-chief- 
as  when  we  speak  of  the  conquests  of  Alexander  or  Ciesar' 
Ihe  monk  that  shook  the  world  '  is  rhetoric  for  the  ao-encv  of 
Luther.  °       -^ 

The  first  attempt  at  a  precise  analysis  of  Causation  was  made  by 
Aristotle.  He  enumerates  four  kinds  of  Causes,  -the  material  the 
formal,  the  efficient,  and  the  final  The  material  cause  is  Uterally 
the  matter  used  in  any  construction ;  marble  or  bronze  is  the 
material  of  a  statue.  The  formal  cause  is  the  form  type  or 
pattern  m  the  mind  of  the  workman  ;  as,  the  idea  or  design  con- 
ceived by  the  statuary.  The  formal  cause  of  a  building  is  the 
architect's  plan.  The  efficient  cause  is  the  power  acting  to  produce 
the  work,  the  manual  energy  and  skill  of  the  workman,  or  the 
mechanical  pnme  mover,  whether  human  power,  wind,  water,  or 
steam.  The  final  cause  is  the  end,  or  motive  on  whose  account 'the 
work  IS  produced  — the  subsistence,  proiit,  or  pleasure  of  the 
artificer. 

Aristotle  gives  the  instance  of  a  physician  curin^  himself,  as 
combining  all  the  four  causes  in  one  subject.  ° 

♦  Whenever  the  existence  or  safety  of  anything  depends  upon  a  sum  or 
system  oi  contrivances  adapted  tea  common  end-which,  tocrether.  are 
conditions  necessary  for  its  preservation -then  the  destruction,  disturbance 
or  removal  of  one  of  these  contrivances— the  failure  of  any  part  of  this 
composite  system  of  safeguards— is  considered  hs  the  came  of  the  ruin  of 
the  whole.  *  or  example,  if  the  action  of  any  one  of  tlie  iunctioiis  or  organs 
necessary  to  human  hfe  is  stopped,  life  is  extinguished,  and  the  circum. 
stance  producing  that  effect  is  said  to  be  the  cauK-  of  death.  So,  if  a  ship 
springs  a  leak  and  sinks,  or  if  an  army  is  surprised  thn.ugh  the  absence  of 
a  sentinel  from  his  post-  the  springing  of  the  leak,  and  the  absence  of  the 
sentinel,  is  said  to  be  the  cause  of  the  loss  of  the  ship  and  the  surprise  of 
the  army.  The  language  by  which  such  an  effect  is  commonly  ascribed  to 
a  merely  negative  cause  is  elliptical.     (G.  C.  Lhwis) 


SCIENTIFIC   CAUSATION. 


249 


This  analysis  is  obviously  taken  from  human  industry,  which 
contams  the  several  circumstances  mentioned.  It  throws  no  h^-ht 
upon  causation  in  the  order  of  nature;  while  the  attempts'" to 
express  natural  phenomena  according  to  such  a  scheme,  have  led 
to  distortions  and  unmeaning  conceptions. 

The  first  and  second  causes  give  the  celebrated  distinction  of 
Matter  and  Eorm,  which  pervades  the  whole  of  Aristotle's  philo- 
sophy. The  third,  the  Efficient,  has  continued  in  the  language  of 
science;  a  better  designation  for  the  meaning  is  Prime  Mover  or 
Moymg  Power.  The  fourth,  the  Final  cause,  is  more  perspicu- 
ously expressed  by  Motive,  End,  Intention,  Purpose,  Object  or 
l^esign ;  it  apphes  to  natm-e  only  as  personified,  or  as  the  work  of 
a  personauty. 

SCIENTIFIC   CAUSATION. 

6.  In  scientific  investigations,  the  Cause  must  be  regarded 
as  the  entire  aggregate  uf  conditions  or  circumstances  re- 
quisite to  the  ea'ect. 

All  the  conditions  suppressed  by  the  practical  man  are 
brought  back  by  the  scientific  man  in  a  full  statement  of  the 
cause.  If  any  are  omitted,  it  is  because  they  are  so  obvious 
that  no  person  could  overlook  them.  There  is  a  legitimate 
ellipsis  ot  expression,  even  in  the  scientific  enumeration  of  con- 
ditions. 

The  cause  of  the  inundations  of  the  Nile  would  be  described 
as  (1)  the  fall  of  moisture  as  snow  on  the  lofty  mountains  of 
Africa  where  the  Nile  has  its  source  ;  (2)  the  melting  of  this 
snow  by  the  summer  heat.  Gravity,  the  laws  of  heat,  the  con- 
stitution of  water,  are  all  a  part  of  the  cause,  and  if  not  men- 
tioned, are  supposed  to  be  fully  present  to  the  mind  of  the 
nearer. 

The  growth  of  plants  is  a  complicated  causation.  There 
must  concur,  the  properties  of  the  germ,  the  contact  with  the 
soil,  air,  water,  saline  bodies  in  the  soil,  heat,  light,  &c. 
The  agriculturist  thinks  only  of  a  select  number  of  these— the 
seed,  the  quality  of  the  soil,  moisture,  and  heat;  the  veo-etable 
physiologist  brings  into  view  the  physical,  chemical,  an°d  vital 
agencies,  which  are  the  causes  of  the  phenomenon  in  the  final 
analysis. 

The  cause  of  vision  is  summarily  given  as  light  ent^-rino'  the 
lenses  of  the  eye.  The  full  enumeration  of  the  circumstances 
would  include  the  optical  action  of  the  lenses,  the  physiolo^v 
of  the  coats  of  the  eye,  and  of  the  nerves  and  brain ;  and 
finally,  the  link  associating  a  certain  activity  of  the  brain  with 
a  feeling  in  the  mind. 


1 


rrr;  ~  '■»  ■■—  _-?~-!»»-rrf»-" 


250 


LAW  OF  CAUSATION. 


The  cause  of  the  Reformation  was  Luther's  preaching  against 
the  sale  of  indulgences,  concurring  with  the  administration  of 
the  church,  and  the  state  of  men's  minds  at  the  time. 

In  speaking  of  antecedents  of  the  French  Revolution,  it  is 
customary  to  use  the  plural— Causes  ;  signifying  that  a  union 
of  many  circumstances  or  conditions  was  involved.  In  the 
enumeration  of  Alison,  no  less  than  sixteen  causes  are  given. 

Gibbon  attributes  the  rapid  growth  of  Christianity  to  one 
primary  cause,  namely,  the  convincing  evidence  of  the  doctrine, 
and  of  the  ruling  providence  of  its  author ;  and  to  five  aiding 
secondary  causes,  *  which  assisted  in  producing  the  effect,  viz.: 
1,  the  inflexible  zeal  of  the  early  Christians ;  2,  the  doctrine 
of  a  future  life,  as  held  by  the  Christian  Church ;  3,  the  mira- 
culous powers  ascribed  to  the  primitive  church  ;  4,  the  pure 
and  austere  morals  of  the  Christians;  5,  the  union  and 
discipline  of  the  Christian  republic' 

The  conditions  of  phenomena  include  netjatlve  as  well  as 
positive  circumstances;  the  absence  of  hindrances  to  the 
operation  of  the  agents  concerned.  The  sun  is  the  cause  of 
vision,  provided  he  is  not  screened,  provided  the  subject  is  not 
asleep  or  blind.  It  is  usual  to  suppress  the  mention  of  all 
such  hindrances,  if  they  are  really  absent. 

7.  The  suppressing  of  essential  conditions  is  a  common 
fallacy  of  Causation. 

When,  in  the  statement  of  a  cause,  there  is  not  merely  an 
ellipsis  of  understood  circumstances,  but  an  omission  of  some 
essential  fact,  the  consequence  is  positive  error. 

When  the  healthy  effect  of  residence  at  a  medicinal  spa  is 
attributed  exclusively  to  the  operation  of  the  waters,  there  is 
a  fallacy  of  causation ;  the  whole  circumstances  and  situation 
being  the  cause. 

This  is  a  common  form  of  Inductive  fallacy,  and  prevails  in 
all  the  complicated  sciences,  as  Politics  and  Medicine. 

CAUSATION  AS  CONSERVATION  OF  FORCE  OR  ENERGY. 

.  8.  A  great  advance,  in  the  mode  of  viewing  Causatiou, 
is  made  by  the  modern  discovery  of  the  law  named  *  Cor- 
relation of  Force/  or  '  Conservation  of  Energy.' 

The  great  generalization  of  recent  times,  variously  designated 
the     Conservation,    Persistence,    Correlation,     Convertibility 
Equivalence,  Indestructibility  of  i/nerf^y,  is  the  highest  expres-' 
sion  of  Cause  and  Eff*ect.     In  every  instance  of  causation,  there 


ai 


LAW  OP  CONSERVATION. 


251 


IS  a  putting  forth  of  force  in  given  circumstances,  and  the  law 
in  question  states  exactly  what  becomes  of  the  force,  and  is 
often  the  sufficing  explanation  of  the  special  phenomena,  as 
well  as  the  embodiment  of  nature's  uniformity  in  successions. 

Statement  of  the  Law  of  Conservation. 
9.  Force,  Energy,  Moving  Power,  or  Woi'k  Power,  is 
embodied  in  various  forms,  all  mutually  convertible  at  a 
definite  (fixed)  rate.  The  extinction  of  energy  in  one  form 
is  accompanied  by  the  creation  of  energy  in  another  form : 
in  the  transmutation  work  is  said  to  be  done,  and  no  force 
is  absolutely  lost. 

(1)  Matter  in  motion  is  Force  manifested  as  actual,  apparent, 
or  kinetic  energy;  but  the  modes  of  motion  may  be  very 
various.  We  are  most  familiar  with  that  of  mechanical 
energy,  as  in  the  case  of  a  flying-ball,  a  water  stream,  or  the 
wind.  There  is,  however,  reason  to  believe  that  the  forces 
named  heat,  light,  and  electricity,  consist  in  minute  move- 
ments of  material  particles. 

Matter  in  -position  corresponds  to  a  possible  production  of 
power ;  or  the  configuration  of  a  material  system  corresponds, 
in  virtue  of  the  mutual  action  of  its  parts,  to  a  definite  amount 
o^ possible  or  potential  energy.  A  head  of  water  represents  a 
certain  amount  of  moving  power  by  its  very  'position.  This 
energy  may  not  be  evoked,  and  may  exist  for  ever  only  as 
potential.  Yet  it  is  as  really  existing  as  when  it  is  employed 
to  turn  a  wheel. 

(2)  The  different  forms  of  energy  may,  under  certain  ar- 
rangements, be  transmuted  one  into  the  other.  Mechanical 
force  may  pass  into  heat,  and  heat  into  mechanical  force  :  an 
energy  of  motion  may  be  exchanged  for  an  energy  of  position 
and  conversly.     The  rate  of  exchange  is  invariable. 

(3)  In  the  interchange  of  energies  nothing  is  lust.  In  every 
case  where  energy  disappears  by  resistance,  and  is  seemingly 
lost,  a  definite  equivalent  of  heat  is  generated. 

If  we  suppose  a  portion  of  the  universe  isolated  so  that  it 
neither  gives  nor  receives  energy  from  without,  then  the 
principle  of  the  Conservation  of  Energy  asserts  that  the  sum 
of  the  kinetic  and  potential  energies  within  this  material  system 
is  constant  and  unalterable.  The  actions  and  reactions  of  its 
parts  can  only  vary  the  relative  proportions  of  kinetic  and 
potential  energies,  but  not  their  amount. 

Of  these  three  circumstances  the  first  matter  in  motion  or  in 
position,  is  the  definition  or  generalisation  offeree  or  energy; 


^ 


252 


CAUSATION  AS  CONSERVATION  OF  FORCE. 


I 


the  second,  transmutation  of  one  form  of  power  into  another  ; 
and  the  third,  conservation  of  the  sum  of  the  energies  of 
motion  and  position  of  any  self-contained  system,  under  all 
chancres,  are  the  properties  or  predicates,  constituting  the  Law 
of  Correlation  or  the  Conservation  of  Energy. 

10.  Ill  explaining  the  principle  of  Conservation  as 
applied  to  the  different  forms  of  actual  energy,  we  may 
rank  them  in  two  divisions,  Molar  and  Molecular, — 
motion  in  mass  and  motion  in  molecule. 

The  Molar  Forces  are  the  same  as  those  termed 
Mechanical. 

The  molar  or  mechanical  forces  are  the  motions  of  sensible 
masses,  as  a  hammer,  a  waterfall,  a  locomotive,  a  planet.  The 
science  of  Mechanics,  or  Molar  Physics,  is  occupied  with  the 
computation  of  these  forces,  in  their  transfer  and  re-distribu- 
tion under  all  varieties  of  circumstances. 

The  Persistence  or  Conservation  of  Force  was  first  distinctly 
conceived  with  reference  to  these  palpable  motions.  Newton's 
First  Law  of  Motion  expresses  the  fact  that  a  mass  once  in 
motion  will,  if  unobstructed,  always  continue  in  motion  at  the 
same  rate ;  which  is  the  same  as  saying  that  force  never 
decays.  In  free  space,  beyond  the  reach  of  molestation  from 
without,  a  moving  body  would  preserve  its  motion  for  ever. 
This  is  the  simplest  aspect  of  Conservation. 

A  moving  body  encouniering  a  second  bod;/,  whether  at  rest 
or  already  in  motion — (1)  if  we  suppose  both  bodies  to  be  per- 
fectly elastic— imparts  its  own  motion,  in  whole  or  in  part,  to 
the  body  struck.  This  is  a  new  situation.  There  is  a  loss  of 
power  on  one  side,  and  a  gain  on  the  other  ;  a  redistribution 
of  the  movements  of  the  two  masses.  Now,  in  this  state  of 
things,  the  Law  of  Conservation  declares  that  in  the  inter- 
change nothing  is  wasted  ;  whatever  the  striking  body  loses, 
the  struck  body  gains. 

If  the  two  masses  are  equal,  there  will  be  simply  an  in- 
terchange of  velocities,  and  of  momenta  ;  and  if  they  are  not 
equal,  still  the  impact  will  not  alter  either  the  total  momentum, 
or  the  moving  energy  of  the  whole. 

(2)  When  the  bodies  are  inelastic,  then  the  visible  energy 
will  disappear  in  whole  or  in  part.     If  a  contemporary  of 
Newton  had  been  asked  what  becomes  of  the  force  of  cannon 
shot  arrested  by  a  dead  wall,  he  would  probably  have  answered 
that  an  intinitesimally  small  movement  was  imparted  to  the 


CONSERVATION   OF  MECHANICAL  FORCE. 


253 


mass  of  rock  and  its  contiguous  materia,!.  This  would  have 
been  regarded  as  a  consistent  following  out  of  the  theory  of 
conservation  in  communicated  momentum.  The  lost  energy 
of  the  quick- moving  ball  would  exist  as  energy  in  a  huge 
mass  very  slowly  moving. 

Had  the  farther  question  been  asked— what  becomes  of  the 

force  of  two  opposing  movements  destroying  one  another 

the  above  answer  would  not  have  served  the  purpose.  No 
motion  is  created  in  any  form ;  there  is  nothing  to  appearance 
but  sheer  waste  on  both  sides. 

The  new  dilficulty  would  in  all  likelihood  have  been  met  by 
a  very  plausible  assumptiom.  It  might  have  been  said  that 
the  conservation  of  force  was  to  be  interpreted  as  force  operat- 
ing in  the  same  direction  ;  all  forces  in  the  opposite  direction 
being  held  as  negative  quantities,  like  debt  to  credit.  It  would 
be  a  sufficient  account  of  any  force  that  it  had  neutralized  an 
equal  and  opposing  motive  force;  as  when  a  payment  of  a 
hundred  pounds  to  any  one's  credit  extinguishes"  a  hundred 
pounds  of  debt. 

Yet  this  explanation   is  fallacious  as  a  principle,  and  in 
opposition  to  the  facts  of  the  case.     Two  bodies  moving  in 
opposing  directions  are  not  to  be  compared  to  positive  and 
negative ;  each  has  a  positive  value,  for  any  purpose  whatso- 
ever.    Two  streams  running  in  opposite  directions,  are  as 
good   for  mill-power  as   two   streams  moving  in  the  same 
direction.     Easy  mechanical  contrivances   can,  without  loss, 
divert  a  moving  power  into  any  direction.     The  two  opposing 
forces  that  by  collision  extinguish  one  another,  could  by  a 
suitable  arrangement,  unite  their  power  in  the  same  course. 
The  destruction,  therefore,  that  ensues  in  a  hostile  collision, 
is  (on  the  present  assumption)  pure  destruction,  unredeemed 
waste,  annihilation.     It  is  at  variance  with  the  Law  of  Con- 
servation, which  would  have  to  be  restricted  and  qualified  to 
moving  bodies  always  following  the  same  course. 

The  principle  of  Conservation  has  been  rescued  from  this 
perplexity  by  the  discoveries  of  recent  times.  If  two  in- 
elastic bodies  encounter  and  arrest  one  another's  movements 
the  mechanical  or  molar  energy  is  indeed  sunk  ;  but  re-appears 
in  an  equivalent  energy  communicated  to  the  molecules,  and 
manifested  as  Heat.  The  molecular  motion  excited  in  the 
encountering  masses  is  exactly  equal  to  the  molar  energy 
consumed.  This  is  an  entirely  new  view  of  Force ;  and 
eaves  the  principle  of  Conservation,  by  giving  it  an 
enlarged  scope.     It  teaches  us  to  take  account   of  all  the 


I     ! 


N'  ft 


254 


CAUSATION  AS  CONSERVATION  OF  FORCE. 


MOLECULAR  FORCES. 


255 


protean  transformations  of  energy,  and  prevents  us  from 
rashly  declaring  that  force  is  destroyed  when  it  has  ceased  to 
appear  in  the  original  shape.  Mechanical  force  in  some  cir- 
cumstances, well  understood,  yields  mechanical  force  ;  in  other 
circumstances,  for  example,  hostile  collision,  it  yields  a  mole- 
cular force,  namely.  Heat. 

Going  back  upon  the  first  query  propounded  to  a  contem- 
porary of  Newton,  —  the  account  to  be  given  of  a  ball's 
impinging  on  a  dead  rock, — we  should  now  answer  the  ques- 
tion not  by  mechanical  transference — a  slow  motion  imparted 
to  the  rock — but  by  molecular  transformation.  The  ball  and 
the  place  where  it  struck  would  both  be  found  to  rise  in  tem- 
perature, and  the  more  as  the  moving  force  of  the  ball  was 
greater.  All  the  energy  would  be  accounted  for  in  this  way. 
In  every  case  of  collision,  and  even  of  impact  without  opposi- 
tion, something  is  lost  by  conversion  into  heat.  The  loss  of 
power  hy  friction  is  a  generation  of  heat. 

11.  The  Molecular  Forces  may  be  provisionally  enu- 
merated as  follows  : — (1)  Heat,  (2)  Chemical  Force,  (3) 
Electricity,  (4)  jNerve  1^'orce,  (5)  Light. 

This  enumeration  is  to  be  held  as  provisional ;  it  may  not 
include  all  the  species  ;  and  it  may  represent,  as  distinct  kinds, 
what  are  only  slight  modifications  of  one  kind. 

(1)  Heat — Probably  the  best  example  for  showing  the  mole- 
cular forces,  in  their  contrast  to  the  molar,  or  mechanical,  is 
Heat.  Our  experience  of  this  influence  is  abundant  and 
various.  Yet,  only  of  late  years  have  we  been  led  to  call  it  a 
form  of  moving  matter,  a  species  of  molecular  motion  or 
vibration,  which  bursts  forth  on  the  shock  that  extinguishes  a 
mechanical  impetus. 

Sach  shocks  of  mechanical  collision  are  the  usual  mode 
of  transmuting  mechanical  energy  into  heat.  Friction  is 
only  a  more  gradual  and  protracted  collision.  A  familiar 
illustration  is  seen  in  hammenng  a  piece  of  cold  iron  till  it 
becomes  red  hot.  The  high  temperature  of  the  sun  is  hypo- 
thetically  accounted  for  by  collisions  of  enormous  swift-moving 
masses,  brought  together  by  gravity. 

Such  is  the  situation  for  converting  mechanical  motion 
into  Heat.  The  transmutation  of  heat  into  Mechanical 
force,  is  effected  through  the  expansion  of  bulk  caused  by 
raising  the  temperature  of  bodies.  In  solids,  and  in  liquids, 
this  expansion  is  small  in  range,  but  great  in  force ;  and  is 
adapted  only  to  special  cases,  as  the  splitting  of  rocks,  where 


there  is  need  for  a  great  power  moving  only  a  very  little  way. 
Through  the  medium  of  gases,  the  expansion  can  be  converted 
into  mechanical  energy,  in  any  form  we  please,  as  in  the 
diversified  performances  of  steam  power. 

In  generating  mechanical  power  by  heat,  as  in  the  steam 
engme,  the  source  of  heat  must  be  of  a  higher  temperature 
than  the  medium  ;  the  fire  must  be  hotter  than  the  water  and 
the  steam.  The  power  is  given  forth  by  the  descent  of  the 
heating  body  to  a  lower  temperature.  Between  bodies  equally 
hot,  there  is  no  development  of  mechanical  power,  no  forcible 
expansion  of  any  one  body. 

There  is  a  peculiar  incontinence  attaching  to  the  Heat 
force.  We  usually  find  that  some  body  possesses  it  in  such 
superior  degree  as  leads  to  radiation  upon  other  bodies,  with 
loss  to  the  radiating  body.  This  is  the  moment  for  obtaining 
a  mechanical  or  other  equivalent.  It  is  also  the  moment  of 
dissipation  of  energy  without  equivalent,  if  the  opportunity  is 
not  turned  to  account.  The  solar  heat  falling  on  the  planets 
gives  an  equivalent  in  raising  their  temperature,  and  in  pro- 
ducing other  forces  ;  what  is  not  intercepted  is  at  once  dissi- 
pated into  empty  space,  without  farther  result  than  to  elevate 
by  a  slight  addition  the  general  temnerature  of  space ;  a  real 
but  unavailable  equivalent  of  the  heat  lost  to  the  sun. 

It   is   as    regards    Heat   that   the   rate  of  exchange   with 

mechanical  force  has  been  settled  with  the  highest  numerical 

precision.     The  assumed  unit   of  mechanical   enercry  is  the 

toot-pound   of  England    (and   the   metre-kilogramme  of  the 

Continent),  meaning  the  force  expended  in  raising  one  pound 

weight   one    foot.     The    unit    of    heat    is    defined    as    the 

amount  that  must  pass  to  one  pound  of  water  in  order  to 

raise  its  temperature    (or   sensible    heat    motion)    by    one 

degree    of   the    thermometer.       The    rate    of    exchange  or 

equivalence    is    772    foot-pounds    to    one    pound    of    water 

raised  1    Fahrenheit;  or  1390  foot-pounds  to  1°  Centigrade. 

in    the    Contmental    scale    of   weights    and    measures,    the 

expression  is  425  metre-kilogrammes  to  one  kilogramme  of 

water  raised    1°   Centigrade.      By   a  perfect  machinery   of 

conversion  of  heat  into  mechanical  power,  the  heat  requisite 

iQQn.!L*  ^^"'l''   ^^^"^  pounds)   of  freezing   water  would  lift 
1389600  pounds  one  foot. 

(2)  Chemical  Force. —Energy,  in  a  form  adapted  to  separate 
chemical  compounds,  and  as  it  appears  when  bodies  combine 
chemically,  IS  chemical  force.  When  water  is  decomposed  into  its 
elements— oxygen  and  hydrogen— a  certain  amount  of  force  is 


256 


CAUSATION  AS  CONSERVATION  OF  FORCB. 


HEAT.— ELECTRICITY. 


257 


il 

i 


absorbed  or  used  up  in  order  to  bring  abont  the  decompoei- 
tion  ;  and  the  same  force  reappears  when  the  elements  are 

re-combined. 

This  chemical  force  is  a  very  slight  modification  of  Heat. 
In  the  case  of  combination,  the  force  evolved  appears  as  heat 
in  its  common  form.  Indeed,  onr  artificial  heat  of  combus- 
tion, is  the  chemical  force  liberated  in  the  chemical  combina- 
tion of  oxygen  and  carbon  (supposing  coal  or  charcoal  to  be 
the  fuel).  By  peculiar  arrangements,  this  force  of  combination 
may  be  prevented  from  appearing  as  sensible  heat,  and  may 
take  other  forms ;  it  may  decompose  other  compounds  (as  in 
the  double  decomposition  of  salts)  ;  or  it  may  pass  into  elec- 
tricity or  into  magnetism. 

Again,  Heat  may  operate  as  a  decomposing  agent.  Many 
compounds  are  decomposed  at  once  by  the  application  of 
heat,  as  the  oxides  of  the  noble  metals.  A  familiar  example  is 
the  decomposition  of  chalk  or  carbonate  of  lime,  in  a  lime 
kiln  ;  the  heat  drives  off  the  carbonic  acid,  and  what  remains 
is  burnt  lime.  Other  compounds  are  decomposed  by  heat, 
when  there  is  an  arrangement  for  combining  one  of  the  de- 
composed elements  with  a  third  substance  ;  as  when  water  is 
decomposed  in  a  red-hot  iron  tube,  the  oxygen  combining  with 
the  iron. 

That  heat,  the  result  of  combination,  should  be  the  means 
of  decomposition,  is  the  proper,  the  natural  consequence  of 
the  Law  of  Conservation.  "W  hatever  is  given  out  when  ele- 
ments combine,  must  be  restored  when  they  separate  again. 
This  is  the  exact  relationship  of  heat  to  chemical  action,  which 
is  disguised  and  apparently  reversed  by  the  familiar  employ- 
ment of  heat  to  make  bodies  comhine,  as  in  lighting  a 
fire.  The  application  of  heat  in  such  a  case,  however,  is  a 
mere  incident ;  it  seems  to  operate  by  disturbing  the  quies- 
cence of  the  elements.  It  no  more  renders  heat  a  combining 
power,  than  the  pailful  of  water  thrown  into  a  pump  before 
pumping  is  the  cause  of  the  subsequent  flow. 

The  rate  of  commutation  of  Heat  and  Chemical  Force,  has 
to  be  given  in  the  detail,  inasmuch  as  different  compounds 
give  forth  different  quantities.  I  quote  as  examples  a  few 
oxygen  compounds.  One  pound  of  hydrogen  burnt  (that  is, 
combined  with  oxygen)  would  elevate,  by  V  C,  about  thirty ' 
four  thousand  pounds  of  water.  This  is  the  most  heating  of 
all  oxygen  combinations  ;  we  have  long  been  familiar  with  the 
intense  heat  of  the  oxy-hydrogen  blow-pipe.  Of  simple 
bodies  burnt,  or  combined  with  oxygen,  the  next  in  rank,  \b 


earhoUj  the  chief  ingredient  of  ordinary  combustion,  and  also 
of  animal  combustion.  The  figure  for  carbon  is  less  than  one 
fourth  the  figure  for  hydrogen  ;  a  pound  of  carbon  burnt 
elevates,  by  1°  C,  about  eight  thousand  pounds  of  water. 
Phosphorus  ranks  next  among  the  simple  bodies  examined 
(5747  pounds)  ;  then  sulphur  (2307)  ;  tbe  metals,  zinc,  iron, 
and  tin,  are  nearly  equal  (zinc,  3301,  iron,  1576,  tin,  1233). 

(3)  Electricity. — This  variety  of  molecular  force  is  distin- 
guished by  two  main  peculiarities.  The  ^rst  is  polarity,  or  the 
development  of  opposite  forces  at  opposite  points  ;  the  magnet 
is  the  most  familiar  example  of  the  power,  operating  in  masses 
of  matter.  The  second  is  named  conduction,  and  means  the 
rapid  transmission  of  the  force  from  one  part  of  a  body  to 
another,  along  a  wire,  for  example  ;  a  process  of  conveyance 
quite  different  from  any  of  the  modes  of  the  transmission  of 
heat.  An  electrical  charge  passes  almost  instantaneously,  and 
with  little  diminution  of  force,  through  miles  of  copper  wire. 

The  name   *  Electricity  *  now  includes  various  phenomena 
marked  by  characters  widely  different.    Three  types  or  species 
may  be  indicated — Magnetism,  Friction  or  Franklinio  Elec- 
tricity,   and   Voltaic   Electricity :    all    these    have   a   molar 
as   well   as   a   purely   molecular   siHe ;    the  last  is  in  close 
relation  to  chemical  force.     Magnetism,  as  a  member  of  the 
group  of  Correlated  Forces,  under  the  Law  of  Conservation, 
is  best  studied  in  the  form  called  Electro-magnetism,  or  mag- 
netism generated  from  electricity  ;  for,  while  the  magnetism, 
which  is   a  mechanical  attraction,  can  be  estimated  by  its 
mechanical  effects,  the  electricity  can  be  estimated  chemically 
by  the  amount  of  acid  and  zinc  combined  in  the  cells  of  the 
battery.   Friction  Electricity,  in  the  common  electrical  machine, 
is  generated  by  mechanical  force  (sometimes  by  heat,  as  in 
crystals);  its  discharge,  being  marked  by  vehemence,  concentra- 
tion, or  intensity,  is  not  measurable  with  accuracy ;  the  effects 
are  seen  in  the  rupture  of  atomic  cohesions,  in  strong  outbursts 
of  heat  and  light,  and  other  indications  of  concentrated  force. 
Voltaic   Electricity  is   the  species   most  closely  allied  with 
Chemical  Force ;    which  force  is  its  source,  its  measure,  and 
one  of  its  results.     Through  chemical  force,  as  measured  by 
the  amount  of  material  chemically  combined  in  the  voltaic 
cells,  we  can  state  the  rate  of  exchange  or  commutation  of 
Voltaic  Electricity  with  Mechanical  force,  and  with  Heat. 

These  three  modes  of  Force — Heat,  Chemical  force.  Elec- 
tricity— are  the  well-defined  species    of  molecular  activity; 


aw-iaLgi.'-JinLJg'..w  m 


258 


CAUSATZON  AS  CONSERVATION  OF  FOECK. 


» 


they  can  all  be  measured  and  pnt  into  strict  equivalence  with 
Mechauical  Energy.  There  still  remain,  however,  Light, 
and  any  mo(les  of  activity  in  living  bodies,  distinct  from,  and 
superadded  to  the  forces  of  the  inorganic  world  ;  the  Nerve 
Force  is  one  well-marked  example.  From  the  close  analogies 
between  this  last-named  force  and  Electricity,  we  may  take  it 
next  in  order. 

(4)  Nerve  i^orce.— The  Nerve  Force  is  the  special  activity  of 
the  nerves  and  brain.    Like  Electricity,  it  is  a  current  force.     It 
differs  from  Electricity  in  moving  at  a  comparatively  slow  rate ; 
and  also  in  depending  for  its  maintenance  upon  chemical  com- 
binations in  the  material  of  the  nerves  ;  hence,  while  electricity 
decreases  as  it  goes,  the  nerve  force  increases.     Although  this 
force  cannot  be  subjected  to  accurate  measurement,  we  con- 
clude from  analogy  that  there  is  an  exact  equivalence  between 
it  and  the  chemical  transformations  that  are  its  source ;  part 
of  the  food  of  the  body  is  expended  in  supplying  it.     It  con- 
tributes to  muscular  power,  in  which  case  it  has  a  mechanical 
equivalent;  and  to  molecular  changes,  chemical  or  other,  also 
on  a  definite  rate.     As  the  physical  concomitant  of  mental 
states,  we  must  still  regard  it  as  definitely  related  in  quantity 
to  these ;  a  double  amount  of  feeling,  other  things  being  the 
same,  involves  a  double  amount  of  nervous  transformation. 

(5)  Light— The  divorcing  of  Light  from  Heat,  in  the  enu- 
meration of  the  molecular  forces,  needs  to  be  explicitly  justified. 
The  divorce  is  at  best  provisional  and  temporary  ;  the  reasons 
Jire  such  as  the  following.     Although  Light  is  a  distinct  product 
of  the  other  forces,  more  especially  Heat,  and  is  instrumental 
in  caumig  at  least  one  of  them,  Chemical  force,  yet  hitherto 
nothing  has  been  done  towards  establishing  the  rate  of  com- 
mutation or  exchange  between  it  and  the  others.     When  a 
body  is  heated  till  it  becomes  luminous,  there  ought  to  be  a 
definite  loss  of  heat,  equivalent,  on  a  certain   scale,  to  the 
light  produced ;    at  present,  however,  we  have  made  no  ap- 
proach  to  such   an   estimate.      Moreover,  although  light  is 
the  instigator  of  chemical  change,  we  cannot  say  that  it  oper- 
ates by  supplying  chemical  power,  as  heat  or  as  electricity 
does ;  the  effect  may  be  similar  to  the  action  of  heat  in  lighting 
a  fire,  a  mere   disturbance   sufficing  to    begin   the    chemical 
union  of  elements  ready  to  ombine.     Chlorine  and  hydrogen, 
mixed  together,  will  not  combine  chemically  in  the  dark ;  the 
combination  begins  nnder  the  light.      It  is  to  be  remarked, 
however,  that  decomposition  is  the  direct  test  of  chemical  force. 
NTow,  light  will  not  cause  decomposition  unless  in  the  presence 


xjLu-iai- 


POTENTIAL  ENERGY. 


259 


of  a  body,  like  hydrogen  or  chlorine,  having  a  powerful 
tendency  to  combine  ;  or,  when,  as  in  vegetation,  li^ht  is 
accompanied  by  heat.  We  are,  therefore,  led  to  Regard  licrht 
chiefly  as  the  'prompter  to  a  change  otherwise  maintained.  And 
m  this  view  there  is  a  numerical  proportion  between  the  amount 
ot  light  and  the  extent  of  the  chemical  action  ;  as  shown  in 
the  researches  of  Bunsen  and  Roscoe  [Fldl.  Trans.,  1857). 

When  mechanical  force  operates  against  gravity,  as  when 
a  projectile  is  thrown  npwards,  the  force  is  at  last  spent :  the 
equivalent  gained  is  a  position  of  advantage,  with  respect  to 
gravity ;  for,   by  the  continued  operation  of  the  gravitating 
energy,  the  whole  of  the  impetus  lost  will  be  restored  in  the 
downward  direction  (the  resistance  of  the  air  being  left  out 
of  the  account).     We  are  familiar  with  this  employment  of 
gravity  m  clocks  propelled  by  weights  regulariy  wound  up  to 
a   height.      To   this   peculiar   situation.    Prof.    Rankine   haa 
applied  the  name  'potential  energy,'  to  distinguish  it  from 
the  energy  of  a  mass  in  actual  motion.     The  placing  asunder 
of  the  celestial  bodies,  all  which  gravitate  towards  each  other 
was  the  primeval  situation  of  advantage,  whence  may  have 
arisen  (by  collisions)  the  heat  of  our  suns  and  planets,  and  by 
consequence  all  the  other  modes  of  force— mechanical,  chemi- 
cal, and  electrical. 

It  is  by  this  operation  that  the  force  of  gravity  is  introduced 
mto  the  circle  of  forces,  and  is  counted  as  a  cause  or  productive 
agent.  Viewed  in  itself,  it  creates  no  force;  what  is  ^ained 
m  visible  force  is  lost  in  position;  to  restore  the  position 
would  require  the  power  to  be  given  back.  It  can,  however 
divert  power;  it  can  also  store  up  and  re-distribute  it,  as  a 
banker  does  money. 

A  similar  position  of  advantage  may  be  found  in  the  mole- 
cular forces.  Thus,  the  existence  of  two  elementary  bodies, 
able  to  combine,  is  a  potential  chemical  energy,  which,  on  the 
occurrence  of  the  opportunity  and  the  stimulus,  is  converted 
into  actual  molecular  energy.  Such  is  the  potential  force  of 
our  coal,  and  of  all  the  nncombined  and  combinable  elements 
of  the  globe,—  as  native  sulphur,  the  native  metals,  and  the 
lower  compounds  susceptible  of  entering  into  higher  com- 
pounds. 

The  molecular  attractions  of  bodies  (as  cohesion)  may  oper- 
ate exactly  in  the  manner  of  gravity.  A  spring  is  an  obvious 
example.  The  elasticity  of  compressed  air  may  be  turned  to 
the  same  account. 


t^ 


260 


CAUSATION  AS  CONSERVATION  OF  FORCE. 


ii|^ 


h 


12.  Causation,  viewed  as  Consen^ation,  is  thus  the  trans- 
ferring or  re-embodying  of  a  definite  amount  of  Force. 

When  a  ship  is  propelled  by  wind  or  by  steam,  the  motion 
is  said  to  be  caused  by  those  agents  ;  which  expend  themselves 
in  producing  the  effect  The  expansiveness  of  steam  is  due  to 
heat  operating  through  the  medium  of  water.  The  heat  arises 
from  the  combustion  or  chemical  union  of  coal  and  oxygen. 
The  coal  was  the  carbon  of  plants  of  former  ages,  whose 
growth  demanded  an  expenditure  of  solar  heat. 

So,  again,  in  the  human  body,  mechanical  force  is  obtained 
by  mucsular  exertion  ;  that  exertion  is  owing  to  the  oxidation 
of  the  materials  found  in  the  blood  ;  these  materials  are  either 
vegetable  products,  or  the  bodies  of  other  animals  fed  on 
vegetables  ;  and,  thus  we  come  round  again  to  the  agency  of 
the  solar  ray  in  vegetation. 

Transferred  energy  is  thus  ihe  final  and  snfiicing  explanation 
of  all  change,  and  the  only  explanation  in  the  highest  sense  of 
the  word.  Any  fact  of  causation  not  carried  up  into  this 
supreme  law,  may  be  correctly  stated,  but  it  is  not  accounted 
for. 

Whatever  appearances  militate  against  the  principle  of  Con- 
servation are  to  be  held  as  fallacious.  The  *  perpetual  motion  * 
has  long  been  rejected  as  incompatible  with  the  mere  mechani- 
cal phase  of  the  principle.  There  still  remain  to  be  removed 
various  errors  against  the  more  comprehensive  view.  For 
example,  the  incautious  remark  is  frequently  made  thai  Light 
is  the  operative  cause  of  vegetative  growth,  meaning  light 
alone ;  but  the  large  amount  of  chemical  power  required  to 
decompose  water  into  its  elements  (the  bodies  of  all  others 
most  costly  in  their  demands)  could  be  furnished  only  by  the 
heating  rays  of  the  sun  ;  however  much  light  may  co-operate 
in  giving  stimulus  or  direction. 

13.  The  Law  of  Conservation  exhausts  Causation,  viewed 
as  the  transfer  of  Force  or  Moving  Power,  but  leaves  many 
complicated,  and,  as  yet,  unsolved  questions  of  Colloca- 
tion. 

If  we  view  causation  as  the  transfer  or  re-distribution  of  a 
certain  definite  amount  of  moving  power,  nothing  can  be 
simpler  than  the  statement  of  the  principle ;  and,  in  many 
instances,  we  find  it  easy  to  make  the  exact  calculation.  But 
the  circumstances  attending  the  transfer,  the  situation  or 
eollocation  of  the  materials  engaged,  may  have  all  degrees  of 
complexity. 


collocations. 


261 


. 


The  simplest  situation  is  the  transfer  of  mechanical  power 
by  impact,  as  when  a  golf  ball  is  impelled  by  the  momentum  of 
the  club.  At  least,  we  usually  suppose  this  to  be  a  simple 
case ;  we  take  no  account  of  the  internal  agitations  of  the 
particles  of  the  body  struck,  being  content  to  assume  that  the 
momentum  is  transferred  with  inconsiderable  loss.  Here, 
then,  the  collocation  is  the  easiest  possible ;  it  is  the  sensible 
contact  of  one  moving  body  with  another,  either  at  rest  or 
already  in  motion.  Even  when  one  moving  body  strikes 
another  moving  in  a  different  direction,  the  difficulty  of  the 
collocation  is  not  much  increased  ;  the  mechanical  theorems  of 
oblique  forces  will  predict  the  new  distribution,  and  assign  the 
directions  after  the  impact. 

When  we  pass  from  the  interchange  of  mechanical  forces,  to 
the  mutual  interchange  of  mechanical  and  molecular,  we  en- 
counter situations  or  collocations  of  various  degrees  of  com- 
plexity. Least  difficult  is  the  relation  of  mechanical  energy 
to  heat.  When  a  moving  body  encounters  a  dead  resistance, 
the  whole  of  the  energy  is  resolved  into  molecular  motion  of 
the  encountering  masses ;  if  the  body  struck  gives  way  in 
part,  and  takes  on  motion,  the  actual  energy  generated  is  so 
much  deducted  from  the  energy  transformed  into  heat. 

The  transfer  of  heat  into  mechanical  force,  as  in  the  steam 
engine,  is  accomplished  by  the  expansiveness  of  the  heated 
matter.  Starting  from  the  fact  of  forcible  expansion,  the  con- 
version is  merely  an  instance  of  mechanical  impact.  The 
difficulties  are  postponed  to  the  next  stage. 

The  interchange  of  Heat  and  Chemical  Force,  the  production 
of  each  from  the  other,  at  will,  is  effected  by  an  arrangement 
that  can  be  expressed  with  considerable  definiteness  in  the 
gi'oss,  although  leaving  the  ultimate  links  of  transition  in  deep 
obscurity.  The  active  combination  of  two  combinable  bodies, 
as  carbon  and  oxygen,  evolves  heat ;  but  the  minute  circum- 
stances of  the  evolution  can  be  only  hypothetically  surmised. 
The  intestine  heat  motions  of  carbon  and  of  oxygen,  in  their 
separation,  when  transferred  to  the  joint  Oirbonic  acid  mole- 
cules, are  in  excess,  and  the  surplus  gives  elevation  of  tem- 
perature, or  sensible  heat,  to  the  mass. 

The  re-conversion  of  Heat  into  Chemical  Force  (potential), 
as  in  chemical  decompositions,  is  somewhat  more  complicated, 
but  an  account  can  be  given  of  the  situation  in  gross.  In  the 
cases  where  decomposition  is  effected  by  heat  alone,  we  have 
the  simple  restoring  of  the  surplus  heat  of  the  combination. 
In  the  other  cases,  where  a  new  combination  must  be  formed. 


262 


CAUSATION  AS  CONSEllVATION   OF  FORCE. 


I 


ti 


we  have  an  additional  circumstance,  still  perfectly  definable, 
and,  in  a  rough  manner,  hypothetically  conceivable. 

The  difficulties  of  Collocation  grow  thiciv  upon  us  when  we 
grapple  with  the  Electrical  group  of  forces.  The  polarized 
state  of  matter,  whether  in  mass,  as  the  magnet  and  the 
Leyden  jar,  or  in  molecule,  as  in  the  decomposing  cells  of  the 
voltaic  battery,  is  a  new  and  unique  phenomenon  ;  and  its 
generation  by  mechanical  force  or  by  heat  may  be  stated  in 
the  extreme  terms,  but  without  intermediate  explanation, 
even  1^  a  plausible  hypothesis.  After  many  laborious  tenta- 
tives,  Faraday  discovered  the  arrangement  for  directly  convert- 
ing mechanical  power  into  voltaic  electricity  (commonly  called 
the  magneto-electric  machine),  but  the  links  of  the  transition 
or  intermediate  molecular  changes  are  as  yet  unassignable. 

Yet  worse  perplexities  surround  the  collocations  for  trans- 
ferring force  in  Living  Bodies.  Even  the  simplest  case— the 
production  of  Animal  Heat  from  chemical  combination  or 
combustion— is  anomalous  when  compared  with  the  same 
phenomenon  out  of  the  body.  The  general  fact  is  oxidation, 
but  the  circumstances  and  arrangements  are  peculiar  and 
unknown.  Again,  the  production  of  Muscular  Force  from  the 
process  of  oxidation  is  in  accordance  with  the  Law  of  Conserva- 
tion, while  the  transition  links  are  hitherto  inscrutable.  Like- 
wise, the  Nerve  Force  has  the  same  common  origin  in  chemical 
transformations  (or  closely  allied  molecular  transformations) 
as  the  other  forces,  and  follows  a  regular  rule  of  exchange, 
while  the  mode  of  derivation  is  involved  in  obscurity. 

14.  Seeing  that,  in  Causation,  there  must  be  provided, 
not  merely  a  sufficient  force,  energy,  or  moving  power,  but 
also  the  suitable  arrangement  for  making  the  transfer  as 
required ;  this  completing  arrangement,  or  collocation,  is  a 
part  of  the  Cause,  and  (by  ellipsis)  is  frequently  spoken  of 
and  investigated  as  the  Cause. 

A  running  stream  is  the  proper  source  of  the  energy  that 
turns  a  mill.  In  order  to  the  effect,  however,  the  due  colloca- 
tion or  connexion  must  be  made  for  bringing  the  water  to 
bear  upon  the  machinery.  Hence,  the  stream  being  taken  for 
granted,  the  cause  of  the  grinding  of  the  corn  is  the  providino- 
of  machinery,  and  the  regulation  of  the  sluices  ;  which  circum^ 
stances  are  of  the  character,  not  offeree,  but  of  collocation. 

So,  in  a  Voltaic  Battery,  intended  to  decompose  water,  or 
to  excite  an  electro-magnet,  the  prime  mover  is  chemical 
force   arising  in   the   cells  of  the    battery;    the   completinc^ 


UNKNOWN  COLLOCATIONS. 


203 


arrangements  include  the  whole  apparatus  of  the  battery  and 
the  final  act  of  closing  the  circuit. 

The  combination  of  the  food  materials  with  the  oxyo^en  of 
the   air,  may  be  reckoned  the  source  of  all  animal  power  • 
but  so  numerous   are   the   conditions  to  be   secured  in  the 
way  of  arrangement  or  due  collocation,  that  we  have  often 
to  think  far  more  of  these  than  of  the  propelling  ao-encv  de- 
rived from  the  primal  source  of  all  moving  power.      We  not 
unfrequently  assign  as  the  cause  of  a  man's  bodily  strencrth  a 
good  digestion,  healthy  lungs,  or  a  good  constitution  gene°raliv 
and  say  nothing  of  the  real  derivation  of  the  stren-th  •  the 
reason  being  that,  without  the  complex  group  of  arrangements 
implied  in  these  facts,  the  power  would  not  be  transferred  from 
the  common  fund  and  embodied  in  the  man's  muscular  and 
nervous  energies. 

When  a  man  properly  supplied  with  food,  goes  throu-h  a 
day  s  work,  we  recognize  a  transfer  of  moving  power,  uSder 
the   Law  of  Conservation.      When  any  one  prostrate  with 
weakness  is  restored  to  strength  by  a  few  drops  of  laudanum 
there  is  no  proportion  between  the  cause  and  the  effect  con-' 
sidered   as   moving   power   giving   birth  to  equal,  although 
diff-erent  moving  power.     The  salutary  interference  must  be 
regarded,  not  as  a  communication  of  moving  energy  corres- 
ponding to  the  access  of  energy  that  follows,  but  as  the  restor- 
ing of  some  arrangement   or   collocation,   necessary  to   the 
conversion  of  the  body's  nourishment  into  the  various  forces 
01  animal  life. 

As  our  knowledge  of  the  Law  of  Conservation  is  such  as  to 
account  for  the  remote  source  of  all  power  whatsoever,  the 
enquiry  usually  presented  for  scientitic  investigation  iL  by 
what  arrangements  a  given  eff-ect  has  been  secured,  or  through 
what  media  the  bank  of  Nature's  Force  has  been  drawn  upon 
m  the  particular  mstance.  Not  many  years  ago  the  pheno- 
menon of  volcanoes  was  regarded  as  wholly  mysterious  ;  since 
the  establishment  of  the  Law  of  Conservation,  all  that  part  of 
the  mystery  connected  with  the  source  of  the  upheavin/power 

vprf^f''/''!?'^"^'  .^*  '^  *^^  ^^^^^^^^  ^^^t  ^^^^^  eafth  con. 
verted  at  certain  points  into  mechanical  energy.  What  re- 
mains for  scientific  investigation  is  a  pure  questioS  of  collocation; 
we  are  still  ignorant  of  the  arrangements  for  eff-ectin..  the 
traiisference  of  power  in  that  particular  manner.  ^ 

In  the  same  way,  all  the  great  cosmical  changes,  marking 

the  earth,  are  referable  te  the  primal  sources  of  energy  ^the 


2G4 


CAUSATION  AS  CONSEKVATION   OB  FOliCE. 


ENQUIRY  INTO  COLLOCATIONS.  ' 


265 


I 


* 


\\\ 


l*> 


moving  power  at  work  is  no  longer  a  secret.  Yet  the  circnm- 
stances,  arrangements,  or  collocations,  whereby  the  power 
operated  to  produce  oar  existing  mountain  chains,  the  rise  and 
fell  of  continents,  the  fluctuations  of  climate,  and  all  the  other 
phenomena  revealed  by  a  geological  examination  of  the  earth, 
are  as  yet  in  uncertainty. 

15.  The  importance  of  Collocation  appears  in  another 
aspect,  as  representing  the  modes  of  Potential  Energy. 

Potential  Energy  is  energy  of  situation,  arrangement,  or 
collocation.  The  Potential  Energy,  stored  up  when  moving 
bodies  work  against  gravity,  till  their  force  is  exhausted,  is 
described  as  a  position  of  advantage^  a  collocation  of  power, 
with  reference  to  a  gravitating  mass.  Here  we  have  the  re- 
markable case  of  force  embodied  in  absolute  stillness  or  quies- 
cence. A  mountain  tarn  is  absolutely  quiescent  while  its 
enclosure  is  perfect ;  the  immense  impetus  to  be  displayed  in 
its  descent  to  the  plains  is  not  at  present  represented  even  by 
molecular  motion. 

A  similar  energy  of  collocation  is  created  when  bodies  are 
distended  in  opposition  to  their  cohesive  attractions,  as  in 
springs. 

Lastly,  there  is  the  energy  of  separation  of  Chemical  ele- 
ments, as  in  coal,  sulphur,  metals,  and  other  combinable  sub- 
stances, simple  or  compound.  Gunpowder  is  a  concentration 
of  potential  chemical  energies,  or  of  combinable  elements  in  a 
situation  of  readiness  to  combine. 

It  is  in  the  case  of  these  potential  energies  that  we  seem  to 
create  moving  power,  to  bring  forth  force,  without  a  prior 
equivalent  force,  to  make  small  causes  yield  great  effects.  The 
apparent  cause,  or  antecedent,  of  a  great  outburst  of  moving 
power,  is  something  altogether  trivial,  as  if  force  were 
evoked  and  absolutely  created.  Cause  and  Effect  cannot,  in 
such  instances,  be  stated  as  one  moving  power  transmuted  into 
an  equal  moving  power,  molar  or  molecular.  A  child's  touch 
might  be  made  to  discharge  a  man-of-war's  broadside,  or 
inundate  a  village.  One  word  of  a  general,  the  signature  of 
a  sovereign,  may  destroy  an  empire. 

Cause,  in  all  these  instances,  has  a  peculiar  and  important 
signification.  It  is  not  a  moving  force  equal  to  the  visible 
energy  of  the  effect,  it  is  the  exertion,  however  easy,  that 
changes  a  situation  of  potential  energy  to  a  situation  of  actual 
energy  ;  the  cutting  of  the  string  that  suspends  a  weight,  the 
drawing  of  a  sluice,  the  setting  a  light  to  a  combustible,  the 
supplying  of  a  motive  to  human  volition. 


The  course  of  experimental  investigation  must  adapt  itself  to 
this  position  of  our  knowledge  as  regards  Causation.  We 
know  the  ultimate,  and,  in  most  instances,  the  proximate 
sources  of  moving  power  or  energy ;  we  know  a  certain 
number,  more  or  less,  of  the  conditions  or  collocations  of  the 
transfer ;  what  we  still  desiderate  is  the  thorough  and  fully 
generalized  knowledge  of  the  remaining  collocations. 

In  the  subtle  actions  of  Light,  we  are  at  this  moment  in 
doubt  whether  the  luminous  ray  operates  as  a  dynamical 
and  force-giving  agent,  like  Heat  and  Electric  Force,  or  only 
as  a  collocating  agent,  either  to  complete  the  medium  for 
ti'ansmitting  a  true  force,  or  to  convert  a  potential  into  an 
actual  force.  As  causing  chemical  combinations,  we  can 
ascribe  to  it  nothing  more  than  the  hberation  of  the  potential 
chemical  energy.  So,  in  acting  on  the  eye  to  rouse  our 
optical  sensibility,  it  may  be  no  more  than  a  disturber  of 
latent  forces. 

The  settling  of  this  preliminary  point  is  necessary  to  our 
progress  in  the  investigations  of  luminous  agency.  In  merely 
completing,  or  else  disarranging  collocations.  Light  muat 
exert  a  dynamical  force,  but  it  may  be  of  the  very  slightest 
amount,  and  out  of  all  proportion  to  the  results  that  ensue. 
There  is  no  proof  that,  in  any  situation,  the  energies  aroused 
by  Hght  are  maintained  at  the  cost  of  the  hght. 

The  character  of  a  disturbing  agent  must  attach  to  many,  if 
not  most,  of  our  sensations.  The  tickling  of  the  nose  by  the 
proboscis  of  a  fly  cannot  be  the  source  of  the  muscular  move- 
ments that  arise  from  the  feeling.  The  irritation  of  a  musical 
discord,  the  revulsion  at  an  odour,  the  energetic  discharge  of 
a  bitter  morsel  from  the  mouth — are  efficacious  as  disturbing 
some  collocation,  and  bringing  potential  force  into  actuality. 

In  the  complicated  animal  framework,  there  may  be  violent 
displays  of  energy  consequent  on  the  withholding  of  the 
regular  supplies  of  energy.  Extreme  hunger  may  lead  to 
nausea  and  retching.  In  the  delirium  of  fever,  when  no 
nourishment  can  be  received,  there  is  great  muscular  exertion. 
We  are  at  no  loss,  on  the  foregoing  principles,  to  solve  the 
apparent  contradiction. 

16.  As  Cause  may  not  always  mean  the  Moving  Power 
transferred,  according  to  the  Law  of  Conservation,  so,  the 
Effect  may  not  always  mean  visible  energy  gained,  but  a 
new  arrangement  or  Collocation  of  materials. 

Moving  Power  is  often  expended,  not  with  a  view  to  repro- 


; 


ft 


!  i.i 


\!i 


iir 


2G6 


CAUSATION   AS   CONSERVATION   OF  FORCE. 


ducinj?  some  equivalent  power,  but  merely  to  re-distribute 
materials,  as  in  transporting  stones  from  a  quarry  to  erect  a 
building.  There  is  a  definite  expenditure  of  power,  corres- 
ponding to  the  collective  amount  of  the  stones,  the  distance, 
and  the  friction  of  the  roads  ;  but  the  whole  effect  consists  in 
a  change  of  position  of  the  materials,  without  any  available 
energy. 

Such  is  the  nature  of  many  Geological  changes.  When  the 
forces  of  the  earth  and  the  sun  raise  mountains,  they  impart  a 
position  of  advantage,  or  of  potential  energy ;  whereas  the 
transport  of  erratic  boulders,  the  deposition  of  strata  at  a  dis- 
tance from  the  source  of  the  material,  are  effects  of  change 
without  any  embodiment  of  moving  power. 

17.  The  evidence  for  Causation  and  for  Conservation  is 
the  same. 

This  follows  from  the  identity  of  the  principles.  Now,  as 
previous  to  the  announcement  of  the  principle  of  Conserva- 
tion, a  great  body  of  evidence  had  been  accumulated  in  favour 
of  Causation  in  the  old  form,  all  the  experimental  proofs  in 
favour  of  Conservation  are  a  pure  addition  to  the  evidence  of 
Causation.  In  point  of  fact,  however,  these  experimental 
proofs  are  themselves  considered  adequate  to  establish  the 
principle  of  Conservation. 

Those  speculators  that  rely  on  an  intuitive  basis  of  proof 
for  this  grand  generalization  treat  the  two  forms  as  identical. 
Thus,  Sir  W.  Hamilton  is  singular  among  metaphysicians,  in 
giving  to  the  Law  of  Causation  a  form  almost  exactly  co-inci- 
dent with  the  principle  of  Conservation,  which  he  may  be  said 
to  have  anticipated. 

Mr.  Herbert  Spencer  holds  that  *  the  total  quantity  of  matter 
in  the  Universe,  cannot  really  be  conceived  as  diminished,  any 
more  than  it  can  be  conceived  as  increased.  Our  inability  to 
conceive  Matter  becoming  non-existent,  is  immediately  con- 
eequent  on  the  very  nature  of  thought.  Thought  consists  in 
the  establishment  of  relations.  There  can  be  no  relation  estab- 
lished, and  therefore  no  thought  framed,  when  one  of  the 
related  terms  is  absent  from  consciousness.  The  annihilation 
of  Matter  is  unthinkable  for  the  same  reason  that  the  creation 
of  matter  is  unthinkable ;  and  its  indestructibility  thus  be- 
comes an  a  priori  cognition  of  the  highest  order — not  one  that 
results  from  a  long-continued  registry  of  experience  gradually 
organized  into  an  irreversible  mode  of  thought :  but  one  that 
is  given  in  the  form  of  all  experiences  whatever  '  (First  Prin- 


EVIDENCE  FOR  CAUSATION. 


267 


ClPLES,  2nd  edit.  p.  175).  So  much  as  regards  Matter.  Now 
as  Matter  is  known  to  us  merely  as  exerting  force,  the  reason- 
ing really  applies  to  Force  as  the  underlying  experience,  the 
real  signification  of  Matter.  Hence,  *  by  the  indestructibility 
of  matter,  we  really  mean  the  indestructibility  of  the  force 
with  which  Matter  affects  us.' 

Without  re-entering  into  the  controversy  as  to  the  test  of 
truth  furnished  by  the  inconceivability  of  the  opposite,  we 
may  remark  that  in  the  absence  of  experimental  confirmations 
and  interpretations,  such  an  a  priori  conception  would  be  very 
hazardous  to  rely  on.  It  would  not  tell  us,  for  example,  that 
all  the  force  of  nature  seems  tending  to  a  mode  of  dissipation 
which  is,  to  all  intents  and  purposes,  annihilation,  namely,  the 
radiation  of  heat  into  space.  Moreover,  the  case  has  already 
been  adduced  of  two  opposing  forces  meeting  to  ncutrahze  one 
another  ;  a  fact  formerly  accepted  as  in  full  consistency  with 
the  indestructibility  of  mechanical  force  ;  the  universal  belief 
of  scientific  men,  as  well  as  of  others,  was  that  nothing  survived 
such  a  collision.  Such  a  priori  renderings  are  of  the  nature  of 
prophecies  made  after  the  event. 

When  the  Inductive  Methods  have  been  fully  explained,  the 
proof  of  the  Law  of  Causation  will  be  reverted  to  with  a  view 
of  indicating  its  logical  character.  We  here  assume  it  as 
sufliciently  established,  and  we  shall  have  to  proceed  upon  it 
deductively  in  several  of  the  methods  of  Inductive  Proof  and 
Elimination.  Without  it,  there  could  be  no  short  cut  to  the 
establishment  of  a  law  of  nature ;  every  separate  induction 
would  have  to  be  proved  by  a  detailed  examination  of  instances 
through  all  nature.  The  most  potent  of  the  Inductive  Methods, 
the  Method  of  Difference,  is  a  deductive  carrying  out  of  the 
law  of  Causation  or  of  Conservation. 

18.  The  Cause,  or  aggregate  conditions,  of  an  Effect 
must  be  sought  among  the  antecedent  circumstances  con- 
joined with  it. 

To  appearance,  Cause  and  Effect  are  a  sequence  or  succes- 
sion ;  the  cause  being  first,  or  the  antecedent;  the  effect, 
second,  or  the  consequent.  It  is,  therefore,  among  the  circum- 
stances preceding  the  effect,  and  in  suflacient  connexion  of 
time  and  place,  that  we  look  out  for  the  cause. 

The  main  difficulty  of  the  determination  is  due  to  the  fact 
that,  in  most  cases,  circumstances  not  entering  into  the  cause 
are  also  found  among  the  antecedents,  in  as  close  connexion  of 
time  and  place  as  the  causal  conditions.     It  is  to  extricate  the 


l\ 


••-t^SS^-' 


! 


M 


ll 


268 


THE   COMPOSITION   OF  CAUSES. 


real  conditions  that  we  mast  enter  on  a  course  of  observation, 
experiment,  and  comparison  of  instances. 

19.  An  invariable  antecedent  is  not  necessarily  the  cause 
or  any  part  of  the  cause  of  an  effect. 

The  familiar  example  is  the  sequence  of  day  and  night ; 
which,  although  invariable,  is  not  a  sequence  of  cause  and 
effect.  So  in  the  evolution  of  a  living  being,  there  are  numer- 
ous links  of  invariable  succession  ;  and  yet  we  are  not  entitled, 
on  that  circumstance  alone,  to  pronounce  the  earlier  the  cause 
of  the  later. 

The  case  of  day  and  night,  being  an  understood  phenomenon, 
illustrates  the  difference  between  causation,  and  mere  invaria- 
bility of  order.  We  know  that  the  cause  of  day,  is  the  light  of 
the  sun  falling  upon  the  earth  ;  that  the  cause  of  night  is  the 
absence  of  the  sun.  We  farther  know  that  the  earth's  rotation 
is  the  circumstance  occasioning  the  periodical  absence  of  the 
light.  The  cause  of  this  entire  phenomenon  is  made  up  of — the 
luminosity  of  the  sun,  our  being  placed  within  reach  of  that 
luminosity,  and  the  earth's  rotation  about  its  axis.  The 
alternation  of  light  and  dark  is  itself  but  a  consequence — a  co- 
effect  of  the  assemblage  of  facts  constituting  the  phenomenon. 

Some  of  the  invariabilities  of  vegetable  and  animal  growth 
may  be  proved,  and  others  presumed,  to  be  only  common  effects 
of  the  real  cause. 

Such  invariabilities  are  part  of  the  difficulty  of  causal 
elimination. 

The  cause  must  be  an  invariable  antecedent,  but  it  must 
farther  be  what  Mr.  Mill  expresses  as  the  *  unconditional  in- 
variable antecedent,'  the  sole  sufficing  circumstance  whose 
presence  makes  the  effect,  and  whose  absence  arrests  it.  Day- 
light is  preceded  by  darkness  ;  but  a  state  of  darkness  is  not 
everywhere  followed,  after  a  certain  duration,  with  day-light. 
We  cannot,  in  the  case  of  day  and  night,  separate  darkness  from 
its  order  of  alternation  with  light ;  but,  in  referring  to  other 
cases,  and  other  situations,  we  do  not  find  that  a  present  dark- 
ness always  alternates  with  illumination. 

THE   COMPOSITION   OF  CAUSES. 

20,  When  several  motive  powers  are  conjoined,  the  com- 
posite effect  is  the  sum  or  difference  of  the  separate  effects, 
according  as  they  conspire  with,  or  are  opposed  to  each 
other. 


COMPUTATION  OF  "COMBINED  CAUSES. 


2e>9 


Causes,  understood  as  prime  movers,  may  be  combined,  and 
the  result  computed  by  a  numerical  operation.  Two  men  pul- 
ling at  the  same  rope,  two  locomotives,  two  weights,  when 
acting  in  the  same  direction,  have  a  total  effect  equal  to  the 
sum  of  the  separate  effects.  When  they  thwart  one  another, 
the  result  is  the  difference.  For  oblique  action,  the  computa- 
tion is  made  by  the  parallelogram  of  forces. 

In  the  molecular  agencies  the  same  rule  applies.  Two  equal 
fires  give  twice  the  heat  of  one  ;  two  bushels  of  coals  make 
twice  the  combustion  of  one,  that  is,  twice  the  heat ;  in  the 
steam  engine,  to  double  the  fuel  is  to  double  the  motive  power. 
Three  identical  wax  candles  produce  a  triple  illumination. 
Two  equal  magnets  put  together  will  sustain  a  double  weig^ht. 
If  a  voltaic  battery  of  ten  cells  decompose  a  pound  of  water 
in  a  given  time,  six  similar  batteries  will  decompose  six  pounds 
in  the  same  time. 

The  same  principle  extends  to  the  Physiological  or  vital 
forces.  Increase  of  heat,  light,  and  assimilating  material 
makes  a  corresponding  increase  of  vegetable  growth.  Food 
and  oxygen  actively  combined,  give  forth  a  proportionate 
amount  of  animal  force. 

Even  in  Mind,  the  ratio  holds,  although  interfered  with  by 
new  forces  arising  out  of  the  complication.  The  pleasures 
and  pains  are  in  accordance  with  the  amount  of  their  several 
agents.  A  mau*s  enjoyments  increase  with  his  gains  and 
diminish  with  his  losses,  other  things  being  the  same. 

The  Social  forces  in  like  manner  combine,  and  may  be  com- 
puted by  adding  the  sum  of  the  effects.  The  addition  of  new 
causes  of  discontent  in  a  people  already  dissatisfied,  makes  a 
corresponding  advance  towards  anarchy  and  revolution.  On 
the  other  hand,  some  agreeable  or  soothing  agency  may  neu- 
tralize an  ill  feeling  already  at  work. 

In  all  these  instances.  Cause  is  to  be  interpreted  as  meaning 
Motive  Power,  or  Force ;  in  no  other  sense  does  the  rule  of 
arithmetical  sum  and  difference  apply.  Causes  that  merely  make 
good  the  collocation  for  bringing  a  prime  mover  into  action, 
or  that  release  a  potential  force,  do  not  follow  any  such  rule. 
One  man  may  direct  a  gun  upon  a  fort  as  well  as  three  ;  two 
sparks  are  not  more  effectual  than  one  in  exploding  a  barrel 
of  gunpowder.  In  medicine,  there  is  a  certain  dose  that 
answers  the  end  ;  and  adding  to  it  does  no  good. 

21.  Composition  of  Causes  is  sometimes  applied  to 
Chemical  actions,  so  as  to  mean  not  a  union  of  forces,  but 


270 


THE  COMPOSITION  OF  CAUSES. 


the  union  of  substances  or  materials.     In  this  way,  oxygen 
and  hydrogen  combine  to  form  water. 

This  part  of  the  chemical  process  comes  under  collocation, 
and  not  under  force.  The  mixing  of  materials,  and  tlie  union 
of  forces,  are  not  the  same  fact. 

In  chemical  action,  thus  understood,  we  cannot  fully  predict 
the  characters  of  the  compound  from  the  characters  of  the 
elements.  It  is  the  speciality  of  (chemical  combination  to 
merge  nearly  all  the  physical  properties  of  the  substances  com- 
bined, and  to  yield  a  new  product,  where  the  combining  ele- 
ments are  not  recognizable.  Sulphur  combines  with  copper 
to  form  a  black  flaky  substance,  the  sulphuret  of  copper. 

There  are  still  wanting  general  laws  that  would  serve  us  to 
compute  the  resultant  of  a  chemical  combination  ;  we  know 
only  that  weight  is  not  lost,  and  that  the  law  of  definite  pro- 
perties holds. 

The  analogy  of  Chemical  Combination  has  been  applied  to 
mental  and  social  combinations.  Thus,  the  complex  emotions 
of  the  mind  are  often  so  far  different  from  their  constituents, 
as  scarcely  to  suggest  these  to  the  mental  analyst.  The  moral 
sense,  for  example,  is  declared  by  many  to  be  a  simple  faculty, 
on  the  ground  of  its  having  no  resemblance  to  any  other  simple 
elements  of  the  mind. 

Again,  in^the  study  of  national  characters,  we  may  know 
that  certain  influences  concurred  in  the  process  of  formation, 
and  yet  find  a  difiiculty  in  tracing  them. 

These,  however,  are  mere  analogies.  Chemical  combination 
is  an  illustrative  metaphor  and  little  besides.  The  analogy 
fails  in  one  essential  circumstance,  definite  combinations.  The 
disguise  of  the  elements  or  components  is  the  only  point  of 
similarity  :  and  that  would  probably  be  better  referred  to  the 
analogy  of  growth^  where  the  constituents  entering  at  one  stage 
form  a  product,  still  farther  combined  in  succesive  operations, 
which  cannot  all  preserve  a  record  of  themselves. 


CHAPTER  V. 

ELIMINATION  OF  CAUSE  AND  EFFECT.— OBSERVA- 
TION AND  EXPERIMENT. 

I.  The  enquiry  into  causation  is  usually  presented  in 
nature  as  a  complication  of  influences  and  arrangements, 
some  concerned  and  some  not  concerned  in  the  cause  or 
the  effect  sought. 

For  instance,  a  man  in  good  health  goes  to  a  new  place  and 
a  new  occupation.  His  health  gradually  fails.  There  must 
be  a  cause  for  the  failure ;  assuming  that  he  could  have 
retained  his  health  in  his  original  abode  and  occupation,  the 
cause  must  lie  in  the  new  circumstances  that  he  is  placed  in. 
These  new  circumstances  are  perhaps  numerous  ;  the  climate 
may  be  hotter  or  moister,  not  to  mention  many  other  variations  ; 
the  man's  new  pursuits  and  recreations  maybe  widely  different 
from  his  old.  Now,  while  some  of  these  differences  must  have 
some  share  in  the  effect,  others  probably  have  no  share  ;  and  the 
problem  lies  in  disentangling  the  one  class  from  the  other;  in 
separating  the  operative  from  the  inoperative  surroundings. 

The  case  now  supposed  represents  the  inductive  search  in 
its  extreme  speciality,  and  as  it  appears  in  the  commoner 
practical  questions.  A  more  general  enquiry  is  exemplified 
in  determining  the  effects  of  given  agents,  as  heat,  moisture, 
electricity,  ozone,  light,  foods  or  medicines,  on  the  human 
constitution.  Every  one  of  those  agents  has  a  variety  of  pro- 
perties, or  modes  of  action ;  in  the  case  supposed,  some  are 
operative  and  some  not ;  and  we  must  discriminate  the  one 
class  from  the  other. 

Again,  we  may  propose  a  still  more  general  enquiry — What 
is  the  common  antecedent  to  the  effect  denominated  Heat,  or 
the  peculiar  fact  or  situation  always  recurring  when  there  is  an 
increase  in  the  temperature  of  material  bodies  ?  In  looking 
at  the  incidents  attending  the  development  of  heat  in  any  in- 
stance, we  find  them  to  be  numerous  and  various  ;  and  we  have 
to  find  some  mode  of  separating  the  inefficient  from  the  efficient 
elements  of  the  situation. 

We  know  from  the  law  of  Causation,  even  in  the  less  ex- 
plicit form  (Conservation  being  left  out  of  view),  that  in  the 


mmm 


272 


ELIMINATION   OF  CAUSE   AND   EFFECT. 


changes  going  on  in  the  world,  the  present  sitnation  is  the  re- 
sult of  the  previous  situation ;  and  if  that  previous  situation 
were  reproduced  so  would  the  present.  But  this  is  not  all ; 
for  we  may  be  able  to  show  that  if  a  certain  part  of  the  previ- 
ous situation  were  reproduced,  the  present  would  follow  ;  we 
can  put  aside  all  otiose  or  inert  accompaniments  and  reduce 
the  antecedent  circumstances  to  those  really  operative.  This 
is  the  process  of  Inductive  Elimination,  required  alike  in 
special  and  in  general  enquiries  as  to  cause  and  effect. 

Yet  farther,  we  may  find  the  sequence  of  a  past  and  a  pre- 
sent situation  to  consist  in  a  plurality  of  distinguishable 
sequences,  which  we  may  analyze  and  isolate  by  the  methods 
to  be  pointed  out.  Political  causation  is  almost  always  a 
complication  of  many  distinguishable  threads. 

2.  Preparatory  to  the  disentaDgling  or  eliminating  pro- 
cess, we  make,  in  our  own  mind,  an  analysis  of  the  situation. 

As  the  final  end  is  to  discriminate  the  necessary  from  the 
unnecessary  elements  of  the  situation,  we  begin  by  a  separate 
enumeration  of  all  the  circumstances,  taking  care  to  reduce 
each  to  its  simplest  components.  If  a  man  has  lost  his  health, 
in  a  certain  locality,  we  first  suppose  to  ourselves  what  may  be 
the  distinct  agents  concerned  ;  we  analyze  the  climate  into  all 
its  constituent  circumstances — temperature,  moisture,  fluctua- 
tions, purity  of  air,  and  so  on  ;  we  analyze  the  peculiarities  of 
his  mode  of  nourishment,  occupation,  habits,  state  of  mind; 
and  the  more  thorough-going  the  analysis,  the  better  are  we 
prepared  for  the  operation  that  is  to  follow.  Indeed,  an  in- 
sufficient analysis  will  of  itself  defeat  the  best  laid  schemes  of 
elimination.  Newton's  investigation  of  the  planetary  motions 
owed  its  success  to  his  analyzing  the  course  of  each  planet 
into  a  centra]  tendency  towards  the  sun,  and  a  tangential 
tendency.  This  separation  was  the  first  clue  to  the  mystery. 
In  any  enquiry  into  the  cause  of  some  effect  due  to  the  sun, 
as  for  example,  sun-stroke,  the  different  known  constituents  of 
the  solar  beam — heating,  lighting,  and  chemical  rays — should 
be  separately  viewed  as  the  possible  cause. 

The  ability  to  perform  these  mental  analyses  is  partly  depen- 
dent on  the  state  of  knowledge  at  the  time.  Thus,  we  now 
know,  what  was  not  known  in  the  beginning  of  the  last  cen- 
tury, the  constituents  of  the  atmosphere;  we  are  therefore  pre- 
pared for  an  enquiry,  according  to  the  methods  of  elimination, 
into  the  precise  cause  of  any  atmospheric  effect.  K  it  is  pro- 
posed for  enquiry,  why  does  meat  putrefy  in  the  air,  we  keep 


VARYING  THE  aRCUMSTANCES. 


273 


in  view  the  distinct  constituents — nitrogen,  oxygen,  water, 
carbonic  acid,  dust,  living  germs ;  as  among  these,  or  among 
some  concurrent  action  of  these  the  cause  must  be  found.  So, 
it  is  only  of  late,  that  the  analysis  of  the  solar  ray  has  indi- 
cated the  so-called  chemical  rays  in  addition  to  the  luminous 
and  the  heat-giving  rays. 

It  may  be  farther  remarked,  that  this  analytic  ability  is  a 
special  mental  aptitude  personal  to  the  enquirer,  and  indicat- 
ing the  scientific  faculty. 

3.  In  separating  the  essential  from  the  non-essential 
accompaniments  in  cause  and  effect,  the  course  is  to  vary 
the  circumstances,  for  which  end  we  must  resort  to  Observa- 
tion and  Experiment 

The  different  antecedents  and  consequents  being  separated 
in  thought,  we  have  to  ascertain  which  antecedent  is  connected 
with  a  given  consequent.  Having  usually  a  plurality  of  ante- 
cedents, or  a  plurality  of  consequents,  or  both,  we  need  to 
single  out  the  connected  couples  of  antecedent  and  consequent. 
This  requii-es  us  to  look  for  other  instances  where  the  group- 
ings are  different,  and  to  note  what  happens  when  particular 
antecedents  or  consequents  are  wanting  :  an  operation  described 
by  Bacon  as  *  varying  the  circumstances.* 

The  varied  circumstances,  or  groupings,  are  so  many  new 
facts  attainable  only  by  Observation,  to  which  we  may  add 
Experiment.  The  distinction  between  these  two  processes  is 
not  fundamental,  and  is  seldom  important.  Observation  is 
finding  a  fact.  Experiment  is  making  one.  The  worth  of  the 
fact  depends  on  what  it  is  in  itself,  and  not  on  the  manner  of 
obtaining  it.     Both  methods  are  used  as  far  as  possible. 

The  advantages  of  Experiment  are  not  confined  to  the 
obvious  circumstance  of  multiplying  the  facts,  important  as  it 
must  often  be  to  multiply  them.  A  second  consideration  is 
the  power  that  we  may  have  of  suiting  the  facts  to  the  case  in 
hand — of  producing  the  sort  of  variation  that  we  need.  Thus, 
in  order  to  ascertain  which  of  the  gases  of  the  atmosphere 
supports  combustion,  or  animal  life,  and  what  are  the  elements 
that  bring  about  putrescence  and  decay,  we  must,  by  means  of 
experiments,  separate  artificially  one  or  another  of  the  gases 
from  the  rest ;    such  separation  not  being  provided  for  us  in 

nature. 

Dr.  Balfour  Stewart  remarks,  with  reference  to  an  investiga- 
tion by  Dulong  and  Petit  as  to  the  cooling  of  a  body  surrounded 
by  a  gas,  that  the  research  was  a  very  troublesome  one,  from 


274 


ELIMINATION   OF   CAUSE   AND   EFFECT. 


COMPLICATIONS   OF  CAUSE  AND  EFFECT. 


275 


the  variations  that  had  to  be  made  in  the  temperature  of  the 
body,  and  in  the  density,  temperature,  and  chemical  nature  of 
the  gas. 

A  third  superiority  of  Experiment  over  Observation  lies  in 
the  power  of  producing  a  phenomenon  under  knoion  circum- 
stances and  surroundings^  so  as  to  take  account  of  all  extraneous 
influences.  Thus,  instead  of  observing  electricity  in  thunder 
discharges,  we  evolve  it  in  a  room  where  we  know  all  the 
modifying  influences.  For  the  examination  of  magnetism,  a 
house  is  constructed  wholly  of  wood,  so  that  the  local  disturb- 
ance of  pieces  of  iron  may  be  prevented.  Likewise,  the  best 
opportunity  for  the  study  of  disease  is  in  hospitals,  where  the 
sick  are  wholly  under  the  control  of  the  physician. 

Experiment  finds  its  greatest  scope  in  Physics  and  in  Chemis- 
try. It  is  admissible  in  Physiology,  in  the  Human  Mind,  and  in 
Human  Society,  with  limitations  easily  divinable  by  any 
reflecting  student. 

In  the  situation  of  enquiring  into  the  Cause  of  a  given 
Effect,  Experiment  is  for  a  moment  unavailing.  We  can  try 
the  effect  of  a  given  cause,  but  we  cannot  try  the  cause  of  a 
given  effect.  Assuming  heat  as  an  agent,  we  can  make  experi- 
ments on  its  various  powers  or  capabilities ;  but  given  the  heat 
of  a  fermenting  mass,  as  an  effect,  we  cannot,  by  experiment, 
get  out  the  cause.  We  must  first  conjecture  a  cause  ;  experi- 
ments may  then  be  instituted  to  find  out  the  effects  of  that 
supposed  cause ;  if  these  tally  with  the  effect  in  question, 
we  have  made  out  our  point. 

The  problem  of  Causation  may  thus  be  presented  in  both 
aspects — given  a  cause  to  find  the  effect,  given  an  effect  to 
find  the  cause — but  the  experimental  solution  is  one  ;  namelv, 
to  watch  the  effect  of  an  assumed  cause.  The  course  of  the 
phenomenon  flows  in  one  way  ;  cause  first,  effect  second. 
When  we  seem  to  be  working  backward,  we  are  in  reality 
working  forward. 

REVIEW  OF  THE   COMPLICATIONS   OF  CAUSE   AND   EFFECT, 

4.  The  Inductive  Elimination  of  Causes  and  Effects  may 
be  illustrated  by  a  review  of  the  various  complicationa 
actually  met  with. 

We  have  already  adduced  examples  of  the  complications 
that  have  to  be  unravelled,  in  order  to  assign  the  neat  effects 
of  a  cause,  or  the  causes  of  an  effect.  We  are  able  to  present 
a  more  comprehensive  view  of  the  actually  occurring  entangle- 
ments. 


Those  natural  aggregates,  termed  Kinds  by  pre-eminence, 
are  marked  by  the  concurrence,  in  a  single  object,  of  many 
different  properties.  Oxygen,  carbon,  phosphorus,  iron,  mer- 
cury, platinum — have  each  a  great  number  of  distinct  powers 
oi  activities  ;  hence,  when  the  introduction  of  any  one  of  them 
is  followed  by  some  change  in  the  things  they  are  brought  into 
contact  with,  we  are  at  first  uncertain  which  of  all  the  many 
properties  of  the  substance  is  the  operative  circumstance. 
Carbon,  for  example,  is  found  to  absorb  gases  in  large  amount; 
which  suggests  the  enquiry,  which  of  the  properties  of  carbon 
is  this  owing  to : — its  specific  gravity,  porosity,  blackness, 
amorphous  structure,  or  any  other  ?  Again,  mercury  has 
certain  medicinal  effects ;  and  we  desire  to  know  which  of  its 
many  properties  is  the  causative  circumstance.  Platinum,  in 
a  finely  divided  or  spongy  state,  brought  into  contact  with  a 
stream  of  hydrogen,  makes  it  ignite.  What  does  this  depend 
upon  ? 

So  then,  in  the  elementary  bodies  of  Chemistry,  the  simplest 
substances  known  to  us,  there  is  a  great  concourse  of  anteced- 
ents present  whenever  any  one  is  brought  into  play.  But,  in 
nature,  these  are  usually  found  mixed  together  (I  am  not 
alluding  to  Chemical  combination,  which  yields  new  substances) 
in  great  varieties  of  compounds.  Thus,  the  Atmosphere  is  a 
mixture  of  two  simple  bodies — nitrogen  and  oxygen  ;  various 
known  chemical  compounds — water,  carbonic  acid,  and  am- 
monia; and  a  great  many  other  gaseous  effluvia,  together 
with  solid  particles,  partly  dust  and  partly  ova  of  plants  and 
animals.  Moreover,  it  possesses  at  each  moment  a  certain 
temperature,  a  certain  electrical  condition,  and  perhaps 
other  peculiarities.  Thus,  when  the  atmospheric  air  is  pre- 
sented to  us  as  a  cause  or  agency,  the  possible  variety  of 
antecedents  is  very  great.  Many  researches  have  been  occu- 
pied in  eliminating  the  causal  conditions  in  combustion,  in 
vegetable  and  in  animal  life,  in  putrefaction,  in  spontaneous 
generation  (so-called),  &c. 

Again,  the  sea  is  not  pure  water,  but  a  solution  of  numerous 
saline  bodies. 

Atost  minerals  are  mixed  substances.  A  geological  stratum 
is  highly  compound ;  and  when  certain  vegetables  are  found 
to  grow  in  a  particular  soil,  elimination  must  be  applied  to 
ascertain  which  are  the  needful  constituents. 

In  Vegetable  and  in  Animal  Kinds,  the  complication  is 
still  greater.  The  chemical  constituents  of  plants  and  of  ani- 
mals have  very  complex  atoms,  whose  disintegration  may  yield 


27G 


WEAPONS  OF  ELIMINATION. 


a  variety  of  different  products.  Hence,  vegetable  and  animal 
Bubstances  used  as  food,  as  medicines,  as  dyes,  <fec.,  have  many 
possible  modes  of  operating.  We  must,  however,  when  living 
bodies  are  agents,  farther  take  into  account  the  organic  or  living 
structure ;  the  poison  of  a  living  plant  or  animal  has  powers 
of  derangement  quite  different  from  the  chemical  action  of  its 
chemical  constituents. 

The  complication  in  the  world  of  Mind  is  very  great.  A 
human  being  is  by  nature  many-sided,  and  by  education  still 
more  so.  Hence,  when  one  person  exercises  an  influence  upon 
another,  it  is  far  from  obvious,  at  first  sight,  by  what  peculiari- 
ties the  effect  arises.  So  again,  in  the  explanation  of  motives, 
a  historian  is  often  baffled  to  select  the  one  that  actually 
swayed  a  given  effect. 

The  operations  of  Government  are  ramified  in  their  conse- 
quences. A  single  enactment — the  imposition  of  a  tax  on 
windows  or  its  removal,  free-trade,  or  its  opposite — operates 
yarionsly  according  to  circumstances. 

WEAPONS   OF   ELIMINATION. 

6.  It  is  in  the  comprehensive  Law  of  Causation  itself, 
once  established  by  Induction,  that  we  have  the  instru- 
ments for  eliminating  causes  and  effects  in  the  detail 

As  already  said,  there  is  but  one  proper  Inductive  Method 
— Universal  Agreement;  there  is,  in  the  first  instance,  no 
shorter  cut  to  an  Inductive  Genei-alization.  We  must  go 
thj'ough  the  labour  of  a  full  examination  of  instances,  until  we 
feel  assured  that  our  search  is  complete,  that  if  contrary  cases 
existed,  they  must  have  been  met  with. 

By  such  thorough-going  examination,  various  inductive  laws 
have  been  established,  including  that  momentous  truth  called 
the  Law  of  Causation.  Now,  in  whichever  of  its  two  properly 
scientific  aspects,  we  view  this  law — whether  in  the  less  sug- 
gestive but  perfectly  accurate  form  of  Uniformity  of  Sequence, 
or  in  the  new  and  better  form  of  Conservation  accompanied 
with  Collocation,  we  find  in  it  a  means  of  shortening  the  labour 
of  ascertaining  specific  causes  and  effects.  By  applying  the 
general  law,  in  either  form,  there  is  often  a  possibility  of  prov- 
ing causation  by  a  single  instance. 

Thus,  to  take  the  first  form  of  Causation—*  Every  event  is 
uniformly  followed  by  some  other  event ;  and  every  event  is 
uniformly  preceded  by  one  or  other  of  a  definite  number  of 
events ': — given  an  antecedent,  one  consequent  succeeds ;  given 


CAUSATION  THE  BASIS  OF  ELIMINATION. 


277 


a  consequent,  some  one  of  a  few  definite  antecedents  has  pre- 
ceded. Now  from  thi»  it  follows,  that  whenever  an  agent  is 
introduced  into  a  quiescent  state  of  things,  and  when  certain 
changes  follow  at  once  on  that  fact,  the  sequence  happening 
once  will  happen  always.  Nothing  springs  out  of  nothing. 
Nature  in  the  matter  of  sequences  is  uniform ;  and  a  single 
case,  cleared  of  aiffbiguities,  establishes  a  law.  By  the  stroke 
of  an  axe,  a  block  is  cleft ;  the  same  effect  will  always  follow 
the  same  cause.  Hence,  a  single  experiment  in  the  laboratory 
may  establish  for  ever  a  casual  property. 

On  the  second  or  more  precise  form  of  Causation,  there  is 
a  definite  transfer  of  motive  power  under  some  given  arrange- 
ment of  things.  We  know,  by  this  law,  without  any  new 
observation,  that  a  blow  with  a  hammer  will  realize  its 
equivalent,  either  in  mechanical  energy,  or  in  some  form 
of  molecular  force.  If  in  a  certain  situation,  it  splinters  a 
stone,  it  will  always  do  the  same  thing,  in  the  same  situation. 
In  a  different  arrangement,  it  raises  the  temperature  of  a 
surface  ;  and  what  it  does  once,  it  does  always.  All  that  we 
have  to  settle  empirically  in  this  form  of  the  law,  is  the 
transfer  attending  each  collocation,  and  the  collocation  attend- 
ing each  transfer.  By  induction  proper  (universal  agree- 
ment) we  have  already  ascertained  this  to  be  uniform,  and 
accordingly  pronounce  upon  a  single  clear  instance. 

There  is  thus  only  one  Inductive  Method  at  the  foundation 
(Agreement),  but  there  are  several  Deductive  Methods,  or 
methods  depending  upon  the  grand  generalization  of  Cause. 
For  instance,  the  method  known  as  the  *  Method  of  Differ- 
ence,' is  not  an  inductive  but  a  deductive  method ;  for,  with- 
out the  law  of  Causation,  the  method  would  be  incompetent. 
Even  the  *  Method  of  Agreement '  as  employed  for  the  pur- 
pose of  elimination,  supposes  the  Law  of  Causation,  and  is  to 
that  extent  a  deductive  method. 

6.  The  Law  of  Causation  involves  the  three  following 
affirmations,  each  of  which  is  the  groundwork  of  a  process 
of  Elimination. 

(1)  Whatever  antecedent  can  he  left  out,  without  preju- 
dice to  the  effect,  can  be  no  pai-t  of  the  cause. 

A  cause  is  what  produces  an  effect.  As  the  presence  of 
the  cause  is  the  presence  of  the  effect,  so  the  absence  of  the 
cause  is  the  absence  of  the  effect.  The  absence  of  the  cause, 
with  the  presence  of  the  effect,  would  be  a  contradiction  of 
the  law.    We  are  sure,  therefore,  that  whatever  can  be  omitted 


!i9<*< 


278 


WEAPONS   OF  ELIMINATION. 


ELIMINATION  FOUNDED   ON  CAUSATION. 


279 


\ 


or  withdrawn  without  making  any  difference  to  the  effect  in 
question,  is  not  the  cause,  or  any  part  of  the  cause.  If  we 
cut  a  string  that  we  suppose  to  be  the  support  of  a  weight, 
and  the  weight  continues  to  be  supported,  the  string  is  not 
the  support. 

Upon  the  Law  of  Causation,  viewed  on  this  side,  reposes 
Mr.  Mill's  Method  of  elimination  by  Agreement.  A  certain 
effect  remains  after  the  successive  withdrawal  of  all  the  ante- 
cedents except  one ;  which  leaves  that  one  in  sole  and  undis- 
puted possession,  and  therefore  the  cause. 

(2)  When  an  antecedent  cannot  be  left  out  without  the 
consequent  disappearing,  such  antecedent  must  be  the 
cause  or  a  part  of  the  cause. 

This  affirmation,  likewise,  is  implied  in  the  law.  It  presents 
the  other  side  of  the  same  linking  of  cause  and  effect ;  absence 
of  the  cause  is  absence  of  the  effect.  Whatever,  by  disappear- 
ing, makes  the  effect  to  disappear,  is  by  that  very  fact  an 
essential  or  causal  condition.  If  the  cutting  of  a  string  is  the 
falling  of  a  weight ;  the  string  is  the  support  of  the  weight. 

This  aspect  of  cause  gives  the  decisive  Method  of  Diference; 
the  method  whereby  a  single  instance  may  be  incontrovertible 
proof  of  a  cause. 

(3)  An  antecedent  and  a  consequent  rising  and  falling 
together  in  numerical  concomitance  are  to  be  held  as  Cause 
and  Effect. 

^  This  is  Causation  in  the  more  special  aspect  of  Conserva- 
tion, and  is  direcMy  implicated  in  that  principle.  In  the 
transfer  of  moving  power,  the  quantity  gained  is  the  quantity 
lost ;  and  the  tracing  of  quantitative  concomitance  is  our  very 
best  clue  to  the  force  operative  in  a  given  effect.  As  the  com- 
bustion of  a  locomotive  is  increased,  so  is  the  steam  power. 

In  those  agencies  that  merely  bring  about  a  collocation, 
there  is  no  numerical  ratio  between  the  agent  and  tlie  result. 
A  slight  touch  is  enough  to  complete  the  electric  circuit,  and 
a  double  vehemence  adds  nothing  to  the  energy  of  the  circuit. 
The  process  now  described  is  the  Method  of  Concomitant 
Variations. 

These  are  the  three  chief  methods  of  Eliminating  the  un- 
concerned circumstances  present  in  cause  and  effect.  After 
considerable  progress  has  been  made  in  the  discovery  of 
causes,  recourse  may  be  had  to  a  farther  proceeding,  namely, 
to  allow  for  the  influence  of  all  known  causes,  and  to  attribute 


what  remains  of  the  effect  to  what  remains  of  the  cause.  This 
also  is  a  proper  inference  from  the  Law  of  Causation.  It  is 
termed  the  Method  of  Residues. 

The  Method  of  Agreement  may  be  employed  negatively ; 
that  is,  cases  may  be  found  where  cause  and  effect  are  uni- 
formly absent  tog  ethers  We  may  call  it  Agreement  in  Absence. 
When  this  circumstance  can  be  conjoined  with  the  positive 
method — Agreement  in  presence — an  approach  is  made  to  the 
decisive  cogency  of  the  Method  of  Difference.  Mr.  Mill  has 
given  to  this  conjoint  mode  the  designation — Joint- Method. 

The  following  chapter  will  exemplify  the  employment  of 
these  Five  Methods  of  Inductive  (or  Deductive)  Elimination 
in  investigating  Cause  and  Effect. 

It  is  not  possible  to  separate  from  the  thorough  working  of 
these  instruments  of  Elimination  the  process  of  generalizing^ 
or  attaining  to  Inductive  generalities.  In  carrying  out  the 
Method  of  Agreement,  for  example,  the  collation  of  a  large 
number  of  instances  where  a  cause  or  an  effect  is  present, 
cannot  fail  to  suggest  laws  of  causation  of  a  higher  generality 
than  the  enquirer  sets  out  with.  Nevertheless,  it  will  not  be 
expedient  to  dwell  upon  this  generalizing  operation  while  we 
are  bent  upon  the  eliminating  process.  Generalization  belongs 
to  Discovery  ;  Elimination  is  Proof;  and  Proof,  more  than 
Discovery,  is  the  end  of  Logic.  Still,  we  shall  have  to  make 
room  for  a  consideration  of  the  best  modes  of  arriving  at  the 
higher  generalities. 


CHAPTER  VI. 
THE  EXPEEIMENTAL  METHODS. 

1.  There  are  three  cbief  methods  of  eliminating  tbe 
cause  of  a  phenomenon  from  the  neutral  or  indifferent 
accompaniments — Agreement,  Difference,  and  Concomitant 
Variations. 

METHOD   OF   AGREEMENT. 

2.  The  Method  of  Agreement  is  expressed  thus  : — If 
two  or  more  instances  of  a  phenomenon  under  investiga- 

13 


280 


THE  EXPERIMENTAL  METHODS. 


tion  have  only  one  circumstance  in  common,  that  circum- 
stance is  the  cause  (or  effect)  of  the  phenomenon. 

The  instances  are  studiously  varied  so  as  to  leave  out  in 
turn  all  the  circumstances  attending  the  phenomenon.  What- 
ever is  left  out,  in  any  one  instance,  without  detriment  to  the 
effect,  cannot  be  the  cause  ;  the  possibilities  are  gradually 
reduced  in  number  ;  and,  if  the  means  of  elimination  are  com- 
plete, the  enquiry  terminates  in  assigning  one  circumstance 
that  has  never  been  wanting  where  the  phenomenon  appears. 

The  method  is  illustrated  symbolically  thus  : — Let  A  repre- 
sent a  cause  and  a  an  effect.  In  nature  we  seldom  have  A 
followed  by  a  alone  ;  were  such  isolation  the  rule,  the  Experi- 
mental Methods  would  be  unnecessary.  What  we  find  is  A  in 
combination  with  other  things  as  A  B  C,  and  a  also  in  com- 
bination, as  in  a  6  c.  But,  now,  if  these  conjunctions  were 
rigid  and  invariable,  we  should  have  no  opening  for  the 
methods.  The  real  fact  is,  however,  that  though  a  cause  may 
be  always  in  combination  with  other  agents,  it  is  not  always 
in  the  same  combination  ;  at  one  time  the  union  is  A  B  C,  at 
another  time  A  B  D,  and  again  ACE;  there  being  corres- 
ponding conjunctions  in  the  effects — a  b  c^  a  b  d^  a  c  e. 

If  we  suppose,  then,  the  instances — 

ABC  giving  a  b  c, 
A  B  D  giving  a  b  d, 
*  ACE  giving  ace, 

we  reason  thus.  So  far  as  the  first  instance  is  concerned — 
ABC  giving  ab  c,  the  effect  a  may  be  produced  by  A,  or 
by  B,  or  by  C.  In  the  second  instance — A  B  D  giving  ab  d, 
the  cause  C  is  absent,  the  effect  a  still  remaining  ;  hence  C  is 
not  a  cause  of  a.  In  the  third  instance — A  C  E  giving  a  c  e, 
— B  is  absent,  a  remaining ;  hence  B  is  not  a  cause  of  a.  The 
only  antecedent  persisting  through  all  the  instances  is  A ; 
when  a  is  present  as  a  consequent,  A  is  always  present  as  an 
antecedent.  If,  then,  we  are  sure  that  every  other  antecedent 
circumstance  has  been  removed  in  turn,  the  consequent  a  still 
surviving,  we  have  conclusive  evidence  that  A  is  a  cause, 
condition,  or  invariable  accompaniment  of  a. 

It  matters  not  which  is  the  form  of  the  enquiry, — given  an 
effect  to  find  a  cause,  or  given  a  cause  to  find  an  effect.  The 
first  is  supposed  to  be  the  more  frequent  occurrence.  Science, 
from  of  old,  was 

rerum  cognoscere  causas. 

If  the  problem  be  given  in  the  first  form,  the  proof  is  always 
given  in  the  second ;    we   try  a  cause   to   see   what  effect 


METHOD   OF  AGREEMENT. 


281 


will  follow,  which  proves  at  once  that  the  consequent  is  the 
effect  of  the  antecedent,  and  that  the  antecedent  is  the  cause 
of  the  consequent ;    the  two  afiirmations  being  identical. 
^  Although  our  professed  object  now  is  to  unfold  the  Induc- 
tive elimination  of  Cause  and  Effect,  having  already  disposed 
of  the  case  of  Co-existence  as  Co-inhering  Attributes,  yet,  in 
expounding   the   Methods,  we  must  receive  instances   indis- 
criminately, as  we  do  not  at  first  know  how  they  will  turn  out. 
There  are  many  connexions  of  Cause  and  Effect  that  appear 
as  Co-existences,  and  there  are  instances  that  we  must  leave 
undecided,  being  unable  to  assign  the  ultimate  nature  of  the 

union.      The  more  obvious  tests  of  Causation  are  these : 

(1)  sequence  in  time,  as  when  innoculation  is  followed  by  the 
small-pox  pustule;  (2)  expenditure  of  energy,  as  when  a 
cannon  ball  shatters  a  fort.  Where  these  tests  are  wanting,  as 
in  co-inhering  powers  of  the  same  substance— for  example, 
gravity  and  inertia — we  are  left  to  presume  co-existence, 
there  being,  as  alternative  possibilifcieF,  mutual  implication,  and 
the  co-existing  effects  of  a  common  cause. 

This  explanation  is  more  especially  called  for  in  commenc- 
ing the  Method  of  Agreement — the  universal  or  fundamental 
mode  of  proof  for  all  connexions  whatever.  Under  this 
method  in  particular,  we  must  be  ready  to  admit  all  kinds  of 
conjunctions ;  reducing  them  under  Causation,  when  we  are 
able,  and  indicating  pure  Co-existence  when  the  presumption 
inclines  to  that  mode. 

As  a  simple  example,  we  may  take  the  case  of  the  conver- 
sion of  solid  bodies  into  liquids,  and  the  farther  conversion  of 
liquids  into  gases.     The  bodies  so  converted  are  of  every 
possible  variety  of  properties  ;  the  one  circumstance  common 
to  all  the  instances  of  such  conversion  is  the  application  of 
heat.     The  elimination  is  complete  as  regards  this  antecedent, 
which  is  therefore  correctly  assigned  as  the  essential  condition 
or  cause.     We  may  apply  in  this  example,  the  most  decided 
test  of  Causation,  the  expenditure  of  energy  or  force ;  we  should 
never  regard  the  fact  as  a  mere  Co-existence. 
The  next  example  is  of  a  different  character. 
The  peculiar  phenomenon   known  as    the  interference  of 
polarized  light— consisting  in  the  exhibition  of  rings  of  alter- 
nating or  *  periodical'  colours,  when    a   polarized   beam   of 
light   passes    through   certain    transparent  substances — may 
be  propounded  for  investigation.     W^e  may  ask— is  there  any 
other  property  or  phenomenon  always  present  in  the  bodies 
that  show  this  peculiar  effect  ?     Now,  tlie  bodies  must,  as  a 


\ 


282 


THE  EXPERIMENTAL  METHODS. 


EXAMPLES  OF  AGREEMENT. 


matter  of  course,  be  traDsparent ;  but  aH  transparent  bodie« 
do  not  exhibit  the  polarized  bands ;  hence,  transparency  is 
eliminated.  By  farther  comparison  of  instances,  we  find  that 
there  is  no  constant  mode  of  colour,  of  weight,  of  hardness, 
of  form  (crystalline),  of  composition  (physical  or  chemical)  ; 
flo  that  no  one  of  all  these  properties  is  concerned  in  the 
phenomenon.  There  is,  however,  one  property  cummou  to 
all  the  substances  that  furnish  these  coloured  bauds,  they  are 
all  doubly  refracting  substances,  that  is,  present  two  imao-es  of 
things  seen  through  them  obliquely.  By  Agreement  through 
all  known  substances,  there  is  proof  of  the  concurrence  of 
these  two  properties. 

It  is  not  ascertained,  however,  and  cannot  be  ascertained  by 
Agreement  alone,  whether  the  two  facts  are  cause  and  effect, 
or  whether  they  are  a  case  of  co-existence  without  causation. 
Agreement  is  the  method  of  proof  for  all  conjunctions  what- 
soever— whether  Causation  or  Co-existence.  The  enquiry 
belongs  to  a  particular  class — the  conjoined  Properties  of 
Kinds,  where  there  may  be  laws  of  co-existence  without  cau- 
sation. The  decisive  criteria  of  causation  are  wanting  in  the 
case. 

To  take  a  third  example.  In  flowers,  there  is  a  remark- 
able concurrence  between  the  scarlet  colour  and  the  absetice 
oi  fragrance.  The  following  quotation  gives  a  selection  of 
instances. 

*  Among  all  the  colours  that  blooms  assume,  none  are  less 
associated  with  fragrance  than  scarlet.  We  cannot  at  present 
recollect  a  bright  scarlet  blossom  that  is  sweet-scented — yet 
no  other  colour  among  flowers  is  more  admired  and  sought 
after.  Scarlet  prevails  among  Balsamina,  Euphorbia,  Pelar- 
gonium, Poppy,  Salvia,  Bouvardia,  and  Verbena,  yet  none  of 
the  scarlets  are  of  sweet  perfumes.  Some  of  the  light-coloured 
Balsams  and  Verbenas  are  sweet-scented,  but  none  of  the 
scarlets  are.  The  common  Sage,  with  blue  blooms,  is  odorifer- 
ous both  in  flower  and  foliage;  but  the  scarlet  Salvias  are 
devoid  of  smell.  None  of  the  sweet-scented-leaved  Pelar- 
goniums have  scarlet  blooms,  and  none  of  the  scarlet  bloomers 
have  sweet  scent  of  leaves  nor  of  blooms.  Some  of  the  white- 
margined  Poppies  have  pleasant  odours ;  but  the  British 
scarlets  are  not  sweet-scented.  The  British  white-blooming 
Hawthorn  is  of  the  most  delightful  fragrance  ;  the  scarlet- 
flowering  has  no  smell.  Some  of  the  Honeysuckles  are 
sweetly  perfumed,  but  the  Scarlet  Trumpet  is  scentless'  (Elder, 
American  Gardener's  Monthly). 


283 


Fourth  Example.  The  Norih-East  wind  is  known  to  be 
E^G^^\\j  injurious  to  a  great  many  persons.  Let  the  enquiry 
be-what  circumstance  or  quality  is  this  owincr  to  ?  Bv  a 
mental  analysis  we  can  distinguish  various  qualities  in  winds: 
j-the  degree  of  violence,  the  temperature,  the  hurniditv  or 
dryness,  the  electricity,  and  the  ozone.  We  then  refer  to 
the  actual  instances  to  see  if  some  one  mode  of  any  of  these 
qualities  uniformly  accompanies  this  particular  wind.     Now 

7.M^'  A.  ^A  ""^FI^^  ''''^^'^'''  ^^«^%  wi^ds  are  generally 
feeble  and  steady,  but  on  particular  occasions,  they  are  stormy  • 
hence,  we  cannot  attribute  their  noxiousness  tolhe  intenS 
of  the  current.  Again,  while  often  cold,  they  are  sometimel 
comparatively  warm ;  and  although  they  are  more  ^^^Tel 
able  when  cold,  yet  they  do  not  lose  their  character  by  be W 
Sh  '"^  temperature  ;  so  that  the  bad  feature  is  not  coldness^ 
ST'.  T  ^^^^.^^^^^'^  degree  o£  moisture;  they  are  some- 
IrZ  I  r  f  ««,^et^mes  dry.  Again,  as  to  elect^city,  there 
IS   no  constant  electric  charge  connected  with  themf  either  ' 

fhe   Zn^  l"^^'"^"'  ^''^!r  ^'.  ^^*"^^^  '  *^^  ^^^«^^i°  tension  of 
Flrfhir^     ^^    generally   rises    as   the   temperature    falls. 

:u^fl\u  ''^T^o'  'T''  ^^^y  *^^^^  undoubtedly  less  of  this 
fhtr   f  ^\*^'  South.  West  winds  ;  yet  an  easterly  wind  a^ 
.  S  a  Lwu^'l^""  more  ozone  than  a  westerly  wind  in^the  heart 
pL^nf  \  •  "^""^^^  *^^^  ^PP^^^  t^^*  *^«  depressing  effect 

When   hLT^"""^  *"  ^^^  ^""  "^  '^''^  fi^«  circumftancel 
Zrfh'^.JT'''  ^^  ^^^estigate  closely  the  conditions  of  the 

wt  /  !lf' ^^  "^^"^^^^^  ""^  ^^^  *^^*  i*  blows  from  the  pole 
towards  the  equator,  and  is  for  several  thousand  miles  do7e 
upon  tJ^  surf  ace  of  the  ground  ;  whereas  the  south-west  wind 
coming  from  the  equator  descends  upon  us  from  a  hei-ht 
Now  m  the  course  of  this  long  contact  with  the^round  a 
great  namber  of  impure  elements-gaseous  effluvia  fne  dust 
SdTlhfir^-T^."^  r°^!^P  -^  may":;m:Li^ 

decTdtlhat*  olTn^^^  •      ^'  Agreement  by  itself  does  not 

decide  that  conjoined  circumstances  are  cause  and  effect  we 

Zli    ''""?  """^^  "'  '^'^'^^'^^  Co-existence,  and  ^nderin- 

tlainlv^-n  «7  ^""""'"^^^  ^^^^"  '^^  *^^  crcumstances  arS 
plainly  m  succession,  as  when  a  fracture  follows  a  blow  uni- 
form agreement  (with  elimination)  proves  causation  'when 
tllZlelt  '^"^^^*^^^^^  -^---'  the  agreement  faiTs  IS 


i 


/ 


284 


THE  EXPERIMENTAL  METHODS. 


EXAMPLES  OF  AGREEMENT. 


285 


Now,  there  is  a  general  belief  that  the  two  events  supposed 
— the  east  wind  and  the  uncomfortable  sensations — are  not 
contemporaneous,  but  in  succession ;  the  wind  first,  the  feel- 
ings afterwards.  This  belief  is  supported  by  the  circumstance 
that  a  change  of  feelings,  must  have,  according  to  the  law  of 
causation,  an  antecedent  condition ;  and  if  all  antecedents, 
besides  the  one  above  named,  are  eliminated,  that  one  is  the 
cause,  or  an  essential  part  of  the  cause. 

The  phenomenon  to  be  explained  is  not  a  permanent  fact 
or  potentiality,  like  polarization  or  double  retraction,  it  is  a 
temporary  manifestation,  and  requires  some  causal  circum- 
stance to  bring  it  forth.  In  this  respect,  it  resembles  the 
actual  display  of  one  of  these  optical  properties ;  it  cannot 
happen  without  a  suitable  agent  and  collocation,  which  is  pro- 
perly a  cause  of  the  appearance. 

If  then,  the  elimination  be  supposed  complete,  there  is  a 
proof  by  Agreement  that  the  deleterious  influence  of  the  east 
wind  is  due  to  the  circumstance  named  ;  and  the  case  exempli- 
fies the  eliminating  efficacy  of  the  method. 

In  the  foregoing  example,  we  cannot  withhold  from  our 
mind  a  certain  'presumption  in  favour  of  the  result,  grounded 
on  our  knowledge  of  the  deleterious  tendency  of  atmosphere 
impurities  caught  up  from  the  surface  of  the  ground.  This 
is  a  circumstance  not  properly  belonging  to  the  proof  by 
Agreement ;  it  is  a  confirmation  from  deductive  sources.  The 
addition  of  such  a  presumption  always  operates  strongly  on 
our  belief ;  the  total  absence  of  it  leaves  a  considerable  shade 
of  uncertainty  in  all  the  methods,  but  most  of  all  in  Agree- 
ment. The  third  example  shows  this  deficiency  ;  we  are  not 
at  present  aware  of  any  connexion  of  a  causal  kind  between 
the  scarlet  colour  of  flowers  and  the  absence  of  fragrant 
odour  ;  the  proof  of  the  law  rests  upon  the  Agreement  alone. 
That  method  of  proof  is  final,  only  when  the  elimination  has  been 
exhausted,  by  variation  of  circumstances,  and  when  the  coin- 
cidence has  been  shown  through  all  nature,  so  as  to  establish 
a  law  of  Universal  Co-existence. 

Fifth  Example.  Let  the  phenomenon  given  be  Ci'ystaUization^ 
and  let  the  thing  sought  be  the  antecedent  circumstances, 
positive  and  negative,  of  the  formation  of  crystals.  This  is  a 
case  of  succession,  and  therefore  of  Causation. 

We  must  begin  by  collecting  instances  of  the  effect.     In  the 
following  series,  the  circumstances  are  purposely  varied  with 
a  view  to  elimination : — 
1.  Freezing  of  water. 


2.  Cooling  and  solidifying  of  molten  metals  and  minerals. 

3.  Deposition  of  salts  from  solutions. 

4.  Volatilizing  of  solutions. 

6.  Deposition  of  solids  from  the  gaseous  state,  as  iodine. 
C.  Pressure. 

7.  Slow  internal  change,  as  in  rocks. 

8.  The  transformation  of  metals  from  the  tough  to  the 

brittle  condition,  by  hammering,  vibration,  and  re- 
peated heatings  and  coolings. 

Looking  at  the  first  and  second  instances — ice,  and  the 
solidifying  of  molten  metal — we  discover  two  antecedent  cir- 
cumstances, namely,  lowering  of  temperature,  aud  change 
from  the  liquid  to  the  solid  state. 

The  third  instance — deposition  of  salts  from  solution — 
agrees  in  the  same  two  circumstances,  there  is  a  loweri|;ig  of 
temperature,  and  also  a  change  from  liquid  to  solid. 

The  fourth  instance — the  volatilizing  of  solutions,  as  in 
boiling  down  sea-water — appears  to  fail  in  the  matter  of  cool- 
ing, but  still  contains  the  circumstance  of  prior  liquidity  ;  the 
prominent  fact  is  that  the  solvent  is  driven  off",  and  the  dis- 
solved substance  thereby  compelled  to  resume  the  solid  state. 

The  fifth  instance — the  deposition  of  solids  at  once  from 
the  gaseous  state,  as  in  the  case  of  iodine — seems  to  eUminate 
prior  liquidity.  We  must  then  shift  the  ground,  and,  for 
liquidity,  substitute  one  of  the  two  higher  states  of  matter. 

The  sixth  instance  is  *  heavy  and  long  continued  pressure 
upon  an  amorphous  substance  ;  '  principally  shown  in  geology. 
This  would  eliminate  the  prior  liquid  or  gaseous  condition,  and 
bring  to  view  the  forced  approximation  of  the  constituent 
particles  of  bodies.  But  the  same  circumstance  accompanies 
all  the  previous  cases,  being  merely  a  different  expression  of 
what  is  common  to  them.  We  know  heat  as  forcibly  enlarg- 
ing the  bulk  of  bodies — making  their  particles  mutually  re- 
pellent ;  the  withdrawal  of  this  force  leaves  the  attractions  of 
the  particles  free  to  operate. 

The  seventh  instance — slow  geological  transformation — 
unless  viewed  by  the  light  of  the  circumstance  just  named,  is 
difficult  to  interpret.  It  is  not,  however,  incompatible  with 
the  predominance  of  the  molecular  attractive  forces  by  the 
abatement  of  the  repellent  forces. 

The  eighth  instance — change  of  metals  from  the  toagh  to 
the  brittle  state — is  a  true  case  of  crystallization ;  brittle - 
ness  is  accompanied  with  an  imperfect  crystalline  arrangement. 
The  effect  is  produced  by  cooling  after  hammering  ;  by  re- 


286 


THE  EXPEfilMENTAL  METHODS. 


COGENCY  OF  AGREEMENT. 


287 


peated  heating  and  cooling ;  hy  long-continued  vibration  or 
concussion  : — all  which  influences  tend  to  expel  the  structural 
heat  of  the  substance ;  the  consequence  being  that  the  mole- 
cular attraction  is  more  preponderant. 

We  have  thus  eliminated  Cooling,  Deposition  from  Solution, 
and  Prior  Liquidity ;  and  have  found  but  one  uniform  antece- 
dent— the  increased  scope  and  operation  of  the  molecular  or 
solid-forming  cohesion ;  to  which  point,  however,  these  other 
circumstances  really  tend  ;  they  are  all  of  them  remoter  ante- 
cedents of  the  one  constant  antecedent.  The  examination  of 
the  instances  has  enabled  us  to  generalize  the  phenomenon,  as 
well  as  to  establish  the  generality  upon  evidence,  namely,  the 
evidence  of  Agreement. 

As  we  have  stated  this  enquiry,  it  is  a  clear  case  of  Cause 
and  Efl^ect.  We  have  sought  the  antecedent  circumstances 
whereby  a  body  in  an  amorphous  or  uncrystallized  state  be- 
comes crystallized  ;  and  we  find  that  there  is  an  expenditure 
and  re-distribution  of  power  or  energy.  The  result  of  the  ex- 
penditure is  not  an  active  manifestation,  as  when  we  produced 
mechanical  force,  or  heat ;  it  is  an  arrangement,  or  structural 
collocation ;  a  case  already  contemplated  (p.  265)  among  the 
results  of  expended  force. 

Sixth  Example.  Let  us  next  apply  the  method  to  eliminate 
the  cause,  or  the  antecedent  conditions  essential  to  the  pro- 
duction and  maintenance,  of  Light. 

Now,  the  most  constant  circumstance  is  a  high  temperature  / 
.  solid  bodies  become  luminous  at  a  temperature  of  from  980° 
to  1000°  Fahrenheit.  So  far,  there  is  a  remarkable  unanimity. 
It  is  found,  however,  that  gases  do  not  always  become  lumin- 
ous at  this  temperature,  nor  at  a  much  higher ;  a  current  of 
gas  may  be  raised  to  upwards  of  2000°  F.  without  being 
luminous ;  whence  we  conclude  that  the  state  of  the  body  is 
also  a  condition.  Again,  the  electric  spark  is  a  luminous 
effect,  which  would  give  the  disturbance  of  the  electric 
discharge  as  an  antecedent.  As  there  is  a  possibility,  however, 
that  the  great  violence  of  the  discharge  may  be  accompanied 
with  sudden  rise  of  temperature,  this  may  be  merely  another 
form  of  heat.  We  should  need  to  show,  by  varying  the 
instances,  that  high  temperature  is  not  essential  to  the  spark. 
In  the  next  place,  certain  substances  give  light  at  common 
temperatures,  to  which  fact  has  been  given  the  na^ne  phosphor- 
escence. Some  minerals,  gently  heated,  emit  a  feeble  light, 
which  soon  ceases,  and  cannot  be  renewed  until  the  body  has 
been  exposed  to  the  sun  or  th©  electric  spark.     This  is  still  a 


form  of  heat,  but  not  of  the  intense  degree  of  ordinary  b'ght. 
More  peculiar  still  is  animal  phosphorescence,  as  the  glow- 
worm, fire-fly,  and  certain  sea  animalcules.  Here  the  accom- 
paniment is  a  special  mode  of  vitality  hitherto  nneliminated, 
and  excluding  the  circumstance  of  high  temperature  (Mr. 
Herbert  Spencer  suggests  that  it  is  an  incident  attending 
oxidation).  Once  more,  a  faint  flash  of  light  occurs  with 
certain  substances  in  tJie  act  of  crystallizing. 

We  may  thus  collect  from  Agreement,  that  ignited  solids  at 
the  temperature  of  1000°  are  luminous,  and  that  an  electric 
discharge  ia  luminous ;  but  we  cannot  at  present  lay  down 
any  wider  generalization.  Excepting  the  very  general  fact  of 
molecular  disturbance  of  some  kind  or  other,  which  we  are 
unable  to  qualify  in  the  precise  mode  concerned  in  the  effect, 
our  comparison  of  instances  does  not  point  to  a  constant 
circumstance.  For  the  present,  we  regard  Light  as  having 
a  plurality  of  causes. 

As  farther  instances  of  Agreement,  we  may  quote  the  proof 
of  the  coincidence  of  Sleep  with  low  nervous  action,  which 
means  a  feeble  cerebral  circulation;  also,  the  connexion  of 
Memory  with  the  intensity  of  Present  Consciousness.  The 
uniformity  of  these  conjunctions  under  all  varieties  of  other 
conditions  is  the  evidence  afforded  by  Agreement.  The  Rela-  " 
tivity  of  Knowledge  is  established  partly  by  Agreement,  partly 
by  the-  method  of  Concomitant  Variations,  as  will  be  shown. 

The  cogency  of  Agreement  is  manifestly  in  proportion  to 
the  thoroughness  of  the  elimination.  Whatever  circumstance 
has  never  been  eliminated  is  a  possible  cause.  There  are  not 
a  few  instances,  as  in  the  action  of  drugs,  where  nature  does 
not  provide  the  variety  requisite  for  a  thorough  elimination. 
The  comphcacy  of  the  Natural  Kinds  passes  our  means  of 
extrication  by  Agreement  alone. 

METHOD   OF  DIFFERENCE. 

^  3.  Elimination  by  Diflference  is  expressed  in  the  follow-: 
mg  canon  : — If  an  instance  where  a  phenomenon  occurs, 
and  an  instance  where  it  does  not  occur,  have  every  cir- 
cumstance in  common  except  one,  that  one  occurring  only 
in  the  first  ;  the  circumstance  present  in  the  first  and 
absent  in  the  second,  is  the  cause,  or  a  part  of  the  cause, 
of  the  given  phenomenon. 

We  are  supposed  to  have  two  instances  and  only  two.    Eaoh 
is  a  complex  sequence,  a  group  of  antecedents  followed  by  a 


/.. 


t,(^\^^ 


288 


THE   EXPREIMENTAL  METHOUS. 


METHOD  OP  DIFFEBENCK. 


289 


^ronp  of  consequents.  The  two  complex  sequences  differ  by 
only  a  single  sequence,  present  in  the  one,  and  absent  in  the 
other.  Thus  the  sequence  A  B  C  D  gives  a  b  c  d^  and  BCD 
gives  bed:  the  only  difference  being  the  presence  of  A  in  the 
antecedent,  and  of  a  in  the  consequent,  of  one  sequence,  and 
the  absence  of  these  in  the  other  sequence.  Supposing  A  B  C  D 
changed  into  B  C  D,  by  the  loss  of  A ;  while  at  the  mom- 
ent abed  is  changed  into  b  o  dhj  the  loss  of  a ;  we  have 
a  proof  of  the  connexion  of  A  with  a.  Indeed,  the  assertions 
are  identical ;  to  say  that  the  disappearance  of  one  thing  is 
followed  by  the  disappearance  of  another  thing,  there  being  no 
other  change,  is  merely  a  way  of  expressing  causal  connexion. 

Difference  plays  a  great  part  in  onr  everyday  inferences. 
The  usual  form  is  the  sudden  introduction  of  some  limited  and 
definite  agency  or  change,  followed  by  an  equally  definite  con- 
sequence. When  the  drinking  of  water  is  followed  at  once  by 
the  cessation  of  thirst,  we  do  not  hesitate  to  pronounce  the  one 
fact  the  cause  of  the  other.  The  human  system  is  a  great 
complication,  but  the  only  difference  made  upon  it  in  two 
successive  minutes  is  the  sequence  of  drinking  and  the  satisfy- 
ing of  thirst ;  there  has  been,  we  presume,  no  time  for  any 
other  change  to  manifest  itself.  So  when  we  waken  a  sleeper 
by  a  noise,  or  strike  a  light  by  the  friction  of  a  match,  we 
infer  causation ;  the  new  agency  being  instantaneously  fol- 
lowed by  the  new  effect. 

The  first  example  given,  under  Agreement,  is  also  proved  by 
Difference.  That  Heat  is  the  cause  of  the  melting  of  ice,  of 
wax,  or  of  lead,  is  proved  by  making,  upon  these  substances, 
the  one  change  of  raising  the  temperature.  Being  quite  sure 
that  in  the  conversion  of  ice  into  water,  no  change  has  been 
made  except  this,  we  have  a  conclusive  experiment  of  Differ- 
ence to  show  that  heat  is  the  cause. 

The  same  substance  in  two  states,  as  solid  and  liquid,  or  as 
amorphous  and  crystallized,  enables  us  to  ascertain  what  effects 
are  due  to  change  of  state.  Thus  charcoal,  uncrystallized,  is 
black,  opaque,  and  a  conductor  of  electricity  ;  as  crystallized, 
in  the  Diamond,  it  is  transparent  and  a  non-conductor. 

A  large  part  of  our  knowledge  of  nature  and  of  living  beings 
is  gained  by  making  experimental  changes  and  watching  the 
consequences.  Onr  proof  is  the  immediate  result.  An  im- 
mediate response  is  satisfactory  evidence  in  almost  any  de- 
partment. Thus,  in  medicine,  there  is  little  doubt  as  to  the 
operative  force  of  purgatives,  emetics,  sudorifics,  diuretics, 
narcotics,  stimulants,  irritants;    the  uncertainty  attaches  to 


alteratives,  tonics,  and  the  protracted  treatment  of  chronic 
cases.  The  effect  of  quinine,  in  ague,  is  established  beyond 
dispute. 

Whether  it  be  to  add,  or  to  withdraw,  a  definite  agent,  a 
change  instantly  following  is  proved  to  be  an  effect.  Even  in 
politics,  we  may  have  a  proof  from  difference ;  as  in  the 
accession  or  resignation  of  a  minister,  like  Chatham,  ^o 
other  circumstances  arising  in  the  ordinary  course  of  a  year 
would  make  that  total  change  in  the  course  of  politics  that 
followed  on  Chatham's  becoming  minister.  It  could  not  be 
denied  that  he  was  the  cause  (in  the  practical  sense  of  cause) 
of  our  successes  in  America,  and  on  the  continent  of  Europe. 
The  consequences  of  his  retirement  were  equally  decided  as 
proving,  on  the  method  of  Difference,  the  vast  superiority  of 
his  powers  as  an  administrator. 

Wherever  Difference  can  be  resorted  to,  the  knowledge  of 
causes  is  gained  at  once.  In  ordinary  cases,  the  method  is  so 
obvious  in  its  application,  so  satisfactory  and  conclusive,  as 
scarcely  to  need  a  master  to  explain  or  enforce  it.  The  special 
discipline  of  Logic,  so  far  as  this  method  is  concerned,  lies  in 
showing  the  precautions  requisite  in  the  more  complicated 
cases. 

In  Physiology,  the  functions  of  the  nerves  were  ascertained 
by  the  experiment  of  dividing  each  in  turn,  and  watching  the 
effect.  Whatever  function  is  immediately  arrested  on  the 
division  of  a  nerve,  is  shown  to  be  due  to  that  nerve,  or  to 
require  that  nerve  in  order  to  its  performance.  Such  experi- 
ments, however,  do  not  exhibit  the  entire  circle  of  conditions 
involved  in  the  function  in  question.  We  know  that  the 
integrity  of  the  spinal  cord  is  necessary  to  sensation  and  to 
movement  in  the  trunk  and  in  the  extremities  of  the  body; 
we  do  not  exhaustively  know  what  else  is  necessary.  For  this 
more  extensive  knowledge  we  should  have  to  multiply  experi- 
ments  all  through  the  brain.  If  the  destruction  of  any  part 
interferes  with  these  functions,  that  part  enters  into  the 
causal  conditions ;  if  otherwise,  it  does  not  enter  into  those 
conditions. 

The  extension  of  this  class  of  experiments  to  the  brain 
exemplifies  one  situation  where  the  method  of  Difference  may 
be  indecisive.  Deep  incisions  in  the  brain,  intended  to  affect 
one  single  organ,  as  the  cerebellum,  may  injure  adjoining 
organs  ;  and  may  therefore  be  inconclusive  as  to  the  functions 
of  the  special  organ  in  view.  It  is  on  this  ground  that 
Brown- Sequard  objects  to  the  views  of  Flourens  regardino-  the 


290 


THE  EXPERIMENTAL  METHODS. 


JOINT  METHOD. 


291 


function  of  the  cerebellum.  The  one  certain  inference  in  such 
cases  is,  that  whatever  function  survives,  in  its  integrity,  the 
destruction  of  an  organ,  cannot  be  exclusively  due  to  that 
organ.  The  obverse  inference  is  certain  only  on  the  supposi- 
tion that  the  injury  has  been  confined  to  the  part  affected. 

With  reference  to  the  connexion  of  scarlet  bloom  with 
absence  of  odour,  we  have  a  seeming  case  of  Difference  in 
comparing  such  varieties  as  the  white-flowering  and  the  red- 
flowering  hawthorn  :  the  one  fragrant,  the  other  not.  In  the 
complicacy  of  Kinds,  we  can  seldom  be  sure  that  a  variation 
is  rigidly  confined  to  the  circumstances  that  are  apparent. 
Moreover,  where  there  is  not  a  clear  case  of  Causation,  Differ- 
ence is  insufficient  to  prove  a  coincidence. 

Sir  G.  C.  Lewis  lays  it  down  as  essential  to  the  validity  of 
a  proof  by  Difference,  that   we  should  know,  by  a  previous 
induction,  the  general  adequacy  of  the  assigned  cause  to  the 
production  of  the  effect.     When  we  infer  that  a  man,  shot 
through  the  heart,  drops  down  dead,  we  need  to  know,  he 
thinks,  that,  as  a  p^eneral  rule,  a  gunshot  wound  in  the  heart, 
is  a  cause  of  death.     To  this  remark  the  reply  is,  that  practi- 
cally we  do  make  use  of  such  previous  knowledge,  but  it  is 
not  essential  to  the  method  of  Dificrence.     Provided  we  are 
quite  sure  that  the  new  agent  is  the  only  change  that  has 
preceded  the  effect,  the  instance  is  conclusive,  on  the  Law  of 
Causation  solely.     The  use  of  a  more  specific  induction  is  to 
supply  the  defect  of  certainty  in  the  instance  itself.     There 
may  be  other   unseen  agencies  at  work,  as  well  as  the  one 
supposed,  and  this  is  the  only  ground  either  for  invoking  a 
general   presumption,   or   for   multiplying    instances   of    the 
phenomenon.      In  practice,  we  seek  both  for  presumptions 
(from  prior  inductions)  and  for  repetition  of  instances  ;    but 
an  ideally  perfect  instance  of  Difference,  in  a  case  of  Causation, 
is  conclusive  in  itself. 

Agreement  and  Difference  can  be  easily  compared  as  to  their 
respective  advantages  and  disadvantages.  Agreement  needs 
a  large  number  of  instances,  but  their  character  is  not  re- 
stricted. Any  instance  that  omits  a  single  antecedent  contri- 
butes to  the  result ;  the  repetition  of  the  same  instance  is  of  use 
only  as  giving  means  of  selection.  Difference  requires  only 
one  instance ;  but  that  one  is  peculiar,  and  rarely  to  be  found. 

A  great  extension  is  given  to  the  power  of  Agreement,  by 
extending  it  to  agreement  in  ahsence.     When  such  cases  are 


conjoined  with  those  where  the  agreement  is  in  presejice,  there 
is  an  approach  to  the  conclusiveness  of  the  method  of  Differ- 
ence. This  double  employment  of  the  method  of  Agreement 
is  brought  forward  by  Mr.  Mill  under  the  designations — the 
*  Joint  Method  of  Agreement  and  Difference,'  and  the  *  Indirect 
Method  of  Difference.'  It  might  also  be  called  the  *  Method 
of  Double  Agreement.' 

JOINT   METHOD. 

4  The  canon  of  this  Method  is : — If  two  or  more  in- 
stances where  the  phenomenon  occurs  have  only  one  cir- 
cumstance in  common,  while  two  or  more  instances  where 
it  does  not  occur  have  nothing  in  common  save  the  absence 
of  that  one  circumstance  ;  the  circumstance  wherein  alone 
the  two  sets  of  instances  differ,  is  the  effect,  or  the  cause, 
or  a  necessary  part  of  the  cause  of  the  phenomenon. 

If  we  require  to  ascertain,  under  this  method,  that  A  is 
the  cause  of  a,  or  a  the  effect  of  A,  we  add,  to  the  instances  of 
uniform  presence  of  A  and  a,  other  instances  of  uniform 
absence,  as  B  F  G  followed  by  6 / ^,  C  H  I  followed  hj  c  hi, 
and  so  on.  If  we  have  never  discovered  A  wanting  as  an 
antecedent  without  having  a  absent  as  a  consequent,  there  is 
a  strong  additional  presumption  that  A  and  a  are  united  as 
cause  and  effect — a  presumption  that  may  approach  to  the 
certainty  of  the  method  of  Difference. 

It  is  a  confirmation  of  the  cause,  suggested  by  Agreement, 
of  the  noxiousness  of  the  North-East  wind,  that  the  South- 
West  wind,  the  genial  and  wholesome  current,  is  wanting  in 
the  circumstance  assigned.  It  descends  upon  us  from  the 
eleyated  regions  of  the  atmosphere,  where  impurities  are 
highly  diluted  by  dissemination. 

Again,  to  revert  to  the  example  of  Crystallization.  Let  us 
review  the  non- crystallized  solids,  and  note  the  mode  of 
their  formation.  The  amorphous  stones  and  rocks,  as  sand- 
stone, chalk,  &c.,  are  known  to  be  sedimentary  deposits  from 
water.  Before  being  solidified,  they  existed  as  solid  particles ; 
they  were  not  dissolved  in  water,  neither  did  they  exist  in  a 
molten  condition.  This  Agreement  in  absence  would  confirm 
the  inference  from  Agreement  in  presence — that  (so  far  as 
certain  instances  went)  crystals  existed  in  a  previous  higher 
condition.  But  the  general  inference,  from  the  full  compari- 
son of  examples,  was  the  superior  play  given  to  the  molecular 
attraction  by  counterworking  the  molecular  repulsion.    Now, 


/ 


292 


THE  EXPERIMENTAL  METHODa 


fi 


this  general  fact  is  absent  from  all  mere  sedimentary  deposits; 
these  bodies  have  no  aid,  in  the  shape  of  loss  of  heat  or  other 
cause,  to  their  molecular  attractions. 

The  comparison  of  the  amorphous  rocks  yields  another 
circumstance,  namely,  the  irregular  mixture  of  different  sub- 
stances. For,  although  in  a  mud  sediment  silica  or  alumina 
may  prevail,  neither  is  ever  pure  ;  and  the  mixture  of  different 
elements  is  a  bar  to  crystallization,  unless  they  are  of  the 
kind  called  isomeric  (from  crystallizing  alike).  There  is  more 
to  be  got  over  in  crystallizing  compounds  of  unlike  elements, 
and  the  crystals  must  be  deficient  in  regularity. 

Another  un crystallized  class  comprizes  the  vegetable  and 
animal  tissues.  In  their  case,  however,  the  antecedent  circum- 
stances are  too  complicated  and  obscure  to  furnish  insight; 
they  rather  stand  in  want  of  illustration  by  the  parallel  lights 
of  more  obvious  cases.  Besides,  there  is  in  them  a  method 
and  order  of  aggregation  more  analogous  to  the  crystallized, 
than  to  the  amorphous  solids. 

A  third  class  includes  the  Colloids,  or  glue-bodies,  of 
Graham  (represented  by  gum,  starch,  gelatin,  albumen,  tannin, 
caramel).  They  are  not  confined  to  the  viscid  form  of  glue, 
but  include  compact  solids,  as  flint.  The  points  of  contrast 
between  these  and  crystallized  bodies  are  numerous  and 
important.  Their  mode  of  formation  is  various ;  many  of 
them  are  the  products  of  living  bodies,  and  therefore  share  in 
the  complication  of  living  growth.  Flint  is  an  aggregate  of 
particles  of  silica,  which  particles  were  originally  the  shells  of 
animals,  and  therefore  also  organic  in  their  formation.  In 
this  case,  the  molecular  atti*action  of  silica,  in  its  progress 
towards  crystallization,  is  thwarted  by  the  pre-existing  forms 
of  the  silicious  particles. 

It  would  require  too  long  a  discussion  to  show  the  bearing 
of  the  colloid  peculiarities  on  the  question  as  to  the  antece- 
dents of  the  crystalline  formation.  Enough  has  been  given  to 
show  the  working  of  the  method  of  Obverse  Agreement. 

METHOD    OF  CONCOMITANT  VAllIATIONS. 

6.  Canon  of  the  Method:  —  Whatever  phenomenon 
varies  in  any  manner  whenever  another  phenomenon 
varies  in  some  particular  manner,  is  either  a  cause  or  an 
effect  of  that  phenomenon,  or  is  connected  with  it  through 
some  bond  of  concomitance. 

Thp  effects  of  Heat  are  known  only  through  proportionate 


CONCOMITANT  VARIATIONS. 


293 


variation.  We  cannot  deprive  a  body  of  all  its  heat ;  the 
nature  of  the  agency  forbids  us.  But,  by  making  changes  in 
the  amount,  we  ascertain  concomitant  changes  in  the  accom- 
panying circumstances,  and  so  can  establish  cause  and  effect. 
It  is  thus  that  we  arrive  at  the  law  of  the  expansion  of  bodies 
by  heat.  In  the  same  way,  we  prove  the  equivalence  of  Heat 
and  Mechanical  Force  as  a  branch  of  the  great  law  of  Con- 
servation or  Persistence  of  Force. 

The  proof  of  the  First  Law  of  Motion,  as  given  by  Newton, 
assumed  the  form  of  Concomitant  Variations.  On  the  earth, 
there  is  no  instance  of  motion  persisting  indefinitely.  In 
proportion,  however,  as  the  known  obstructions  to  motion — 
friction  and  resistance  of  the  air — are  abated,  the  motion  of  a 
body  is  prolonged.  A  wheel  spinning  in  an  exhausted  receiver 
upon  a  smooth  axle  runs  a  very  long  tirae^  In  Borda's  experi- 
ment with  the  pendulum,  the  swing  was  prolonged  to  more 
than  thirty  hours,  by  diminishing  friction  and  exhausting  the 
air.  Now,  comparing  the  whole  series  of  cases,  from  speedy 
exhaustion  of  movement  to  prolonged  continuance,  we  find 
that  there  is  a  strict  concomitance  between  the  degree  of 
obstruction  and  the  arrest ;  we  hence  infer  that  if  obstruction 
were  entirely  absent,  motion  would  be  perpetual. 

The  celebrated  experiment  of  carrying  the  barometer  to  the 
top  of  Puy  de  Dome  was  a  proof  by  variation  of  the  connexion 
between  the  pressure  of  the  air  and  the  rise  of  the  mercury. 

By  Concomitant  Variations,  we  derive  one  of  the  proofs  of 
the  connexion  between  the  brain  and  the  mind.  In  the  same 
manner,  we  learn  to  associate  health  with  the  healthy  agencies, 
and  diseases  with  noxious  agencies. 

The  doctrine  that  change  of  impression  is  an  essential  con- 
dition of  consciousness,  from  which  proceeds  the  theory  of 
Relativity  as  applied  to  feeling  and  to  knowledge,  is  most 
strikingly  attested  by  Concomitant  Variations.  The  intensity 
of  a  mental  impression  notably  varies  according  to  the  greatness 
of  the  transition  from  one  state  to  another :  witness  the  in- 
fluence of  novelty,  of  all  great  changes  of  circumstances,  of 
(Suddenness  and  surprise. 

The  Statistics  of  Crime,  reveal  causes  by  the  method  of 
Variations.  When  we  find  crimes  diminishing  according  as 
labour  is  abundant,  according  as  habits  of  sobriety  have  in- 
creased, according  to  the  multiplication  of  the  means  of 
detection,  or  according  to  the  system  of  punishments,  we  may 
presume  a  causal  connexion,  in  circumstances  not  admitting 
of  the  method  of  Difference. 


< 


294 


THE   EXPERIMEJSTAL  METHODS. 


The  Concomitance  may  be  inverse.  Thus  we  find  that  the 
tendency  to  chemical  action  between  two  substances  increases 
as  their  cohesion  is  diminished,  being  much  greater  between 
liquids  than  between  solids.  So,  the  greater  the  elevation  of 
the  land,  the  less  the  temperature,  and  the  more  scanty  the 
vegetation.  -^ 

Parallel  Variation  is  sometimes  interrupted  by  critical 
pomts,  as  in  the  expansion  of  bodies  by  heat,  which  suffers  a 
reverse  near  the  point  of  freezing.  Again,  the  energy  of  a  solu- 
tion does  not  always  follow  the  strength  ;  very  dilute  solutions 
occasionally  exercise  a  specific  power,  not  possessed  in  any 
degree  by  stronger.  So,  in  the  animal  body,  food  and  stimu- 
lants  operate  proportionally  up  to  a  certain  point,  at  which 
their  farther  operation  is  checked  by  the  peculiarities  in  the 
structure  of  the  living  organs. 

The  properties  of  highly  rarefied  gases  do  not  exhibit  an 
exact  continuity  of  the  phenomena  that  vary  with  density.  In 
a  perfect  vacuum  there  is  no  electrical  discharge;  but  the 
variations  of  the  discharge,  in  highly  rarefied  air,  do  not  pro- 
ce^in  exact  accordance  with  the  degree  of.  rarefaction. 

We  cannot  always  reason  from  a  few  steps  in  a  series  to  the 
whole  series,  partly  because  of  the  occurrence  of  critical  points, 
and  partly  from  the  development  at  the  extremes  of  new  and 
nnsuspected  powers.  Sir  John  Herschel  remarks,  that  until 
very  recently  the  formulaa  empirically  deduced  for  the  elas- 
ticity  of  steam,  those  for  the  resistance  of  fluids,  and  on  other 
similar  subjects,  have  almost  invariably  failed  to  support  the 
theoretical  structures  that  have  been  erected  upon  them.' 

The  method  of  Concomitant  Variations  is  powerful  in 
suggesting,  as  well  as  eflicacious  in  proving,  causal  connexions, 
ihe  mmd  is  apt  to  be  aroused  to  the  bond  between  two 
circumstances  by  encountering  several  conjunctions  of  the 
two  m  unequal  degrees.  Very  often,  we  are  not  alive  to  a 
connexion  of  cause  and  effect  till  an  unusual  manifestation  of 
the  one  is  accompanied  with  an  unusual  manifestation  of  the 
other.  We  may  be  using  some  hurtful  article  of  food  for  a 
len^h  of  time  unknowingly ;  the  discovery  is  made  by  an 
accidental  increase  of  quantity  occurring  with  an  aggravation 
of  some  painful  sensation.     This  is  one  form  of  the  efficacy  of 

Aetoric'*^'"^  '    ^"^  ^^''^''^  ^^^*  ^""^^  '"^  ^'''^''''^   ^^  ^ 

A  remarkable  case  of  Concomitant  Variations  is  furnished  by 

the  discovery  of  a  connexion  between  the  solar  spots  and  the 

positions  of  the  planets.     Thus,  as  regards  Venus,  *  spots  are 


CONTINUOUS  COMPARISON. 


295 


nearest  to  the  solar  equator  when  the  heliographical  latitude 
ot  Venus  is  0°,'  and  obversely. 

An  important  device  for  discovering,  and  also  for  provino- 
laws  of  causation,  consists  in  arranging  things  possessino- ''a 
common  property  in  a  serial  order,  according  to  the  deo-ree  of 
lu'  PI,^P^^*^7-      Thus,  we  may  arrange  bodies   accordm?  to 
their  iransparency  or  Opacity,  according  to  Specific  Gravity, 
to  Conduction  of  Heat  and  Electricity,  and  so  on.     We  are 
then  m  a  position  to  detect  any  corresponding   increase  in 
some  accompanying  property,  and  thereby  to  establish  a  law  of 
concomitance  or  causation.      This  method  is  designated,  by 
^""'^"H'  p^^/^fication  by  Series,  and  by  Sir  G.  C.  Lewis, 
the  Method  of  Continuous  Comparison.    The  progress  of  Life 
m  the  animal  scale ;    the  progress  of  mental  development  in 
human    bemgs ;    the    progress   of    civilized    institutions,  as 
Government,  Judicature,  the  Representative  System,— may  be 
expressed  m  a  series,  so  as  to  trace  concomitant  variations. 

It  is  greatly  to  be  desired  that,  in  Physical  Science,  all  the 
substances  in  Nature  should  be  set  forth  in  distinct  tabula- 
tions, according  to  the  degree  of  every  important  property. 
It  was  when  transparent  bodies  were  arranged  in  the  order  of 
their  refracting  power,  that  the  connexion  was  discovered 
between  high  refracting  power  and  combustibility. 

METHOD   OF  RESIDUES. 

6.   The   canon   of  Eesidues   is  :~  Subduct   from  any" 
phenomenon  such  part  as  previous  induction  has  shown 
to  be  the  effect  of  certain  antecedents,  and  the  residue  of 
the  phenomenon  is  the  effect  of  the  remaiiling  antecedents. 

After  a  certain  progress  is  made  in  the  inductive  determina- 
tion of  Causes,  new  problems  are  greatly  simplified  by  sub- 
ducting from  a  complex  sequence,  the  influence  of  known 
causes.  Sometimes  this  of  itself  may  amount  to  a  complete 
ehmmation  Such  procedure  is  styled  the  Method  of  Residues. 
It  IS  an  instrument  of  Discovery  as  well  as  of  Proof. 

The  method  is  symbolically  illustrated  thus  .—  Suppose  the 
antecedents  ABC  followed  by  the  consequents  abc;  and 
that  by  previous  inductions,  we  have  ascertained  that  B  gives 
6,  and  C  gives  c.  Then  by  subtraction,  we  find  A  to  be  the 
cause  of  a.  The  operation  is  substantially  the  method  of  Dif- 
ference, and  has  all  the  decisiveness  belonging  to  that  method 

Sir  John  Herschel  was  the  first  to  show  the  importance  of 
studying  residual  phenomena.     His  examples  are  very  strik- 


296 


THE  EXPERIMENTAL   METHODS. 


ing  (Introduction  to  Natural  Philosophy,  p.  156).  Thus, 
the  retardation  of  the  comet  of  Encke  has  been  the  means  of 
suggesting,  and  may  ultimately  suffice  to  prove,  the  existence 
of  a  resisting  medium  diffused  throughout  space.  Again,  the 
observation  of  Arago — that  a  magnetic  needle,  set  a  vibrating, 
is  sooner  brought  to  rest  when  suspended  over  a  plate  of  copper 
— was  the  first  clue  to  the  discovery  of  Magneto-Electricity. 

The  anomalies  in  the  motion  of  Uranus  led  Adams  and  Le 
Verrier  to  the  discovery  of  Neptune. 

The  study  of  the  electrical  odour  was  the  first  step  to  the 
discovery  of  the  remarkable  substance — Ozone. 

Sir  G.  C.  Lewis  remarks  that  *  the  unforeseen  effects  of 
changes  in  legislation,  or  of  improvements  in  the  useful  arts, 
may  often  be  discerned  by  the  Method  of  Residues.  In 
comparing  statistical  accounts,  for  example,  or  other  registers 
of  facts,  for  a  series  of  years,  we  perceive  at  a  certain  period 
an  altered  state  of  circumstances,  which  is  unexplained  by  the 
ordinary  course  of  events,  but  which  must  have  some  cause. 
For  this  residuary  'phenomenon,  we  seek  an  explanation  until  it 
is  furnished  by  the  incidental  operation  of  some  collateral 
cause.  For  example,  on  comparing  the  accounts  of  live  cattle 
and  sheep  annually  sold  in  Smithfield  market  for  some  years 
past,  it  appears  that  there  is  a  large  increase  in  cattle,  while 
the  sheep  are  nearly  stationary.  The  consumption  of  meat  in 
London  may  be  presumed  to  have  increased,  at  least  in  pro- 
portion to  the  increase  of  its  population;  and  there  is  no 
reason  for  supposing  that  the  consumption  of  beef  has  increased 
faster  than  that  of  mutton.  There  is,  therefore,  a  residuary 
phenomenon,  viz.,  the  stationary  numbers  of  the  sheep  sold 
in  Smithfield— for  which  we  have  to  find  a  cause.  This  cause 
is  the  increased  transport  of  dead  meat  to  the  metropolis, 
owing  to  steam  navigation  and  railways,  and  the  greater 
convenience  of  sending  mutton  than  beef  in  a  slaughtered 

state.* 

The  question  as  to  the  existence  of  a  special  force  of  Vitality — 
the  vital  force,  or  the  vital  principle— takes  the  form  of  an 
enquiry  into  a  residuum.  We  have  first  to  make  allowance 
for  the  operation  of  all  the  known  forces  of  inorganic  matter  ; 
and  when  these  have  been  exhaustively  computed,  the  re- 
mainder may  be  set  down  to  a  special  influence,  or  vital 
principle.  For  anything  we  know  at  present,  the  inoryanio 
forces,  operating  in  the  special  collocations  of  organized  bodies, 
may  be  competent  to  produce  all  the  observed  effects. 

The   only  proof    of    an  exhaustive   Analysis,  whether  in 


PROOF   OF  AN   ANALYSIS  BY   RESIDUES. 


297 


material  actions  or  in  mental  processes,  is  there  being  nothing 
left.  Thus,  in  the  Human  Mind,  it  is  disputed  whether  there 
be  a  separate  and  unique  faculty,  called  the  Moral  Faculty,  or 
the  Moral  Sense.  Now,  there  can  be  no  doubt  as  to  the 
presence  of  common  elements  of  Feeling,  Will,  and  Thought,  in 
our  moral  judgments  and  actions  ;  as,  in  the  case  of  the  vital 
principle,  the  question  is,  what  remains,  when  these  are  all 
allowed  for.  The  same  application  of  the  Method  of  Residues 
occurs  in  the  controversy  as  to  Instincts,  and  Innate  Ideas ; 
does  Experience,  concurring  with  the  usually  admitted  Intel- 
lectual Powers,  account  for  the  whole  of  the  facts  ? 


CHAPTER  YIL 

EXAMPLES  OF  THE  METHODa 

The  Experimental  Methods  have  been  regarded  mainly  as 
instruments  of  Elimination  and  Proof,  or  of  separating  irrele- 
vant accompaniments  from  causal  accompaniments.  In  their 
working,  however,  they  unavoidably  lead  to  inductive  generali- 
zations, in  which  aspect  they  are  methods  of  Discovery.  Ibe 
same  search  for  instances,  the  same  comparison  of  them  when 
found,  both  conduct  us  to  new  principles  or  laws,  and  prove 
them  when  once  attained.  Still,  it  was  rot  desirable  to  keep 
up  the  double  illustration  throughout.  In  the  miscellaneous 
examples  that  are  to  follow,  occasional  allusion  will  be  made 
to  the  procedure  suited  to  the  discovery  of  generahties. 

The  proofs  adduced  to  show  that  the  mode  of  action,  in 
Smelling,  is  Oxidation,  may  be  quoted  in  illustration  of  the 
Methods.  The  phenomenon  is  one  of  great  interest,  and  ot 
some  perplexity.    The  following  important  facts  were  mdicated 

by  Graham.  ^  ,  .x,      tx. 

The  sweet  odours  are  due  to  hydro-carbons,  as  the  ethers, 
alcohol,  and  the  aromatic  perfumes.  Now,  all  these  substances 
are  highly  oxidizable  at  common  temperatures,  being  speedily 
decomposed  in  the  air.  Again,  sulphuretted  bydrogen,  the 
most  familiar  of  malodorous  substances,  is  readily  oxidized, 
and  is  destroyed  in  that  manner.  These  are  instances  of 
Agreement  (in  presence). 


i 


298 


EXAMPLES   OF  THE  EXPERIMENTAL   METHODS. 


RESEARCH   ON  DEW. 


299 


A  farther  instance  of  Agreement  is  shown  in  the  decomposi- 
tion of  hydrogen  compounds,  in  the  act  of  causing  smell. 
When  a  small  quantity  of  seleniuretted  hydrogen  is  inhaled 
by  the  nose,  the  metallic  selenium  is  found  reduced  upon  the 
lining  membrane  of  the  cavities.  The  sensation  is  an  intensely 
bad  smell. 

A  remarkable  case  of  Agreement  in  Absence  is  furnished  by 
the  marsh  gas — carburetted  hydrogen.  This  gas  has  no  smell. 
As  the  proof  of  the  concurring  absence  of  its  oxidation  at  com- 
mon temperatures,  Graham  obtained  it  from  the  deep  mines 
where  it  existed,  for  geological  ages,  in  contact  with  oxygen. 
Again,  hydrogen  itself,  if  obtained  in  purity,  has  no  smell ;  and 
it  does  not  combine  with  oxygen  at  the  usual  temperature  of 
the  air. 

An  instance  approaching  to  Difference  is  the  following.  If 
oxygen  is  excluded  from  the  cavities  of  the  nose,  there  is  no 
smell.  Also,  a  current  of  carbonic  acid  arrests  the  odour  ;  an 
influence  which  may  (although  not  with  absolute  certainty) 
be  supposed  hostile  to  oxidation; 

To  make  the  evidence  complete,  it  is  requisite  that  all  the 
instances  of  the  effect  should  be  of  the  same  unvarying  tenor,  or 
that  there  should  be  no  exceptions.  Until  every  apparent  dis- 
crepancy is  reconciled,  the  facts  are  inconclusive.  A  seeming 
exception  is  the  pungency  of  ozone^  which  is  looked  upon  as  a 
more  active  form  of  oxygen.  Now  we  can  hardly  suppose  that 
ozone  combines  with  oxygen  ;  a  more  likely  supposition  is 
that,  by  its  superior  activity,  it  combines  with  the  nasal  mucus. 

The  research  into  the  cause  of  Dew  has  been  used  by  Sir 
John  Herschel,  and  again  by  Mr.  Mill,  as  a  happy  example  of 
experimental  elimination  involving  nearly  the  whole  of  the 
methods.  All  the  stages  of  this  inductive  determination  are 
highly  instructive. 

The  first  point  is  to  settle  precisely  the  phenomenon  to  be 
explained.  This  is  an  exercise  of  Definition,  and  can  never  be 
too  rigidly  attended  to.  There  is  some  danger,  in  the  present 
case,  of  confounding  the  effect  with  certain  other  effects  ;  and 
hence  the  expediency  of  defining  by  an  exhaustive  contrast. 
Well,  Dew  is  moisture ;  but  that  moisture  is  not  rain,  and  not 
fog  or  mist ;  it  is  moisture  spontaneously  appearing  on  the 
surface  of  bodies  when  there  is  no  visible  wetness  in  the  air. 
In  a  perfectly  clear  and  cloudless  night,  there  may  be  a  copious 
moisture  on  the  surface  of  the  ground,  and  this  moisture  is  the 
thing  to  be  accounted  for. 


Now,  the  problem  being  given  as  an  effect,  with  the  cause 
unknown,  we  cannot  make  experiments,  until  a  cause  is  sug- 
gested. This  is  a  pure  effort  of  Discovery,  preparatory  to  the 
application  of  the  methods  of  inductive  proof.  On  the  various 
occasions  when  dew  appears,  we  must  look  out  for  the  atten- 
dant circumstances,  with  a  view  to  their  successive  elimination. 
We  know,  for  example,  that  dew  appears  chiefly  at  night, 
which  would  suggest  some  of  the  circumstances  connected 
with  night- fall,  as  darkness,  cold,  and  any  of  the  concomitants 
of  these.  That  darkness  is  not  the  cause  could  be  shown  if 
either  dew  appears  before  sunset,  or  if  it  ever  fails  to  appear 
at  night.  As  the  last  alternative  is  very  frequent,  we  must, 
80  far  as  the  Experimental  Methods  are  concerned,  pronounce 
against  darkness.     There  would  then  remain  the  agency  of 

Cold. 

Farther,  in  this  preliminary  stage  of  looking  out  for  a  pos- 
sible cause,  we  need  not  confine  ourselves  to  the  actual  pheno- 
menon. In  the  conduct  of  the  research,  as  recorded,  much 
stress  was  laid  upon  the  reference  to  analogous  effects,  or  to 
other  cases  where  moisture  spontaneously  appears  on  surfaces, 
in  the  absence  of  visible  wet.  All  such  analogies  are  valuable 
for  suggestion  or  discovery,  in  the  first  instance,  and  for  proof 
afterwards.  They  are  these : — (1)  the  moisture  that  gathers 
on  cold  stone  or  metal  when  breathed  upon  ;  (2)  the  moisture 
on  the  outside  of  a  tumbler  of  spring  water  fresh  from  the 
well  in  hot  weather ;  (3)  the  moisture  that  often  appears  on 
glasses  when  brought  into  a  hot  room  full  of  people;  (4) 
what  appears  on  the  inside  of  windows  when  a  room  is 
crowded,  and  during  changes  in  the  outside  temperature  ;  (5) 
what  runs  down  our  walls,  especially  outer  passages,  when  a 
warm  moist  thaw  succeeds  to  frost.  AH  these  cases  correspond 
to  the  definition ;  and  their  comparison  is  likely  to  indicate 
some  circumstance  to  be  subjected  to  experimental  elimination. 
To  take  the  first  instance — the  breath  upon  a  cold  metallic  sur- 
face ;  the  wai-mth  of  the  air  and  the  coldness  of  the  surface 
are  obvious  accompaniments.  Some  of  the  others  would  sug- 
gest the  same  conjunction,  while  all  are  compatible  with  it. 
Now,  this  is  the  situation  already  suggested  by  the  original 
phenomenon,  the  dew  at  night-fall.  Consequently,  we  are  in 
a  position  to  proceed  experimentally  ;  we  can  tiy  the  cooling 
down  of  surfaces  under  variation  of  circumstances. 

An  easy  experiment  will  tell  us  whether  the  cooling  of  the 
surface  be  a  uniform  fact,  in  the  p'-oduction  of  dew.  Lay  a 
thermometer  on  the  dewed  graps,  hanging  another  in  the  air ; 


( 


h 


// 


800 


EXAMPLES  OF  THE  EXPERIMENTAL  METHODS. 


and  repeat  this  on  many  successive  nights.  The  actual  result 
is  that  whenever  a  surface  is  dewed,  it  is  colder  than  the  air 
around  it.  This  is  a  proof  from  Agreement ;  but  proofs  from 
Agreement,  unless  they  can  be  multiplied  through  all  nature, 
in  all  climes,  seasons,  and  situations,  will  not  of  themselves 
decide  either  causation,  or  universal  coincidence. 

By  varying  the  circumstances,  we  can  bring  to  bear  the 
other  methods.  We  may,  for  example,  try  Agreement  in 
Absence  ;  that  is,  make  the  same  appeal  to  experiment  in 
nights  where  there  is  no  dew  anywhere.  The  phenomenon, 
however,  would  be  found  to  evade  this  test ;  there  would  be 
cases  of  actual  cooling  of  surfaces  below  the  temperature  of 
the  air,  and  yet  without  dew.  Hence  the  necessity  of  a  dif- 
ferent course  of  proceeding. 

Observation  reveals  to  us  the  fact  that  on  the  same  night, 
and  in  the  same  spot,  some  surfaces  are  dewed,  and  others 
not.  This  holds  out  the  prospect  of  an  appeal  to  the  Method 
of  Difference.  On  the  surface  of  a  plate  of  glass,  there  may  be 
dew,  while  on  a  polished  metallic  surface,  there  is  none.  Unfor- 
tunately, however,  such  a  couple  is  not  suited  to  the  canon  of 
Difference.  The  points  of  diversity  between  glass  and  metal 
are  too  numerous  to  comply  with  the  stringent  requisite  of  that 
canon.     We  must,  therefore,  shift  our  ground  once  more. 

It  being  apparent  that  the  nature  of  the  material  enters 
into  the  effect,  let  us  expose  a  great  variety  of  different 
materials — metals,  glass,  stone,  wood,  cloth,  &c.  We  now 
find  that  there  is  a  scale  of  degree  ;  between  the  extremes  of 
no  dew  and  copious  dew,  there  is  a  gradation  of  amount.  The 
enquiry  then  arises,  is  there  any  other  property  of  these 
different  materials  varying  in  concomitance  with  their  being 
dewed  ?  Does  their  temperature  (which  is  the  clue  that  we 
are  going  upon)  change  in  exact  accordance  with  the  amount 
of  dew  ?  There  was  here  scope  for  a  direct  appeal  to  the 
thermometer.  We  have  not,  however,  to  record  the  issue  of 
such  an  appeal ;  the  history  of  the  research  pursues  another 
and  more  circuitous  route  for  arriving  at  the  conclusion.  It 
so  happened,  that  the  experiments,  begun  by  Sir  John  Leslie, 
upon  the  conduction  and  the  radiation  of  heat,  came  in  to  the 
aid  of  the  present  enquiry ;  and  the  use  made  of  these  is 
sufficiently  illustrative  of  the  canons  of  Elimination.  It 
appeared,  on  the  comparison  of  the  various  materials,  that  the 
rate  of  becoming  dewed  varies  inversely  with  the  conducting 
power  of  the  substance  ;  the  good  conductors — the  metals — 
are  not  dewed,  the  bad  conductors  are  dewed  according  to 


RESEARCH  ON  DEW. 


301 


their  badness  as  conductors.  This  is  the  method  of  Concomi- 
tant Variations ;  what  it  points  to  will  be  seen  presently. 

It  is  next  desired  to  ascertain  how  far  difference  of  surface 
operates,  material  being  the  same.  The  comparison  shows 
that  rough  surfaces  are  more  dewed  than  smooth,  and  black 
more  than  white.  Instead  of  the  direct  test  of  the  thermo- 
meter, the  appeal  here  also  is  to  Leslie's  experiments  on  the 
radiation  of  heat  from  surfaces  ;  those  surfaces  that  are  most 
dewed — rough  and  black — are  the  best  radiators  of  heat.  The 
interpretation  of  this  will  be  taken  with  the  foregoing. 

In  the  meantime,  make  another  variatiort,  namely,  for  texture; 
compare  the  compact  textures  of  metal,  stone,  wood,  velvet,  eider- 
down, cotton,  &c. ;  the  compact  bodies  are  little  dewed,  in  the 
comparison,  the  loose  bodies,  much.  Now,  as  regards  heat,  the 
loose  bodies  are  very  bad  conductors  ;  they  resist  the  passage 
of  heat  through  them,  and  are  therefore  chosen  as  clothing. 

Let  us  now  seek  the  interpretation  of  these  three  last  re- 
sults of  Concomitant  Variations.  The  first  and  third  relate  to 
bad  conduction  of  heat  as  a  concomitant,  the  second  to  good 
surface- radiation.  Now,  both  circumstances  point  to  one  re- 
sult, that  is,  surface  cooling,  in  a  cold  atmosphere.  A  surface 
is  cooled  down  by  a  cool  contact,  but  if  heat  is  rapidly  sup- 
plied from  within  (which  is  good  conduction)  the  lost  heat  is 
made  good,  and  the  fall  of  temperature  is  delayed,  until  the 
interior  has  cooled  also.  In  bad  conductors,  the  loss  is  not 
made  good  in  the  same  way,  and  the  surface  temperature  falls. 
Thus,  bad  conductors  sooner  become  superficially  cold,  in  a 
cold  atmosphere.  Next  as  to  Radiation.  The  explanation 
here  is  still  more  easy.  Good  radiation  is,  by  implication,  sur- 
face cooling  ;  bad  radiation,  as  from  a  polished  metal  surface, 
is  retention  of  surface  heat.  We  thus  come  round  to  the  con- 
clusion, which  a  series  of  trials  by  the  thermometer  would 
have  given  at  once,  namely,  that  surfaces  become  dewed  exactly 
as  they  fall  in  temperature.  To  all  appearance,  therefore,  we 
have  established  a  link  of  connexion  between  cooling  and  dew. 

The  appearance  is  not  the  reality.  There  is  still  outstand- 
ing the  fact  that  the  same  fall  of  surface  temperature  will  not 
always  bring  out  dew.  Neither  the  same  absolute  surface 
temperature,  nor  the  same  difference  between  the  surface 
temperature  and  the  air  temperature,  is  constantly  followed 
by  a  deposit  of  moisture.  We  have  here  obviously  a  residual 
circumstance,  whose  investigation  should  next  follow.  The 
instances  where  the  same  thermometric  difference  is  unattended 
with  dew  need  to  be  studied  by  exactly  the  same  routine  as 


W 


1-'. 


302 


EXAMPLES   OF  THE  EXPERIMENTAL  METHODS. 


sU 


has  now  been  followed.  We  mnst  look  oat  for  the  snggestion 
of  a  possible  agency ;  and  next  subject  that  to  experimental 
trial,  with  a  view  to  proof  or  disproof.  This  residuum  would 
have  given  rise  to  a  very  arduous  research  if  it  had  been  left  to 
experimental  determination.  The  difficulty  was  conquered  in 
another  wa3^  Already  (1799)  had  Dalton  published  his  theory 
of  Aqueous  Vapour,  or  the  Atmosphere  of  Steam,  which  was  the 
missing  link  in  the  explanation  of  Dew.  His  positions  were — 
that  the  aqueous  vapour  contained  in  the  atmosphere  is  vari- 
able in  amount,  according  to  circumstances,  and  that  the 
amount  is  limited  by  temperature.  To  each  degree  of  temper- 
ature corresponds  a  certain  amount,  which  is  the  saturation  of 
the  air  at  that  temperature.  An  amount  equal  to  one  inch  of 
mercury  is  sustained  at  80°,  half  an  inch,  at  59°.  Supposing 
the  air  saturated  at  any  one  moment,  a  fall  of  temperature 
will  lead  to  precipitation  as  visible  moisture  ;  but  as  the  air  is 
not  always  saturated,  a  fall  of  temperature  will  not  bring 
dew  or  mist,  unless  the  fall  extends  below  the  degree  corres- 
ponding to  saturation,  called  the  temperature  of  the  Dew- 
point.  This  is  the  residual  circumstance,  the  thing  wanted  to 
complete  the  proof  of  the  connexion  of  d&w  with  surface  cold- 
ness. 

The  present  instance  is  a  case  of  Cause  and  Effect ;  as  may 
be  shown  in  various  ways.  In  the  way  that  the  case  has  been 
stated,  there  is  not  apparent  any  transfer  of  energy^  which  is 
the  best  criterion  of  causation ;  but  underneath  the  appearance, 
we  find  there  is  such  a  transfer.  Heat  is  necessary  to  convert 
water  into  steam,  and  this  conversion  is  an  instance  of  the 
transmutation  of  power  according  to  a  definite  rate  of  exchange. 
The  withdrawal  of  the  heat  is  followed  by  the  re-collapse  of 
the  invisible  vapour  into  water  or  visible  moisture.  So  that 
the  production  of  dew  is  clearly  a  sequence  under  the  great 
law  of  transferred  energy.  Other  proofs  of  causation  are  dis- 
pensed with  by  this  decisive  consideration.  Mr.  Mill,  however, 
remarks,  as  a  distinct  criterion  of  cause  and  effect,  as  well  as  a 
means  of  settling  which  is  cause,  and  which  is  effect,  that  cool- 
ing is  a  consequence  of  known  and  independent  antecedents, 
and  therefore  cannot  be  set  down  as  consequent  on  the  occur- 
rence of  dew. 

The  next  example  is  of  value  as  showing  the  Experimental 
Methods  in  their  purity,  or  in  the  absence  of  all  deductive 
applications  of  laws,  such  as  completed  the  enquiry  into  the 
caase  of  Dew. 


MUSCULAE  IRRITABILITY   AND   PUTREFACTION. 


'603 


On  the  16th  of  May,  1861,  Dr.  Brown-Sequard  delivered  the 
Croonian  Lecture  before  the  Royal  Society,  and  took  for  his 
subject  the  *  Relations  between  Muscular  Irritability,  Cada- 
veric Rigidity,  and  Putrefaction.'  In  this  he  adduced  facts 
to  maintain  the  following  position  : — 

*  The  greater  the  degree  of  muscular  irritability  at  the  time  of 
death,  the  later  the  cadaveric  rigidity  sets  in  and  the  longer  it 
lasts,  and  the  later  also  putrefaction  appears  and  the  slower  it 
ftr ogresses.* 

By  muscular  irritability  is  meant  muscular  power  or  apti- 
tude for  contracting.  A  man  fresh  in  the  morning  for  his 
day's  work  would  be  said  to  have  a  good  store  of  muscular 
irritability :  at  the  end  of  the  day's  work,  the  stock  is  com- 
paratively exhausted.  It  would  of  course  be  still  more  ex- 
hausted after  protracted  fatigues  continued  through  many 
days. 

The  cadaveric  rigidity  is  a  stifi'ening  of  the  muscles  that 
occurs  in  all  animals  some  time  alter  death.  The  time  when 
the  stiffening  begins,  and  the  duration  of  it,  are  variable,  and 
Dr.  Brown  Sequard  tries  to  establish  the  law  or  cause  or  con- 
dition of  this  variation.  This  he  does  by  a  series  of  observa- 
tions, whose  force  will  be  appreciated  by  noting  how  far  they 
comply  with  the  exigencies  of  the  experimental  methods. 

First  set  of  Experiments, — Paralyzed  muscles.  Here  he  has 
two  connexions  to  establish,  in  order  to  the  end  in  view. 
He  first  shows  that  the  paralysis  of  a  muscle  leaves  it  for  a 
time  with  more  irritability  than  the  unparalyzed  or  exerted 
muscles.  He  paralyzed  the  muscles  of  one  leg  in  a  dog,  by 
section  of  the  nerve.  Five  hours  afterwards  the  dog  is 
killed  (by  asphyxia).  In  the  paralyzed  muscles  the  irritability 
lasted  ten  hours  ;  that  is,  it  was  possible  to  induce  contrac- 
tions in  them  (by  stimulants)  up  to  that  time.  In  the  healthy 
lee,  the  irritability  lasted  only  four  hours  ;  in  other  words 
was  very  much  less.  Now  compare  the  results  as  regards 
Rigidity  and  the  delay  of  Putrefaction — 

Duration  of  irrit.    Daration  of  rigidity. 

Paralyzed  M.  10  hours  13  days 

Healthy      „  4     „  5    „ 

Here  then  is  an  experiment  clearly  of  the  nature  of  Differ- 
for  two  legs  of  the  same  animal  were  compared,  and 


Putrefaction 

commenced. 

17th  day. 

7th    „ 


ence 


the  only  difference  was  the  paralysis  of  one  of  them.      It  is 
true,  as  in  all  cases  of  vivisection,  that  an  experiment  of  Dif- 
ference must  always  be   received  with  caution,  seeing  that 
14 


^^f 


,'/ 


I 


f 


\ 


304:       EXAMPLES   OF  THE  EXPERIMENTAL  METHODS. 

other  changes  may  be  made  by  the  means  taken  to  prodnce 
the  difference.     Yet,  at  all  events,  here  is  a  strong  presumption. 

The  doctrine  is  confirmed  farther  by  another  aspect  of  the 
paralysis.  If  an  animal  is  allowed  to  live  a  month  after 
paralysis  of  a  member,  the  paralyzed  muscles  are  then  inferior 
in  irritability,  and  when  compared  under  those  circumstances, 
they  become  rigid  and  putrefy  sooner. 

Second  set  of  Experimeids.^Effeds  of  dlminutinn  of  tem- 
perature upon  muscles.— Dr.  Brown-Sequard  had  determined, 
by  previous  experiments,  that  cold  increases  the  vital  proper- 
ties of  the  nerves  and  muscles — a  fact  on  which  the  stimulating 
power  of  cold  upon  the  animal  system  depends.  He  now 
applies  this  fact  to  the  enquiry  in  hand. 

Two  kittens  of  the  same  litter  were  placed  in  different  tem- 
peratures. After  death,  the  following  differences  were  discern- 
ible. The  one,  kept  at  a  temperature  of  98°.6,  assumed  the 
rigidity  in  3^  hours  ;  this  lasted  three  days,  putrefaction 
commencing  in  the  fourth.  In  the  other,  which  had  been  kept 
so  cool,  that  a  thermometer  inserted  in  the  rectum  stood  at 
77°,  the  rigidity  was  delayed  till  the  10th  hour,  and  lasted 
nine  days,  putrefaction  commencing  on  the  tenth.  This  experi- 
ment was  repeated  with  many  animals,  and  is  also  an  experi- 
ment according  to  the  Method  of  Difference.  This  is  the 
general  principle  of  the  fact  known  in  hot  climates,  that  the 
dead  putrefy  almost  immediately  after  death,  and  must  be 
interred  without  a  moment's  delay.  The  relaxation  of  the 
vital  powers  in  hot  climates  is  only  a  part  of  the  same  fact. 
The  full  explanation  of  this  point,  or  the  resolution  of  the  law 
into  still  higher  laws  is  not  yet  fully  made  out. 

Influence  of  death  by  lightning  and  galvanism.  —  It  was 
thought  by  John  Hunter  that  animals  killed  by  lightning  did 
not  stiffen.  This  has  been  found  not  the  case.  Still  there  are 
instances  where  the  rigidity  has  either  not  set  in,  or  been  of 
so  short  duration,  that  its  existence  has  not  been  traced. 
Lightning  may  kiU  in  various  ways  : — 1st,  By  fright ;  2nd,  By 
hromorrhage ;  8rd,  By  concussion  of  the  brain.  In  all  these 
three  modes,  there  ought  to  be  a  manifestation  of  the  rigidity. 
But  there  is  a  fourth  mode,  which  is  to  convulse  all  the 
muscles  so  violently  as  utterly  to  exhaust  their  irratibility ;  in 
which  case  the  rigidity  may  fail  to  be  noticed.  This  is  the 
way  that  galvinism  acts  upon  animals. 

Experiments  were  accordingly  tried  by  galvanizing  the 
limbs  of  Rabbits;  comparing  the  galvanized  with  the  un- 
galvanized  limbs,  with  respect  to  the  time  of  rigidity. 


' 


musculah  irritability  and  putrefaction. 


305 


Galvanized  Limb.  Not  Gralvanized, 

Duration  of  Irritability,  7  to  20  minutes.      120  to  400  min, 

„         of  Rigidity,      2  to  8  hours.  i  to  8  days. 

Putrefaction  advanced,  within  a  day.     After  several  days. 

The  experiments  were  repeated  on  dogs  with  the  very  same 
results. 

Also,  guinea-pigs  were  subjected  wholly  to  galvanism,  but 
in  different  degrees.  In  those  powerfully  galvanized,  the 
irritability  lasted  a  short  time,  and  the  rigidity  was  correspond- 
ing rapid  and  brief.  With  a  less  degree  of  galvanism,  the  time  of 
both  phenomena  was  protracted.  We  have,  therefore,  an 
additional  corroboration  of  the  law,  still  by  the  powerful 
Method  of  Difference. 

Influence  of  prolonged  muscular  exercise.  —  This,  of  course, 
is  a  cause  of  diminished  irritability.  Now,  there  are  well- 
ascertained  facts  that  connect  prolonged  exertion  with  rapid 
putrefaction.  Over-driven  cattle  and  animals  hunted  to  death 
putrify  speedily.  So  in  cocks  killed  after  a  fight.  Soldiers 
killed  in  a  very  prolonged  fight  show  the  same  phenomenon. 
The  rigidity  is  quickly  over,  and  the  putrefaction  rapid. 

These  are  instances  of  the  Method  of  Agreement. 

Infltience  of  nutrition  on  muscles. — Dr.  Brown-Sequard 
here  collects  confirming  instances,  from  the  comparison  of 
cases  where  death  happens  in  a  well  nourished  condition  of  the 
muscles,  with  cases  where  death  had  been  preceded  by  inanition. 
Thus,  when  men  strong  and  fresh  have  been  killed  suddenly, 
the  rigidity  and  putrefaction  have  appeared  very  late.  A  case 
is  recorded  of  muscular  irritability  continuing  twenty-six  hours 
in  a  decapitated  man.  Here  is  Agreement  in  pi'esence. 
Compare  those  instances  with  others  of  persons  dying  of  slow 
exhaustion,  and  the  appearance  is  reversed.  A  man  dying  of 
prolonged  typhoid  fever,  for  example,  was  found  to  show  no 
trace  of  rigidity,  and  putrefaction  commenced  in  less  than  an 
hour.     This  is  Agreement  in  Absence. 

Influence  of  Convulsions  on  rigidity  and  putrefaction. — It 
appears  that  muscles  much  attacked  with  cramps  before  death 
speedily  give  way  to  putrefaction. 

Certain  poisons  (as  strychnine)  sometimes  produce  con- 
vulsions before  death,  and  in  those  cases  the  rigidity  and 
putrefaction  progress  rapidly. 

Such  is  an  ample  body  of  evidence  from  observation  and 
experiment  to  establish  the  position  laid  down.  The  Methods 
of  A<jreement,  of  Difference,  the  Joint  Method,  and  the  Method 
of  Variations,  have  been  all  bi'ought  into  play.     And  if  there 


II 


I 


1 


306   FRUSTRATION  OF  THE  KXPRIMENTAL  METHODS. 

are  any  doubts  about  the  decisiveness  of  the  experiments  on 
the  Method  of  Difference,  from  the  possibility  of  making  other 
changes  besides  the  one  intended,  these  doubts  are  dispelled 
by  the  coincidence  of  results  from  so  many  distinct  experi- 
ments. The  research  is  purely  Inductive.  No  consideration 
of  a  Deductive  kind  has  been  introduced  ;  although  there 
are  general  considerations  that  give  great  probability  to  the 
conclusion.  Muscular  irritability  is  the  living  condition 
of  the  muscle — its  vitality — which  may  be  greater  or  less ; 
and  the  greater  it  is,  the  longer  the  muscle  will  retain  its 
living  characters,  or  the  longer  it  will  be  in  passing  to  the 
characters  of  death,  which  are  rigidity  and  putrefaction. 
These,  therefore,  are  delayed  by  fulness  of  vitality  ;  while  loss 
of  vitality  hands  the  system  over  all  the  sooner  to  the 
destroyer. 

When  we  form  conclusions,  on  an  insufficient  employment 
of  the  methods  of  elimination,  we  commit  Fallacies  of  Induc- 
tion. Of  these,  numerous  examples  might  be  given,  and  the 
proper  place  for  them  is  in  the  course  of  the  exposition  of  the 
Methods  themselves.  As  it  is  still  the  custom,  however,  to 
retain,  in  works  of  Logic,  a  separate  chapter  or  book  on 
Fallacies,  we  shall  reserve  for  that  part  of  the  subject,  the 
instances  of  Inductive  £a.llacy. 


CHAPTER  Vin. 

FRUSTEATIOK  OF  THE  METHODS. 

1.  In  the  Inductive  Methods  as  hitherto  contemplated, 
two  conditions  have  been  supposed ;  first,  that  an  effect 
has  only  one  cause,  or  set  of  antecedents  ;  secondly,  that 
different  effects  are  kept  apart  and  distinguishable.  Both 
conditions  may  be  wanting. 

In  the  method  of  Agreement,  for  example,  it  is  assumed,  that 
the  effect  a  has  only  the  cause  A ;  should  A  and  C  both  be 
causes,  the  method  would  be  defeated.  The  absence  of  A 
would  not  prove  that  it  is  not  a  cause  ;  for  the  effect  might 
still  be  due  to  C.  The  special  difficulties  attending  this  ca.se 
must  now  be  considered. 


"a 


PLURALITY  OF  CAUSES  NOT  FINAL. 


307 


Again,  the  effects  a  b  c  are  supposed  to  stand  out  distin- 
guishable. They  may,  however,  be  fused  or  united  in  one 
simple  effect  2  a  c,  or  Sa.  This  is  the  Intermixture  of  Effects ; 
and  is  still  more  baffling  to  the  inductive  methods,  as  hitherto 
given. 

PLURALITY  OF  CAUSES. 

2.  In  many  instances,  the  same  effect  is  produced  by  a 
PLURALITY  OF  CAUSES  :  as  Motion,  Heat,  Pleasure,  Death. 

Bodies  are  put  in  motion  by  all  the  different  agencies  termed 
Prime  Movers — animal  strength,  wind,  water,  steam,  combus- 
tion (as  in  gunpowder),  &c.  Finding  a  body  in  motion, 
therefore,  we  cannot  ascribe  it  to  any  special  agent^  merely 
from  the  fact  that  it  is  in  motion  :  we  see  a  wheel  turning  and 
doing  work,  but  we  may  not  be  able  to  attribute  its  motion  to 
one  agent  rather  than  another.  In  like  manner,  there  are 
various  sources  of  Heat ;  the  solar  ray  and  combustion  are 
the  most  familiar  ;  but  friction  and  electricity  are  also  sources. 
Hence  the  fact  of  the  evolution  of  heat  does  not  point  out  the 
cause  ;  as  an  example,  uncertainty  still  attaches  to  the  immedi- 
ate antecedent  of  animal  heat. 

There  are  numerous  causes  of  pleasure  and  of  pain  :  nume- 
rous modes  of  stimulating  the  nervous  system  ;  numerous 
agencies  of  good  health  and  of  bad  health;  numeious  ways  of 
getting  a  livelihood  ;  numerous  causes  of  death. 

It  is  to  be  noted,  however,  that  the  plurality  in  some  of 
these  instances  is  on  the  surface  only.  As  regards  Motion,  the 
law  of  the  Persistence  of  Force  assigns  a  common  origin  to  all 
the  so-called  prime  movers ;  these,  therefore,  are  'proximate^  and 
not  the  ultimate  sources.  The  same  law  covers  the  produc- 
tion of  Heat,  however  various  the  apparent  antecedents.  The 
causes  of  Pleasure  can  be  generalized  into  a  small  number  of 
agencies,  if  not  into  one.  Possibly  all  stimulants  may,  in  the 
last  analysis,  be  found  to  have  a  common  effect  on  the  sub- 
stance of  the  nerves.  The  ways  to  Wealth  may  be  apparently 
many,  but  we  can  cover  them  all  by  one  general  expression, — 
earning  and  saving.  In  Health  and  Sickness,  there  might 
possibly  be  generalized  expressions  of  the  many  proximate 
causes.     So  with  Death. 

Nevertheless,  for  practical  purposes,  we  have  to  ascertain 
not  simply  the  primal  cause,  but  the  special  embodiment  of 
that  cause,  on  a  certain  occasion.  It  is  not  enough,  when  a 
man  is  found  dead,  to  assign  the  stoppage  of  the  heart,  or  of 


\  \ 


f 


i 


308      FRUSTRATION   OF  THE  EXPERIMENTAL  METHODS. 

the  luDffS,  or  the  extinction  of  the  vital  forces ;  we  desire  to 
know  in  what  form  and  circnm stances  these  generahzed  causes 
were  specialized  ;  whether  by  cold,  by  inanition,  by  poison,  by 
mechanical  violence,  or  otherwise. 

3.  The  chief  consequence  of  Tlurality  of  Causes  is  to 
frustrate  the  Method  of  Agreement. 

The  Method  of  Difference  remains  intact.  Whatever  be  the 
plurality  of  causes  of  motion,  if  we  observe  the  introduction  o£ 
some  one  agent  followed  by  the  effect,  we  kuow  tne  cause  m 
that  instance.  There  may  be  many  ways  of  keeping  up  the 
animal  heat,  but  the  transition  from  the  temperature  of  bO  to 
30°  bv  causing  an  immediate  sense  of  chillmess  shows  that  the 
external  temperature  is  essential  to  comfortable  warmth  on 

that  particular  occasion.  l  -  l     t.^  +i.^ 

The  operation  of  Plurality  is  to  give  uncertainty  to  the 
Method  of  Agreement.  For  example,  we  observe  numerous 
cases  of  unhealthy  human  beings  whose  parents  were  un- 
healthy :  this  would  be  to  a  certain  extent  a  proot  trom 
Ain-eement.  On  the  other  hand,  many  unhealthy  persons  are 
the  children  of  perfectly  healthy  parents  ;  wheuce,  concluding 
by  the  strict  rule  of  Agreement,  we  should  affirm  that 
nnhealthiness  in  the  parents  is  in  no  case  a  cause  of  unhealthy 
Bess  in  the  children  ;  that  the  two  facts  are  not  in  any  way 
connected  as  cause  and  effect.  The  conclusion  is  obviously 
wrong ;  it  would  be  correct  were  there  only  one  cause  ot  lU 
health  ;  it  is  illegitimate  if  there  be  many  causes. 

Plurality    is   illustrated   by    our    English    spelhng.       ihe 
method  of  Agreement  is  nullified  in  this  instance.     In  certain 
words,  the   letters  ough  agree  with  a  peculiar  sound,  as  m 
'  rouffh  *    The  same  word  occurs  with  other  letters,  as  in  rutt,^ 
and  the  same  letters  occur  with  a  different  sound,  as  m  'bough. 
Whence,  by  the  Method  of  Agreement,  we  should  infer  that 
there  was  never  any  connexion   between   either   sound  and 
*  onirh.'      A   similai^   illustration   is   afforded    by   ambiguous 
words      The  word  *  air '  is  spoken  in  company  with  a  musical 
melody  •  at  other  times  it  is  spoken  where  there  is  no  music; 
any  one  unprepared  lor  plurality,  and  following  out  Agreement, 
would  conclude  that  the  connexion  with  music  was  purely 
casual;  that  there  was  no  fixed  bond  of  union  between  the 
two.    Wo  acquire  the  meanings  of  the  vocables  of  our  language 
chiefly  by  the  method  of  Agreement.    We  gradual  y  eliminate 
all  accompaniments  that  may  be  absent  consistently  with  the 
employment   of  each    word.      We   find,   alter  a  number   of 


1  » 


ff 


FAILURE   OF  THE   METHOD   OF  AGREEMENT 


ao9 


repetitions  of  the  word  *  fire  *  in  various  connexions,  that  the 
one  fact  common  to  all  is  blazing  combustion  with  heat.  Wo 
learn  in  course  of  time  to  extend  the  word  to  metaphorical 
significations.  These  being  conjunctions  of  pure  co-existence, 
without  causation,  they  cannot  be  dealt  with  by  any  other 
method,  while  the  occurrence  of  plurality,  even  when  under- 
stood and  allowed  for,  is  a  serious  and  paiutul  distraction  to 
the  inductive  process. 

Again,  pressure  on  the  brain  is  a  cause  of  insensibility; 
yet,  as  we  find  insensibility  w^here  there  has  been  no  pressure, 
we  should  say,  according  to  Agreement,  that  pressure  is  not 
a  cause.  In  the  same  way,  every  one  of  the  causes  might  be 
proved  not  to  be  a  cause — deficiency  of  blood,  excess  of  dark 
unhealthy  blood,  rupture  of  the  nervous  continuity,  &c. 

Extraordinary  facts  have  come  to  light  showing  the  possi- 
bility of  exerting  the  mental  powers,  under  disease  of  very 
large  portions  of  the  brain.  These  facts  would  seem  to 
prove  that  such  parts  have  no  share  in  the  mental  functions. 
The  safer  inference  is  that  there  is  a  plurality  of  nervous  seats 
or  tracks  for  the  same  functions.  It  has  long  been  supposed 
that  the  two  hemispheres  have  common  functions. 

The  discussion  of  the  problem  of  Beauty  is  often  rendered 
fruitless  by  the  neglect  of  Plurality.  The  attempt  is  made  to 
assign  some  one  circumstance  present  in  all  beautiful  things — 
as  Colour,  Harmony,  Fitness,  Unity,  Suggestion  of  Mental 
qualities.  Now,  by  the  unqualified  method  of  Agreement, 
every  assignable  circumstance  could  be  disproved  ;  with  refer- 
ence to  each  one  in  turn,  would  it  be  possible  to  find  objects 
of  unquestioned  beauty  where  that  one  is  not  present.  Jeffrey 
thinks  it  a  sufficient  refutation  of  the  theories  he  opposes, 
to  produce  beautiful  objects  where  the  alleged  source  of  beauty 
is  absent. 

4  The  counteractives  to  the  failure  of  Agreement,  in 
the  case  of  Plurality,  are  (1)  great  multiplication  of  in- 
stances, and  (2)  Agreement  in  absence,  that  is,  the  Joint 
Method. 

(1)  One  remedy  for  the  failure  of  the  Method  of  Agreement, 
under  Plurality,  is  multiplication  of  itislances.  This  will 
operate  in  various  ways.  It  will  tend  to  bring  out  all  the 
causes ;  which  is  one  desirable  issue  of  Plurality.  An  ex- 
tended statistics  of  Crime  or  Pauperism  will  show  us  the  pos- 
sible agencies,  by  giving  a  wide  scope  for  elimination.  The 
long   experience   of  medical  practitioners  has    taught   them 


a 


I 


810 


FHUSTKATION   OF   EXPERIMENTAL  METHOD& 


nearly  all  the  possible  causes  of  the  greater  nnmber  of 
diseases.  At  this  stage  of  exhausted  plurality,  the  only  point 
for  enquiry,  in  the  special  instance,  is — Which  of  the  causes 
are  present,  and  are  these  free  to  operate  ?  Knowing,  all  the 
contributing  causes  of  Pauperism,  we  ask  which  of  these  occur 
in  England,  in  Ireland,  or  in  Scotland,  and  are  they  free  or 
■Qncounteracted  ?  Being  aware  of  the  various  antecedents  of 
dyspepsia — bad  food,  too  much  food,  too  little  food,  hard  labour, 
want  of  exercise,  intemperance,  mental  wear  and  tear,  bad  air, 
a  hot  climate,  &c. — we  can  judge  what  brought  on  the  disease 
in  a  given  instance. 

If  we  do  not  know  which  causes  are  present  on  a  given 
occasion,  and  whether  those  actually  present  are  counteracted, 
mere  Agreement  is  wholly  fallacious.  The  fallacy  named  J90si 
hoCf  ergo  propter  hoc,  is  an  abuse  of  Agreement,  where  elimina- 
tion is  vitiated  by  Plurality,  as  in  a  great  number  of  political 
inferences.  It  is  remarked  that  Protestantism  is  accompanied 
with  superior  industry ;  the  instances  attainable  are  insuffi- 
cient in  number  to  eliminate  other  causes. 

(2)  The  other  remedy  is  the  Joint  Method.  We  should  seek 
out  cases  of  Agreement  in  ahsencCy  which  are  of  a  very  decisive 
nature.  If  in  all  cases  where  a  particular  effect  fails,  one  par- 
ticular cause  is  absent,  there  is,  in  spite  of  possible  plurality, 
a  strong  presumption  that  the  two  circumstances  are  cause 
and  effect  in  those  instances.  The  reason  grows  out  of  that 
close  approach  to  the  Method  of  Difference  furnished  by 
Agreement  in  absence.  Although  there  are  various  causes  of 
l^gb^>  yet  the  union  of  agreement  in  presence  with  agreement 
in  absence  is  sufficiently  decisive  of  the  connexion  of  light 
with  a  high  temperature.  The  special  connexions  of  light 
with  hw  temperature  are  not  denied ;  they  are  admitted  as 
exceptions  to  agreement  in  absence,  as  a  residuum  to  be  ac- 
counted for.  We  know  one  cause  thoroughly  ;  we  find  there 
are  other  causes,  as  yet  imperfectly  known,  which  have  this 
uncertainty,  namely,  that  a  body  at  the  common  temperature 
of  the  air  may  possibly  be  luminous. 

THE   INTERMIXTUEE   OF  EFFECTS. 

6.  The  Methods  of  Elimination  suppose  different  effects 
to  remain  separate  and  distinguishable  ;  whereas  cases 
arise  where  the  effects  of  different  causes  unite  in  a  homo- 
geneous total. 

When,  in  an  aggregate  phenomenon,  distinguishable  ante- 


INTERMIXTURK  OF  EFFECTS. 


311 


cedents  produce  distinguishable  consequents— A  B  C  giving 
a  6  c,  and  A  D  E  giving  a  d  e,  the  experimental  methods 
operate  to  advantage.  The  combination  of  wind,  rain,  and 
increased  temperature,  produces  a  combination  of  distinguish- 
able effects— waves  on  the  surface  of  water,  flooding  of  streams, 
the  sensation  of  warmth. 

In  other  cases,  and  these  very  numerous,  the  effect  of  the 
several  causes  is  homogeneous,  and  is  merely  increased  in 
amount  by  the  concurrence.  The  sea  is  fed  by  innumerable 
rivulets.  The  wind  often  concurs  with  tidal  agency,  so  as 
to  produce  a  higher  tide.  A  body  propelled  by  several  prime 
movers,  as  when  a  train  is  urged  by  three  locomotive  engines 
shows  only  one  effect,  velocity  of  movement  The  moon's 
path  IS  a  resultant  of  the  attractive  forces  of  the  sun  and 
the  earth  combined  with  its  projectile  movement.  The  path 
of  a  comet  is  the  resultant  of  many  influences  ;  it  does  not 
bear  on  the  face  of  it  the  story  of  them  all.  An  invalid  repairs 
to  some  salubrious  spot,  and  plies  all  the  means  of  restoration 
to  health;  many  influences  combine  to  the  result,  but  the 
effect  is  one  and  indivisible. 

A  still  more  perplexing  situation  is  the  conflict  of  opposing 
agencies.  In  an  equal  balance  nothing  is  seen,  and  yet  great 
powers  have  been  at  work.  In  unequal  contests  there  is  an 
effect ;  but  that  effect  does  not  suggest  the  fact  of  conflict.  A 
trader  has  a  net  profit  at  the  end  of  the  year  ;  the  statement 
of  that  profit,  however,  gives  no  information  of  his  expenditure 
and  receipts.  The  patient  maybe  under  various  healthy 
stimulants,  each  working  its  proper  effect;  but  some  one 
noxious  agency  may  counteract  the  whole. 

Natural  agencies  can  never  be  suspended ;  they  may  be 
counteracted  by  opposite  agents.  The  force  of  gravity  is  not 
interfered  with  when  a  balloon  rises,  it  is  merely  opposed  by  a 
greater  force  ;  it  still  operates  but  in  a  different  form.  Instead 
of  causing  the  usual  appearance,  namely,  the  descent  of  bodies 
to  the  ground,  it  operates  to  diminish  the  effect  of  an  upward 
force,  the  buoyancy  of  the  air  (itself  an  indirect  consequence 
of  gravity). 

A  counteracted  force  is  technically  said  to  exist  in  tendency. 
There  is  a  tendency  in  all  bodies  to  descend  to  the  ground ;  in 
water  to  find  its  level ;  in  the  moon  to  move  towards  the  earth, 
and  towards  the  sun.  There  is  a  tendency  in  human  beings  to 
seek  their  own  interest ;  in  despotic  sovereigns  to  abuse  their 
power.  The  tendencies  are  not  annihilated  when  they  fail  to  be 
realized;  they  are  only  counteracted  by  some  opposing  tendencies. 


w 


mmssmm 


ii 


T 


312      FRUSTRATION   OF   THE   EXPERIMENTAL  METHODS. 

A  farther  circumstaace  working  to  invalidate  the  operation 
of  the  methods  is  the  mutuality  of  cause  and  effect.    In  pohtical 
causation,  this  is  illustrated  by  Sir  G.  C.  Lewis  as  follows  :— 
*  It  happens  sometimes  that  when  a  relation  of  causation  is 
established  between  two  facts,  it  is  hard  to  decide  which,  m 
the  given  case,  is  the  cause  and  which  the  effect,  because  they 
act  and  re-act  upon  each  other,  each  phenomenon  being  in 
turn  cause  and  effect.     Thus,  habits  of  industry  may  produce 
wealth  ;  while  the  acquisition  of  weal  oh  may  promote  industry : 
again,  habits  of  study  may  sharpen  the  understanding,  and 
the  increased  acuteness  of  the  understanding  may  afterwards 
increase  the  appetite  for  study.     So  an  excess  of  population 
may,  by  impoverishing  the  labouring  classes,  be  the  cause  of 
their  living  in  bad  dwellings  ;    and,  again,  bad  dwellings,  by 
deteriorating   the   moral  habits  of  the  poor,  may  stimulate 
population.     The  general   intelligence  and   good  sense  of  a 
people  may  promote  its  good  government,  and  the  goodness  of 
the  government  may,  in  its  turn,  increase  the  intelligence  of 
the  people,  and  contribute  to  the  formation  of  sound  opinions 
among  them.     Drunkenness  is  in  general  the  consequence  of 
a  low  degree  of  intelligence,  as  may  be  observed  both  among 
savages  and  in  civilized  countries.     But,  in  return,  a  habit  of 
drunkenness   prevents  the  cultivation  of  the   intellect,  and 
strengthens   the   cause   out   of  which  it   grows.      As   Plato 
remarks,  education  improves  nature,  and   nature   facilitates 
education.      National    character,   again,   is   both    effect  and 
cause  ;    it  re-acts  on  the  circumstances  from  which  it  arises. 
The  national  peculiarities  of  a  people,  its  race,  physical  struc- 
ture, climate,  territory,  &c.,  form  originally  a  certain  character, 
which  tends  to  create  certain  institutions,  political  and  domes- 
tic,  in   harmony   with   that   character.      These    institutions 
strengthen,  perpetuate,  and  reproduce  the   character  out  of 
which  they  grew,  aud  so  on  in  succession,  each  new  effect 
becoming,  in  its  turn,  a  new  cause.     Thus,  a  brave,  energetic, 
restless  nation,  exposed  to  attack  from  neighbours,  organizes 
military  institutions  ;  these  institutions  promote  and  maintain 
a  warlike  spirit ;  this  warlike  spirit,  again,  assists  the  develop- 
ment of  the  military  organization,  and  it  is  furt^her  promoted 
by  territorial  conquests  and  success  in  war,  which  may  be  its 
result— each  successive  effect  thus  adding  to  the  cause  out  of 
which  it  sprung.'  (Methods  of  Politics,  I.  p.  375). 

6.  The  Intermixture  of  Effects  is  a  bar  to  the  Experi- 
mental  Methods. 


INTERMIXTURE   OF  EFFECTS. 


313 


A  i  n  T?  •  iP  ^.?°«P^^^  ^  yield,  not  a  &  c  d,  but  a;  and  if 
ABO  F  yield  still  a,  nothing  is  eliminated,  there  is  no  pro- 
gress.  If  a  were  precisely  measurable,  and  if  its  variations 
fu'''*?^P°J' .  ^  definitely  to  the  removal  of  particular  agents, 
the  Method  of  Difference  would  cope  with  the  case  f  the 
omission  of  A  followed  by  the  reduction  of  a  to  |  a,  would  be 
a  proof  that  A  produced  i  a.  But  the  Method  of  Agreement, 
in  Its  proper  character  of  varying  the  circumstance  by  ex- 
cluding some  agents  and  including  others,  could  not  furnish 
effectT'^^  ^^^°*'  ^°  ^^""^  ^  ^  represented  the  sum  of  several 

Now,  as  in  many  departments,  effects  are  thus  inextricably 
blended,  we  should  be  at  a  stand-still,  were  we  not  in  posses- 
sion of  some  method  more  searching  than  Agreement.  Even 
in  the  Inorganic  Sciences,  as  Mechanics  and  Chemistrv.  we 
have  this  complication ;  in  Biology,  Mind,  and  Society,  we 
have  It  still  more.  A  good  crop  is  a  single  effect ;  the  agency 
may  be  multifarious.  A  voluntary  action  may  be  the  result- 
ant of  several  motives.  The  rise  and  fall  of  prices,  the  general 
prosperity  of  a  country,  the  increase  of  population,  seldom 
depend  on  one  cause  exclusively  ;  yet  the  effect  in  each  case 
IS,  to  our  eyes,  homogeneous. 

Concomitant  Variations  is  the  only  one  of  the  Methods  that 
can  operate  to  advantage  in  such  cases.  If  a  cause  happens 
to  vary  alone,  the  effect  will  also  vary  alone,  and  cause  and 
effect  may  be  thus  singled  out  under  the  greatest  complica- 
tions. Thus,  when  the  appetite  for  food  increases  with  the 
cold,  we  have  a  strong  evidence  of  connexion  between  those 
two  lacts,  although  other  circumstances  may  operate  in  the 
same  direction. 

^  The  assigning  of  the  respective  parts  of  the  sun  and  moon, 
m  the  action  of  the  Tides,  may  be  effected,  to  a  certain  degree 
ot  exactness,  by  the  variation  ^  the  amount  according  to  the 
positions  of  the  two  attracting  bodies. 

By  a  series  of  experiments  of  Concomitant  Variations,  directed 
to  ascertain  the  elimination  of  nitrogen  in  the  human  body 
under  varieties  of  muscular  exercise.  Dr.  Parkes  obtained  the 
remarkable  conclusion,  that  a  muscle  grows  during  exercise, 
and  loses  bulk  during  the  subsequent  rest. 

For  the  first  of  the  difficulties  now  illustrated— Plurality 
with  the  aggravation  of  counteracting  influences— an  import-' 
ant  mstrument  remains,  an  additional  Method  of  Elimination 
termed  *  Elimination  by  the  Computation  of  Chance  '     For 


i-»r'*^^ 


J 


314 


CHANCE,   AND  ITS  ELIMINATION. 


dealing  with  the  same  uncertainty,  and  for  the  still  greater 
(and  often  accompanying)  uncertainty  of  Intermixture  of 
Effects,  the  chief  resort  is  to  Deduction-  The  two  next  chap- 
ters will  be  occupied  with  those  two  subjects. 


CHAPTER  IX 
CHANCE,  AND  ITS  ELIMINATION. 

1.  An  important  resource  in  eliminatincj  the  irrelevant 
antecedents  or  accompaniments  of  an  effect  is  obtained 
through  the  calculation  of  Chance  or  Probability. 

This  is  to  approach  the  problem  of  Induction  from  a  novel 
aspect.  Instead  of  varying  the  circumstances  so  as  to  procure 
the  absence  of  the  several  antecedents  A  B  C  in  turn,  we 
consider  whether  these  agents  might  not  be  present  of  them- 
selves without  any  regard  to  the  effect  in  question.  Thus,  a 
person  dies  at  midnight,  when  the  sun  is  below  the  horizon 
and  due  north.  Now,  seeing  that  this  event  happens  every 
twenty-four  hours,  as  a  consequence  of  cosraical  operations,  it 
must  come  round  and  must  coincide  with  a  great  many 
things  that  happen  on  the  earth.  The  fact  of  such  coincidence 
is  not  of  itself  held  as  proving  causation  or  regular  concomi- 
tance with  everything  that  happens  at  that  time.  Before  we 
presume  a  concurrence  of  causation  between  two  coinciding 
things,  we  enquire  whether  the  two  things  are  not  equally 
liable  to  concur,  whether  connected  or  unconnected. 

The  night  that  Oliver  Cromwell  died,  a  great  storm  devas- 
tated London.  The  coincidence  might  affect  the  minds  of  the 
superstitious,  but  there  was  no  proof  of  causal  connexion. 
Each  event  grew  out  of  its  own  independent  series  of  causes 
and  conditions  ;  the  one  was  a  consequence  of  the  bodily  con- 
stitution and  manner  of  life  of  Cromwell ;  the  other  was  a 
consequence  of  the  laws  of  the  atmosphere.  They  concurred 
in  time,  and  that  is  all  that  should  be  said  regarding  them. 

Every  event  of  every  man's  life  must  concur  with  some  one 
position  of  the  planets,  on  the  supposition  of  their  being  no 
connexion  whatever.  Hence,  such  concurrences  prove  nothing 
at  all ;  they  are  left  out  of  account  without  even  the  trouble  of 
elimination. 


MEANING  OF  A  CHANCE  COINCIDENCE. 


315 


There  are  cortain  cases,  where  a  cause  fails  to  produce  its 
effect,  being  counteracted  by  some  other  cause.  A  B  C  is 
followed  by  b  c  d,  from  which  the  inference,  by  Agreement 
would  be,  that  A  is  not  the  cause  of  a.  Bark  is  administered 
to  a  patient  in  ague,  but  the  symptoms  are  not  alleviated.  The 
strict  application  of  the  Method  of  Agreement  would  lead  to 
the  inference  that  bark  does  not  cure  ague.  Yet  we  do  not, 
in  practice,  lose  faith  in  medicines  from  individual  failures. 
We  are  prepared  to  encounter  exceptions  to  cases  of  compli- 
cated causation.  The  question  then  comes,  how  far  is  this  to 
go  ?  How  are  we  to  be  sure  of  causes  at  all,  if  they  fail  to 
work  their  effects  ?  What  difference  can  we  draw  between 
such  instances  and  mere  accidental  concurrences  ? 

The  theory  of  Chances,  or  Probabilities,  applies  to  both  the 
situations  now  illustrated  ; — the  dropping  without  the  trouble 
of  elimination  what  would  be  present  whether  another  thing 
were  present  or  not ;  and  the  proving  of  a  causal  agent, 
although  not  uniform  in  producing  the  proper  effect. 

2.  A  chance  coincidence  is  one  where  there  is  no  implied 
connexion  of  cause  and  effect,  or  one  that  would  be  the 
same  in  the  absence  of  any  such  connexion. 

Instances  have  been  already  given,  and  could  be  multiplied 
at  pleasure.  A  person  walking  on  the  sea  shore  at  a  certain 
hour  every  day,  will,  on  a  given  day,  walk  at  low  water ;  but 
the  concurrence  is  said  to  be  a  chance  concurrence,  as  the 
person's  walking  is  not  in  any  way  regulated  by  the  state  of 
the  tide.  On  the  other  hand,  the  concurrence  with  the  time 
of  day  is  not  chance.  There  is  a  concurrence  in  both  cases  ; 
the  one  without  cause,  or  a  matter  of  chance,  the  other  with 
a  cause,  and  not  a  matter  of  chance. 

If  it  is  proposed  to  enquire  what  coincidences  are  due  to 
chance  and  what  not,  the  method  is  dictated  by  the  so-called 
rules  of  Chance. 

Common  sense  suggests  the  principle  of  the  solution.  We 
know  that  low  tide  coincides  with  a  certain  hour  of  the  day 
twice  a  month.  If,  on  a  long  average,  the  coincidences  of  low 
tide  and  the  person's  walking  on  the  shore  happened  exactly 
twice  a  month,  we  should  say  the  relationship  is  casual, 
accidental,  or  without  any  link  of  causation ;  for  on  the  supposi- 
tion of  there  being  no  connexion,  this  number  of  coincidences 
might  occur  through  the  laws  of  tides.  If,  on  the  other  hand, 
the  two  facts  coincided  daily,  we  shouid  presume  a  coincidence. 
Moreover,  even  if  it  did  not  occur  daily,  but  once  or  twice  a 


\ 


316 


CHANCE,  AND  ITS  ELIMINATION. 


PROOF  OF  LAWS  NOT  UNIFORM. 


317 


■5     ' 


; 


S 


week,  this  would  be  more  than  chance  would  account  for,  and 
there  would  be  a  presumption  of  a  causal  connexion,  which, 
however,  is  liable  to  be  defeated  or  counteracted. 

So  with  the  connexion  between  the  walking  and  the  hour 
of  the  day.  Suppose  the  person  might  walk  at  any  time  dur- 
ing fifteen  hours  of  the  day,  he  would,  by  mere  chance,  walk 
during  any  particular  hour,  once  every  fifteen  days  on  a  long 
average,  if  in  fact,  some  one  hour  coincided  with  the  walking 
only  once  in  sixty  days,  there  would  be  proof  of  an  influence 
hostile  to  going  out  at  that  hour ;  if  at  some  other  hour,  the 
walking  occurred  six  days  in  seven,  there  would  be  proof  of 
positive  connexion  with  the  said  hour. 

These  obvious  considerations  are  reduced  to  principles  and 
rules  in  the  logico-mathematical  science  called  the  *  Doctrine 
of  Chances  or  Probabilities.' 

3.  The  principle  is  as  follows  :--Coiisider  the  positive 
frequency  of  the  phenomena  themselves,  and  how  great 
frequency  of  coincidence  must  follow  from  that,  supposing 
there  is  neither  connexion  nor  repugnance.  If  there  be  a 
greater  frequency,  there  is  connexion  ;  if  a  less,  repugnance 

This  may  be  called  the  general  case,  as  distinguished  from 
certain  modified  cases  to  be  stated  afterwards. 

If  we  find  from  observation  (sufliciently  extended  to  genera- 
lize the  facts)  that  A  exists  in  one  instance  out  of  every  two, 
and  that  B  exists  in  one  instance  out  of  eveiy  three;  then,  if 
A  and  B  are  wholly  indifi'erent  to  each  other— neither  con- 
nected nor  repugnant— the  instances  of  A  and  B  happening 
together  will  be  (in  the  Arithmetic  of  Chances)  one  out  of 
every  six,  on  a  sufficient  average.  If,  really,  the  two  co-exist 
oftener,  there  is  connexion ;  if  seldomer,  repugnance. 

By  this  method  singly,  could  we  determine  a  connexion  of 
cause  and  efiect  in  the  instance  of  rain  occurring  with  a  par- 
ticular wind,  say  the  South- West.  The  experimental  methods 
fail  in  such  an  instance.  It  is  well  remarked  by  Mr.  Venn 
(Logic  of  Chance,  p.  127)  *that  in  Probability  we  distinctly 
take  notice  of,  and  regard  as  evidence,  reasons  so  faint  that 
they  would  scarcely  bo  called  by  any  other  name  than  mere 
hypothesis  elsewhere.  * 

In  the  Chinese  astronomical  observations,  frequent  entry 
was  made  of  new  stars  ;  and  by  far  the  larger  number  of  these 
appeared  m  the  milky  way.  The  coincidences  implied  some 
Jaw  of  connexion,   but  no  such  law  was  suspected  by   the 


Chinese  astronomers.  We  now  know  that  the  milky  way 
contains  the  great  mass  of  the  stars  of  our  galaxy ;  conse- 
quently all  changes  connected  with  the  stars  will  be  most 
nunaerous  there.  The  circumstance  has  been  adverted  to  as 
an  important  confirmation  of  the  accuracy  of  the  Chinese 
astronomical  records. 

In  the  generalizations  of  co-inhering  attributes,  in  Physics 
and  in  Chemistry,  there  is  often  a  want  of  perfect  agreement 
m  the  details :  yet  the  agreement  is  too  extensive  to  be  the 
product  of  chance,  and  hence  we  must  admit  the  existence  of 
a  law  which,  in  the  complications  of  the  phenomena,  is  occa- 
sionally crossed  and  counteracted.     It  is  a  law  that  the  alka^ 
hue  bases  are  oxides  of  the  metals  ;   a  remarkable  exception 
occurs  in  ammonia.      The  law  does  not  become  waste  paper 
because  of  this  exception.      The  coincidence  is  one  that  mere 
chance  cannot  account  for ;   and  some  way  has  to  be  sought 
out  to  reconcile  the  discrepancy.     Perhaps  an  expression  will 
be  found  that  will  apply  alike  to  ammonia  and  to  the  other 
alkalies.      The  discovery  of  a  metal  in  ammonia  has  been 
looked  to  as  a  solution  of  the  difficulty. 

Many  genera  of  plants  are  centralized  in  definite  geogra- 
phical  areas.  Erica,  for  example  ;  the  species  being  collected 
within  a  certain  tract,  at  some  one  point  of  which  there  is 
tound  the  maximum  number  of  species.  As  chance  cannot 
account  for  such  localizations,  the  endeavour  is  made  to  trace 
out  laws  of  connection  (cause  and  efiect)  between  the  plants 
and  the  locality.  ^ 

In  the  controversies  raised  on  the  subject  of  Phrenolof^y, 
the  opponents  of  the  system  have  considered  that  they  dis- 
proved it  by  instancing  decided  exceptions  to  the  phrenological 
allocation  of  faculties— cases  of  mathematicians  with  a  small 
organ  of  number,  or  musicians  with  a  small  organ  of  tune. 
Ihe  facts  supposed,  however,  are  not  conclusive  against  the 
system.    For,  in  the  first  place,  the  disproof  of  the  coincidences 
alleged,  m  respect  of  one  or  two  faculties,  or  any  number, 
would  not  disprove  all  the  rest.     But,  in  the  second  place,  a 
tew  exceptions  would   not  thoroughly  disprove   the  allecred 
connexion  ;  they  would  only  disprove  its  unfailing  uniformity. 
Ihe  phrenologist   could  still  retreat  upon   the   principle  we 
are   now    discussing;    for,    if  the   coincidences  of  a  certain 
distinguished  mental  aptitude,— as  number,  music,  colour— 
with  the  unusual  size  of  a  certain  region  of  the  head,  were 
more  frequent  than  it  would  be  on  mere  chance,  or  in  the 
absence  of  all   connexion,  he   would   be  entitled  to  infer  a 


\ 


818 


CHANCE,   AND   ITS  ELIMINATION. 


COMBINATION   OF  CHANCE  AND  LAW. 


319 


f 


I 


I 


f- 


relatlonship  between  the  two.  No  doubt,  the  practical  value 
of  the  facts  would  be  very  much  lowered  by  the  supposed 
relationship  being  frequently  defeated  ;  still,  the  bond  must  be 
considered  as  established.  In  this  view,  an  extensive  series  of 
observations  on  the  size  and  form  of  the  human  head,  and  on 
the  accompanying  mental  qualities,  if  reduced  to  a  statistics 
of  comparative  frequency,  could  yield  indications  of  the  loca- 
lizing of  mental  functions,  if  such  be  the  actual  case. 

The  homoeopathic  maxim  *  similia  similibus  curantur,'  may 
be  subjected  to  the  same  criticism.  Exceptions  do  not  nullify 
the  principle,  although  they  reduce  its  value  as  a  guide.  Both 
this  and  the  opposite  maxim  (*contraria  contrariis  curantur ') 
may  hold  in  nature.  The  coincidences  in  both  cases  may  be 
greater  than  chance  would  account  for. 

The  prevalence  of  the  different  forms  of  Christiauity  after 
the  Reformation  shows  a  coincidence  with  Race  that  chance 
would  not  account  for.  The  Greek  clmrch  was  propagated 
principally  in  the  Slavonic  race  ;  the  Roman  Catholic  church 
coincides  largely  with  the  Celtic  race  ;  and  the  Protestant 
church  has  found  very  little  footing  out  of  the  Teutonic  races. 
From  this  coincidence  must  be  presumed  a  positive  affinity 
between  the  several  forms  and  the  mental  peculiarities  of  the 
races  : — which,  as  an  empirical  law,  may  be  applied  to  cases 
immediately  adjacent,  and  as  a  derivative  law  (so  it  may  be 
considered)  may  be  applied  still  wider.  We  may  fairly  con- 
clude, that  any  speedy  conversion  of  one  church  to  another  is 
very  unlikely.  But  the  law  being  at  best  a  derivative  law, 
involving  a  plurality  of  simpler  uniformities  under  collocations 
or  co-efficients,  may  be  subverted  by  circumstances  arising  in 
the  lapse  of  time.  It  might  also  happen  that  change  of  place 
and  of  circumstances  might  defeat  the  law  ;  such  as  emigra- 
tion to  other  countries,  or  great  political  revolutions. 

We  may  apply  the  principle  to  the  problem  of  the  Spread  of 
Language.  The  articulate  modes  of  the  human  voice  beincr 
nearly  the  same  in  all  races,  there  would  be  a  great  many 
common  words  struck  out,  without  any  communication  be- 
tween the  races.  Then  it  might  happen  too  that  some  of 
these  common  words  might  be  applied  to  the  same  objects, 
because  some  name  or  other  must  be  applied.  Of  course,  the 
probability  of  the  same  sound  as  the  radical  ma,  being  ap- 
plied to  the  maternal  parent,  by  different  races  independently 
is  a  very  small  probability ;  and  the  probability  of  any  great 
number  of  such  coincidences  is  still  smaller.  Therefore,  if  we 
find  in  the  languages  of  India,  and  of  Great  Britain,  a  very 


considerable  number  of  names  almost  the  very  same,  applied 
to  the  same  things,  we  must  conclude  that  the  coincidence  is 
not  the  work  of  chance,  and  is  the  result  of  some  cause. 

4.  A  special  case  of  the  elimination  of  chance  is  pre- 
sented by  the  combinatidn  of  Chance  with  Law,  or  of 
casual  and  causal  links.  In  a  sufficiently  prolonged  ex- 
perience, chance  may  be  eliminated. 

Thus,  so  far  as  the  mere  decay  of  the  human  system  is  con- 
cerned, deaths  would  be  equally  frequent  at  all  periods  of  the 
year,  and  at  all  hours  of  the  day.    In  the  statistics  of  Mortality, 
however,  we  find  that  some  months  are  marked  by  an  exces- 
sive number  of  deaths  ;  as  December,  January,  and  February. 
This  points  to  a  law  of  connexion  between  winter  severity  and 
mortality.     In  the  same  way,  if  we  had  the  statistics  of  the 
deaths  occurring  at  different  hours  of  the  day.  we  might  find 
a  greater  number  occurring  in  the  depressing  hours  of  the 
night,  namely,  between  midnight  and  dawn.     There  is  an 
element  of  chance,  and  an  element  of  law  ;  the  chance  can  be 
eliminated  by  statistics,  and  the  law  ascertained  and  estimated. 
The  combination  of  chance  and  law  is  seen  in  the  progress  of 
the  seasons.     The  Chance  element  is  the  fluctuation  from  day 
to  day,  due  to  meteorological  changes,  which,  in  our  ignorance, 
we  view  as  fortuitous.     The  Law  is  the  progress  of  the  sun, 
which  if  undisturbed  would  be  shown  in  the  steady  increase  of 
temperature  from  January  to  July,  and  reversely.     The  influ- 
ence of  the  winds  interferes  with  this  regular  course  ;  but  by 
averages  taken  for  many  years,  we  could  ascertain  for  any  one 
place  the  temperature  proper  to  each  day  of  the  year,  through 
the  solar  influence  alone. 

The  skill  of  a  player  at  cards  is  shown  by  his  winnings  at  a 
year's  end.  So,  the  keeper  of  a  gaming  table,  in  spite  of  daily 
fluctuations,  has  a  sure  profit  in  the  long  run  ;  the  table  being 
constructed  with  a  definite  percentage  in  his  favour. 

In  taking  observations,  it  is  usual  to  multiply  instances,  and 
to  strike  an  average.  This  eliminates  mistakes  of  the  senses, 
accidents,  and  all  errors  that  do  not  grow  out  of  some  perma- 
nent bias. 

5.  A  third  form  of  the  elimination  of  chance  is  the 
discovery  of  causes  so  small  in  amount  as  to  be  submerged 
by  the  casual  accompaniments. 

Loaded  dice  are  detected  after  a  long  series  of  throws. 
Actual  trials  have  shown  that,  in  the  course  of  1200  throws^ 


•tifiUnirMWMinriiiiillKMM 


3m3S 


»mmm 


^1 


1 


320 


CHAKCK,   AND   ITS   ELIMINATION. 


! 


/ 


\ 


there  would  be  very  nearly  200  turns-op  of  each  side.  Any 
great  deviation  from  equality  would  be  a  proof  of  loading. 

It  was  by  the  average  of  many  daily  observations  of  the 
barometer  that  the  diurnal  variations  were  discovered.  Those 
periodical  variations  were  too  small  to  be  noticed  in  the  midst 
of  the  fluctuations  from  day  to  day ;  but  the  elimination 
of  these  last  by  a  long  course  of  observations  brought  the  other 
to  light,  and  gave  their  amount. 

A  small  bias  in  an  instrument  might  be  detected  by  great 
multiplication  of  instances.  All  the  chance  errors  would  be 
eliminated,  and  would  show  a  residuum,  to  be  accounted  for 
only  by  some  permanent  bias. 

PRINCIPLES   OF   CHANCE   OU   PKOBABILITY. 

6.  Probability  expresses  a  state  of  the  mind,  and  also  a 
situation  among  objective  facts. 

As  a  state  of  the  mind,  it  is  a  grade  or  variety  of  Belief. 
The  highest  degree  of  belief  is  called  Certainty ;  the  inferior 
degrees  are  degrees  of  Probability.  The  psychological  criterion 
of  strength  of  belief  is  readiness  to  act. 

As  a  situation  of  objective  facts,  it  points  to  our  experience 
of  the  recurrence  of  events  with  more  or  less  uniformity, 
What  happens  always,  under  certain  circumstances, — as  the 
rise  of  the  sun,  the  termination  of  human  life — is  called  cer- 
tain ;  our  assurance  in  such  instances  is  at  the  hicrhest.  What 
happens,  not  always,  but  sometimes, — as  that  the  sun  rises  in 
a  cloudless  sky,  that  men  live  seventy  years—  is  not  certain. 
Neither  the  fact,  nor  the  failure  of  the  fact,  is  certain.  To 
this  middle  situation,  is  applied  the  term  Probability. 

At  a  first  glance,  we  might  be  disposed  to  say  that  such 
events  are  positively  uncertain  ;  that  any  judgment  as  to  their 
happening  is  incompetent ;  that  we  are  in  as  great  ignorance 
as  to  whether  the  sun  will  ever  rise  clear,  or  whether  any  man 
will  live  to  seventy,  as  if  we  had  never  known  the  sun  to  rise 
or  any  man  to  die.  In  this  emergency,  however,  we  derive 
an  aid  from  extended  observation.  If,  in  the  same  locality, 
we  observe  the  rise  of  the  sun  for  a  great  many  days,  we  find 
that  the  rise  in  a  clear  sky  happens  in  a  certain  fixed  propor- 
tion, which  is  more  and  more  steady  as  observation  is  pro- 
longed. So,  if  we  keep  a  record  of  the  duration  of  men's 
lives,  for  a  considerable  period  of  time,  we  find  the  seventy 
years'  lives  to  recur  in  a  fixed  proportion,  the  more  steady  the 
longer  the  records  are  extended.     Hence,  if  it  is  of  any  valae 


PRINCIPLES   OF  CHANCE. 


321 


to  ns  to  know  how  many  days  in  the  year  the  sun  rises  cloud- 
less in  a  given  climate,  or  how  many  men  live  to  seventy,  we 
can  obtain  the  information  with  absolute  certainty. 

Now,  there  are  many  occasions  when  this  knowledge  of 
proportionate  recurrences  of  events,  or  of  what  is  called 
averages,  is  of  the  highest  practical  moment.  It  is  needless 
to  cite,  among  other  examples,  the  system  of  Insurance,  which 
is  wholly  built  upon  it. 

7.  When  a  sufficiently  extended  series  of  observations 
shows  a  fixed  proportion  in  the  relative  occurrence  of 
events,  this  proportion  is  called  the  Probability  of  the 
occurrence  of  any  single  event ;  which,  however,  is  a  fiction, 
meaning  only  the  certainty  of  the  proportion,  or  average, 
on  the  whole. 

If,  in  the  run  of  many  years,  it  appears  that  there  have  been, 
in  some  one  place  four  dry  days  for  three  wet,  then  it  is  a 
matter  of  inductive  certainty,  that  in  the  future  that  propor- 
tion will  hold.  We  may  stake  any  practical  interest  upon  the 
recurrence  of  that  proportion.  But  we  are  unable  to  say,  be- 
fore hand,  of  any  one  day  whether  it  will  be  wet  or  dry.  Still, 
a  convenient  fiction  is  used  applicable  to  a  single  day.  We 
see  that  the  chances  or  probabilities  are  that  some  given  day 
will  be  dry.  A  numerical  expression  is  used  for  the  degree  of 
the  probability ;  it  is  said  to  be  four  to  three  in  favour  of  dry- 
ness, or  against  rain.  This  does  not  mean  that  we  gain  any- 
thing in  a  single  case ;  a  case  taken  apart  must  be  held  as 
|ibsolutely  uncertain.  Unless  we  act  upon  the  gross  or  total, 
we  gain  nothing  by  taking  into  account  the  numerical  pro- 
babilities with  a  view  to  a  single  instance. 

But  although  we  are  no  wiser  as  to  the  individual  day  that 
we  desire  to  be  dry  or  wet,  yet,  as  there  are  a  great  many 
similar  emergencies  in  life,  where  we  have  to  apply  averages 
to  single  cases, — by  following  the  measure  of  probability  on  all 
such  occasions,  and  on  all  subjects,  we  shall  be  oftener  right 
on  the  whole,  than  if  we  were  to  neglect  this  probability. 
This  is  the  justification  of  our  presuming  that  a  given  day  will 
be  dry  and  not  wet,  under  the  probability  assigned. 

8.  It  is  found  that  the  experienced  recurrence  of  events 
coincides  with  an  estimate  formed  thus  : — Suppose  that  we 
know  of  several  events  that  some  one  will  certainly  happen, 
and  that  nothing  in  the  constitution  of  things  determines 
one  rather  than  another ;  in  that  case  each  will  recur,  ia 


-   tWftWgllii   HiiriMllt  -        V 


322 


CHANCE,  AND  ITS  ELIMINATION. 


COIUBINATION   OF  PROBABILITIES. 


II 


{ 


the  long  run,  with  a  frequency  in  the  proportion  of  one  to 
the  whole. 

Thns,  in  the  familiar  case  of  tossing  a  penny,  there  is  sup- 
posed to  be  nothing  in  the  form  of  the  coin,  or  in  the  impulse 
given  to  it,  to  determine  one  side  rather  than  another.  In 
this  case,  every  second  throw  will,  in  the  long  run,  be  heads. 

So,  in  throwing  dice,  if  they  are  fair,  every  sixth  throw,  on 
a  long  series  of  trials,  will  give  ace. 

An  a  priori  necessity  has  been  assumed  for  this  proportionate 
recurrence  of  events.  Such  a  necessity  appears  to  be  justified 
in  the  tossing  of  a  penny  ;  we  seem  to  be  in  a  state  of  equipoise 
between  the  two  possibilities  of  head  and  tail,  and  feel  that 
any  inequality  in  the  result  would  be  without  reason  or  cause. 
Accordingly,  we  are  apt  to  assume,  as  a  necessity  of  the  case, 
that  the  turning  up  of  head  and  of  tail  should  be  equally 
balanced  at  the  end  of  a  long  trial.  The  fact  is,  however,  that, 
in  this  and  like  casoe,  we  are  exceptionally  circumstanced  in 
point  of  knowledge  ;  we  know  what  are  the  causes  at  work, 
and  that  there  is  nothing  to  give  a  bias  in  the  long  run  to 
either  side  of  the  penny. 

In  the  more  complicated  cases,  as  human  life,  shipwrecks, 
fires,  &c.,  we  should  not  be  disposed  to  predict  anything  before 
hand  from  such  considerations  as  the  above.  We  should  not 
consider  all  years,  from  one  to  ninety,  as  equally  open  for  men 
to  die  in,  or  that  the  year  of  age  is  quite  indifferent.  We  soon 
come  to  know  better ;  and,  refraining  from  a  prion  supposi- 
positions  we  trust  solely  to  induction  from  a  sufficiently 
prolonged  basis  of  actual  observation. 

9.  The  important  theorems  growing  out  of  the  general 
principles  and  applied  to  problems  in  Logic,  are  these. 

I.  The  probability  of  the  concurrence  of  two  indepen- 
dent events  is  the  product  of  the  separate  probabilities. 

If  A  occur  once  in  six  times,  its  probability  is  J,  or  one  for 
and  five  against ;  if  B  occur  once  in  ten  times,  its  probability 
is  y^^,  or  one  for,  and  nine  against ;  the  probability,  or  relative 
frequency  in  the  long  run,  of  the  concurrence  of  the  two  is 
^ — one  for  and  fifty-nine  against. 

This  rule  is  an  arithmetical  consequence  of  the  general  for- 
mula, and  does  not  need  a  separate  appeal  to  observation  and 
induction.  Suppose  two  days  in  three  are  dry,  and  one  in 
three  haa  a  westerly  wind,  then  (if  the  two  phenomena  were 


323 


independent),  the  chance  is  |  X  J  or  f ;  that  is  two  for  and 
seven  against. 

10.  II.  The  probability  of  the  occurrence  of  one  or  other 
of  two  events  that  cannut  concur  is  the  sum  of  the  separate 
probabilities. 

*  If  one  man  in  ten  is  over  six  feet,  and  one  in  twelve  under 
five ;  then  in  a  large  number,  say  120,U0  3,  there  will  be  about 
12,000  over-six-feet  .men,  and  about  10,000  under-five-feet 
men  ;  the  sum  of  the  two  22,000,  will  represent  the  number  of 
such  as  are  one  kind  or  the  other.' 

11.  III.  The  rule  for  the  cumulation  of  independent 
Testimonies  in  favour  of  a  fact,  is  to  multiply  the  numbers 
expressing  the  proportionate  value  of  each  Testimony. 

If  a  witness  is  correct  six  times  out  of  seven,  or  speaks  six 
truths  for  one  error,  his  relative  testimony  is  six  for  and  one 
against,  or  ^.  Two  witnesses  of  this  character  concurring 
would  give  a  probability  of  6  to  1  multiplied  by  6  to  1,  or 
36  to  1,  and  so  on. 

12.  IV.  The  rule  for  the  deterioration  of  testimony  in 
passing  from  one  person  to  another,  that  is,  for  the  weaken- 
ing of  traditional  evidence  through  lapse  of  time,  is  to 
multiply  the  fractions  expressing  the  separate  probabilities. 

If  one  witness  speaks  truth  five  times  in  six,  the  fraction  is 
^ ;  if  another  witness  speaks  truth  nine  times  in  ten,  the  value 
is  ^^.  If  the  one  repeats  what  he  has  heard  from  the  other, 
the  testimony  is  weakened  by  the  transmission  to  #  < 
A  =  I  &»  or  |.  Of  facts  attested  by  the  second  witness,  de- 
riving from  the  first,  three  will  be  true  and  one  false.  A  few 
such  transitions  bring  the  evidence  below  probability,  and 
render  it  worthless.  Four  successive  witnesses  each  valued 
I,  would  give  t^^t,  which  would  be  a  probability  against  their 
testimony.  Now,  there  are  many  cases  where  a  testimony  is  not 
put  too  low  by  the  above  fraction  ;  if  a  want  of  perfect  veracity 
is  joined  with  inadequate  comprehension  of  the  statement, 
weak  memory,  or  other  infirmity,  a  witness  would  not  be  correct 
three  times  in  four. 

The  application  of  the  Theory  of  Probabilities  to  the  induc- 
tive determination  of  Causes  is  given  in  the  folio  win  o-  theorem 
taken  by  Mill  from  Laplace. 


tmmmmmn^mt 


ii^ii  <  •mmmmimr* 


'mami'mf 


324 


CHANCE,  AND  ITS   RUMINATION. 


H: 


tf 


13.  '  Given  an  effect  to  be  accounted  for,  and  there  being 
several  causes  that  might  have  produced  it,  but  of  whose 
presence  in  the  particular  case  nothing  is  known;  the 
probability  that  the  effect  was  produced  by  any  of  these 
causes  is  as  the  antecedent  probability  of  the  cause,  7nultipked 
hy  the  probability  that  the  cause,  if  it  existed,  woidd  have  fro- 
duced  the  given  effect. 

» Let  M  be  the  effect,  and  A,  B,  two  causes,  by  either  of 
which  the  effect  might  have  been  produced.  To  find  the  pro- 
babihty  that  it  was  produced  by  the  one  and  not  by  the  other, 
ascertain  which  of  the  two  is  most  likely  to  have  existed,  and 
which  of  them,  if  it  did  exist,  was  most  likely  to  produce  the 
effect  M ;  the  probability  sought  is  a  compound  of  these  two 

probabilities.  ,     .      ,  j 

*  Case  I.  Let  the  causes  A  and  B  be  both  alike  m  the  second 
respect :  either  A  or  B,  when  existing,  being  supposed  equally 
likely  (or  equally  certain)  to  produce  M  ;  but  let  A  be  itself 
twice  as  likely  as  B  to  exist,  that  is  twice  as  frequent  a  pheno- 
menon. Then  it  is  twice  as  likely  to  have  existed  in  this  case, 
and  to  have  been  the  producing  cause  of  M. 

*  Case  IL  Reversing  the  last  supposition,  let  us  suppose  that 
the  causes  are  equally  frequent,  equally  likely  to  have  existed, 
but  not  equally  hkely,  if  they  did  exist,  to  produce  M  ;  that  in 
three  times  that  A  occurs,  it  produces  that  effect  twice,  while 
B,  in  every  three  times  produces  it  but  once.  Since  the  two 
causes  are  equally  frequent  in  their  occurrence,  in  every  six 
times  that  either  exists,  A  is  three  times  and  B  three  times. 
But  A  in  three  occurrences  produces  M  in  two  ;  while  B  in 
three  occurrences  produces  M  in  one.  Thus,  in  the  whole  six 
times,  M  is  produced  thrice,  but  twice  by  A  and  once  by  B. 
So  that  the  probability  is  in  favour  of  A  in  the  proportion  of 

two  to  one.  i       t   a 

*  Case  III.  Let  there  be  an  inequality  in  both  respects.  Let 
A  be  twice  as  frequent  as  B  ;  and  let  A  produce  the  eflect 
twice  in  four  times;  B  thrice  in  four  times.  Then  the 
antecedent  probability  of  A  to  B  is  2  to  1  :  the  probability 
of  their  producing  M  is  as  2  to  3  ;  the  product  is  4  to  3. 
In  other  words  the  probabilities  in  favour  of  A  being  the 
cause  are  as  4  to  3.     And  so  on  with  any  other  combination.* 

The  principle  may  be  applied  to  distinguish  casual  coin- 
cidences from  those  that  result  from  law.  *  The  given  fact 
may  have  originated  either  in  a  casual  conjunction  of  causes, 
or  in  a  law  of  nature.     The  probabilities,  therefore,  that  tlie 


CHANCE  APPLIED  TO   CAUSATION. 


325 


« 

V 


i 


fact  originated  in  these  two  modes,  are  as  their  antecedent 
probability,  multiplied  by  the  probabilities  that  if  they  existed 
they  would  produce  the  effect.  But  the  peculiar  combination 
of  chances,  if  it  occurred,  or  the  law  of  nature  if  real,  would 
certainly  produce  the  series  of  coincidences.  The  probabilities, 
therefore,  are  as  the  antecedent  probabilities  of  the  causes! 
One  of  these — the  antecedent  probability  of  the  combination  of 
mere  chances  that  would  produce  the  given  result — is  an 
appreciable  quantity,  on  the  principles  already  laid  down. 
The  antecedent  probability  of  the  other  may  be  estimated  more 
or  less  exactly,  according  to  the  nature  of  the  ca^ie.* 


CHAPTER  X. 
ETOUCTION  AIDED  BY  DEDUCTI02T. 

1.  It  is  desirable  at  every  stage  to  carry  out  luductive 
laws  into  their  Deductive  applications.  Now,  Deductions 
cannot  be  made  or  verified  without  Observation  of  facts. 

Deduction  or  Ratiocination,  in  its  purely  formal  aspect,  is 
given  in  the  Syllogism.  In  its  material  side,  it  involves  the 
comparison  of  facts,  and  is  akin  to  Induction.  We  have  yet 
to  view  it  as  it  plays  a  part  in  the  Inductive  Sciences. 

2.  The  full  scope  of  the  Deductive  Method  comprises 
three  operations. 

I.  There  must  be  certain  pre-established  Inductions. 

We  must  somehow  arrive  at  Inductive  Generalizations,  and 
next  prove  them  when  arrived  at.  The  Experimental  Methods 
have  in  view  these  two  ends,  and  especially  the  last,  namely, 
Proof.  Incidentally,  the  methods  indicate  the  mode  of  Dis- 
covery, but  they  have  not  been  expressly  aimed  with  that  view. 
It  has  been  apparent,  however,  that  the  collection  and  study  of 
instances,  under  the  Method  of  Agreement,  must  suggest  the 
points  of  Agreement,  when  we  are  ignorant  of  them,  which  is 
to  suggest  a  general  law.  Our  examination  of  the  problem  of 
Crystallization,  and  the  enquiry  into  the  cause  of  Dew,  led 
first  to  the  discovery,  and  next  to  the  proof,  of  generalized 
coincidences.     Still,  it  was  not  advisable  to  carry  on  a  double 


I 


326 


INDUCTION   AIDED  BY  DEDUCTION. 


illustration,  by  means  of  the  Experimental  Methods,  to  eluci- 
date at  once  Discovery  and  Proof;  of  the  two  ends,  the 
logician  has  most  to  do  with  the  second  ;  Proof  is  his  main 
object,  for  which  he  can  lay  down  definite  laws  ;  Discovery  is 
a  valuable  end,  likewise,  but  it  is  not  equally  amenable  to 
prescribed  rules. 

In  the  management  of  particular  instances,  with  a  view  to 
the  Discovery  of  generalities,  assistance  may  be  obtained  in  the 
three  following  ways  : — 

(1)  The  number  of  instances  should  be  as  extensive  as  pos- 
sible. In  the  comparison  of  a  large  number  the  mind  will  be 
struck  with  points  of  community,  from  the  very  fact  of  the 
recurrence ;  as  in  the  examples  collected  in  the  research  on 
Dew.  Moreover,  there  will  start  forth  some  one  that  contains 
the  circumstance  sought,  in  startling  prominence ;  these  are 
the  glaring  or  suggestive  instances.  Such,  in  the  case  of 
Dew,  was  the  example  of  the  warm  breath  upon  a  cold  iron 
surface,  as  a  knife  blade. 

(2)  When  out  of  mere  number  and  variety  of  instances,  ihe 
identity  does  not  flash  upon  the  mind,  the  next  thing  is  to 
select  a  few  for  careful  scrutiny.  Each  instance  should  be 
studied  in  isolation,  should  be  gone  over  in  every  minute  point, 
and  examined  from  every  side ;  the  features  being  exhaustively 
set  down  in  writing.  After  a  few  separate  instances  have  been 
considered  in  this  thorough  way,  the  resemblances  (unless  at 
the  time  inscrutable  for  want  of  other  lights)  will  become 
apparent  to  the  view.  Newton's  study  of  the  phenomenon  of 
the  coloured  rings  of  the  soap-bubble,  was  an  exercise  of  the 
severe  mental  concentration  now  described. 

(3)  The  general  laws  of  phenomena  must  be  sought  in  the 
cases  where  they  are  least  complicated  or  combined  with  other 
laws.  This  is  an  obvious  precaution  conducing  to  Discovery. 
The  laws  of  motion  are  studied  in  simple  cases,  such  as  straight- 
lined  movements,  or  wheel-movements,  under  a  single  impulse. 
Gravity  is  lest  stiu'ied  in  bodies  falling  parpendicularly,  where 
there  is  no  other  force  operating.  Neither  the  first  law  of  motion, 
nor  the  law  of  gravity,  could  have  been  advantageously  genera- 
lized, in  the  flow  of  rivers,  or  in  the  motions  of  the  planets. 
These  complications  are  not  suited  for  inductive  discovery,  but 
for  deductive  application,  as  at  present  contemplated.  The 
first  principles  of  Optics  are  sought,  not  in  the  workings  of  the 
eye,  nor  in  complicated  lenses,  but  in  the  simple  mirror  fop 
reflexion,  and  in  the  plane  transparent  surface  for  refraction. 
So  the  more  tiaisre  dental  powers  of  light,  in  cai  sing  mole* 


[ 


♦,-  V.^2 


SIMPLE  DEDUCTION. 


327 


cnlar  change,  are  not  studied  on  the  retina  of  the  eye,  but  in 
the  easier  (although  still  obscure)  cases— chemical  action  and 
photography.  The  osmotic  action  of  cells  is  illustrated  by 
Graham's  experiments  on  the  passage  of  liquids  through  por- 
celain partitions.  The  capillary  circulation  of  the  blood  is 
compared  to  the  flow  of  liquids  in  capillary  tubes.  Salivation 
and  digestion  are  examined  by  withdrawing  saliva  and  gas- 
tric juice  from  the  animal  body,  and  subjecting  difierent 
materials  to  their  action  apart.  The  laws  of  Mind,  which  are 
to  be  carried  out  deductively  in  resolving  the  complicated 
situations  of  human  beings,  as  in  Society,  are  to  be  generahzed 
from  observations  of  the  individual  man  in  favourable  situa- 
tions. For  the  laws  of  mental  growth,  we  have  to  begin  at 
infancy ;  for  the  germs  of  moral  sentiment,  we  refer  to  the 
uncivilized  races.* 

3.  II.  Deduction  proper  involves  two  stages  of  com- 
plexity ;  (I)  The  simple  extension  of  an  inductive  law  to 
a  new  case ,  and  (2)  the  combination  of  several  laws  in  a 
conjoint  result,  involving  processes  of  Computation. 

(1)  Simple  Deduction  is  the  extending  of  an  inductive 
generalization  to  new  cases.  As  in  all  enlargements  of  know- 
ledge, so  in  this,  there  is  both  discovery  and  proof.  The  cases 
have  first  to  be  suggested  to  the  mind,  and  next  to  be  rigor- 
ously verified  by  the  procedure  suited  to  the  case. 

Without  dwelling  upon  the  means  of  suggesting  new 
applications  of  laws,  let  us  consider  the  mode  of  proving  such 
applications.     This  resolves  itself  into  a  question  of  identity. 

Supposing  that  the  inductive  preposition  *  all  matter  gi'avi- 
tates '  has  been  formed  upon  solids  and  liquids,  shall  we  apply 
it  to  gases  ?  This  depends  upon  whether  gases  are  matter — 
whether  any  property  of  gases  is  identical  with  the  defining 
property  of  matter.  Now,  the  defining  property  of  matter  is 
inertia,  and  gases  are  proved  to  possess  this  property ;  whence, 
the  proposition  *  matter  gravitates'  is  extended  to  them. 
Again,  Does  Ether  (the  supposed  medium  of  Light  and  Heat) 
also  gravitate  ?  As  before,  we  must  test  its  identity  with  the 
characteristic  property  of  matter.  Now,  if,  as  seems  to  be 
implied  in  the  retardation  of  Encke's  comet,  the  ether  is 
a  resisting  substance,  then  it  is  matter,  and  accordingly 
gravitates. 

•  The  Arts  of  Discovery,  brought  out  by  scattered  allusions  throughout 
the  work,  will  be  sj  stematic  lly  given  in  Appendi  ;  H. 
15 


m 


328 


INDUCTION  AIDED  BY  DEDUCTION. 


ii 


\ 


Questions  of  identifcy  to  establish  a  minor  are  necessarily 
part  and  parcel  of  inductive  research  ;  but  they  must  not  be 
confounded,  as  they  sometimes  are,  with  the  process  of  induc- 
tive generalization  to  establish  a  major  •  or  a  general  law. 
Thus,  it  is  a  moot  point,  whether  any,  and  what  alloys  are 
chemical  compounds;  which  must  be  settled  by  examining 
the  characteristics  of  alloys,  and  comparing  them  with  the 
essentials  or  characteristics  of  chemical  combination. 

We  may  instance  important  researches  that  have  for  their 
end  the  proof  of  an  identity.  Thus,  Dr.  Andrews  insti- 
tuted a  series  of  experiments  to  identify  Ozone  (formed  by 
Electricity)  with  the  atmospheric  constituent  that  decomposes 
Iodide  of  Potassium.  He  selected  thre^  peculiarities  of 
ozone  ;— (1)  the  power  of  oxidizing  mercury,  (2)  the  destruc- 
tion of  ozone  reactions  by  dry  peroxide  of  manganese,  (3)  the 
destruction  of  its  reactions  at  a  high  rate  of  temperature 
(237°  C)  ;  and  tried  the  element  found  in  the  atmosphere  by 
these  tests.  It  answered  to  them  all.  The  first,  however, 
(the  oxidizing  of  mercury)  is  not  conclusive,  as  other  bodies, 
besides  ozone,  tarnish  mercury.  The  last  of  the  three  tests 
(high  temperature),  answers  to  no  known  substance,  except 
ozone.  The  three  tests  conjoined  furnish  superabundant 
evidence  of  the  identity  of  the  so-called  ozone  of  the  air,  with 
ozone  as  obtained  by  electrolysis,  and  by  the  electrical  machine. 

Another  remarkable  discovery  of  Identity  is  seen  in  Graham's 
experiments  on  the  relations  of  Hydrogen  to  Palladium. 
There  have  always  been  chemical  reasons  for  believing  that 
hydrogen  gas  is  the  vapour  of  a  highly  volatile  metal. 
Graham  has  contributed  new  evidence  in  favour  x)f  the 
identity.  The  metal  palladium  is  capable  of  absorbing  eight 
or  nine  hundred  times  its  volume  of  hydrogen  gas  ;  and, 
when  so  charged,  is  found  to  undergo  changes  in  Density, 
Tenacity,  Electrical  Conductivity,  Magnetism,  relations  to  Heat, 
and  Chemical  properties.  On  investigating  these  changes, 
Graham  shows  that  they  correspond  to  the  alterations  made 
on  one  metal  when  united  in  an  alloy  with  another  metal ;  so 
that,  as  far  as  metallic  properties  can  be  shown  in  such  a  union, 
hydrogen  is  metallic.  The  metal  *  hydrogenium '  has  a  white 
aspect,  is  of  sp.  gr.  2,  has  a  certain  amount  of  tenacity,  and  is 
magnetic.  The  cumulation  of  proof  is  all  but  equivalent  to 
the  separate  production  of  the  solid  metal. 

Sir  G.  C.  Lewis  confounds  the  establishment  of  a  minor,  as 
a  part  of  Deduction,  with  the  establishment  of  an  Inductive 
major  by  the  method  of  Difference.     He  considers  that  the 


COMBINATION  OP  DEDUCTIONS. 


329 


^u'v  ^i  *  ^^^gla^  in  a  Court  of  Law,  or  the  proof  that  Sir 
ftLiiip  J^rancis  wrote  Junius,  is  an  employment  of  the  Experi- 
mental or  Inductive  method  of  Difference  as  one  of  the 
Inductive  methods.  In  reality,  all  such  cases  are  the  making 
good  of  an  identity  to  prove  a  minor.  The  kind  of  Diflerence 
employed  consists  in  bringing  out  successive  details  or  cir- 
cumstantials, to  exclude  by  degrees  every  person  but  one: 
and  thereby  to  complete  the  identity  of  that  one  person  with 
tne  actor  m  the  given  case. 

(2)  The  more  difficult  employment  of  Deduction  is  in  the 
concurrence  of  different  agents  to  a  combined  resalt ;  as 
when  we  deduce  the  path  of  a  projectile  from  gravity,  the 
torce  of  projection,  and  the  resistance  of  the  air ;  or  the  tides 
trom  the  united  action  of  the  sun  and  the  moon.  This  is  the 
torm  of  the  Deductive  Method,  whereby  we  cope  with  the 
otherwise  intractable  situation  called  Intermixture  of  Effects 

Physical  Astronomy  will  ever  remain  the  grand  exemplar 
ot  JJeductive  Investigation,  as  the  computation  of  joint  causes 
producing  an  effect.  The  causes  can  be  estimated  with  numeri- 
cal precision,  and  their  combined  operation  can  be  calculated 
by  the  higher  Mathematics.  In  other  parts  of  Physics,  there 
are  instances  of  the  Deductive  Method.  The  calculations 
respecting  Machinery,  Fluid  Pressures,  Motions  of  Fluids 
Gaseous  Pressure  and  Movements,  Sound,  Light,  Heat,  Elec-' 
tncity,— proceed  upon  inductive  laws,  often  united  in  their 
opei-ation,  and  requiring  to  be  computed  in  their  joint  effect. 

It  has  been  seen,  in  the  research  on  Dew,  that  Dal  ton's 
generalization  of  the  laws  and  constitution  of  the  atmosphere 
of  vapour,  deductively  applied,  made  up  the  wanting  liuk  in 
the  experimental  investigation. 

Equally  telling  examples  of  the  Deductive  Method  may  be 
culled  from  the  recent  applications  of  Chemistry  to  Animal 
Physiology.      The  laws  of  chemical  combination  enable  us  to 
trace  the  metamorphosis  of  tissue,  by  means  of  the  products 
of  waste.      The  single  fact  of  oxidation  is  all-pervading  in  the 
animal  system,  and  the  deductions  from  it  clear  up  at  once 
many  obscurities  beyond  the  reach  of  experimental  elimina- 
tion.    The  difficult  question  of  Animal  Heat  is  to  a  great 
extent  solved  already  by  this  deductive  application,  and  its 
complete  solution  will  probably  depend  on  the  same  method. 
We  may  quote  farther  the  special  applications  of  Chemistry 
under  the  great  law  of  Persistence,  to  the  phenomenon  of 
muscular  power,  of  which  no  adequate  account  could  be  given 
by  mere   observation  or  experiment.      We  now   know  that 


.^  ^1 


iJ] 


II 


330 


INDUCTION   AIDED  BY  DEDUCTION. 


VEKIFICATION  OF  DEDUCTIONS. 


331 


muscular  expenditure  represents  a  definite  combustion  of  the 
material  of  the  food,  although  we  do  not  kuow  the  precise 
links  of  the  transmutation. 

When  purely  Inductive  or  Experimental  proofs  are  sup- 
ported by  reasons^  or  by  a  consideration  of  the  nature  of  t/ie 
case,  the  meaning  is  that  Deduction  is  brought  to  the  aid  of 
Induction.  The  conclusion  respecting  the  N.  E.  wind  was 
confirmed  by  the  general  operation  of  atmospheric  impurities. 
The  result  gained  from  the  comparison  of  instances  of  Crystal- 
lization, is  in  accordance  with  the  theoretical  views  of  the 
two  opposing  molecular  forces  —  attraction  and  repulsion. 
The  experimental  facts  as  to  the  exhaustion  of  the  mind  along 
with  the  body,  are  supported  by  what  we  know  of  the  brain 
as  the  organ  of  the  mind.  Our  inductions  respecting  despotic 
governments  are  aided  by  deductions  from  the  laws  of  human 

nature. 

The  applications  to  the  Human  Mind,  to  Character,  and  to 
Society,   will    be  more    fully    exemplified  afterwards,    in  the. 
special  chapters  on  the  Methods  of  these  Sciences. 

4.  III.  The  Deductive  process  is  completed  by  Verifi- 
cation. 

This  applies  more   particularly  to  the  Couiputation  of 

combined  causes. 

The  way  to  verify  the  deductive  extension  of  a  single  law  to 
a  new  case,  is  actual  observation  of  that  case.  We  apply 
deductively  the  law  of  gravity  to  air,  and  verify  the  deduction 
by  observing  whether  the  air  has  weight.  As,  however,  we 
may  dispense  with  deduction  when  we  have  actual  observation, 
such  an  instance  does  not  show  the  power  of  the  Deductive 
Method.  The  thing  meant  is,  that  after  verifying  a  deduction 
by  one  or  more  instances,  we  shall  be  able  to  apply  it  to  other 
instances  without  farther  verification  ;  these  last  instances 
depending  for  their  proof  solely  on  the  deductive  process. 

When  an  effect  is  the  result  of  several  conspiring  causes,  we 
may  deduce  it  from  a  computation  of  the  causes ;  as,  for 
example,  the  lunar  and  planetary  perturbations.  To  show 
that  we  have  taken  account  of  all  the  causes,  that  we  have 
obtained  a  proper  estimate  of  each,  and  that  we  have  correctly 
computed  their  conjoined  action,  we  must  compare  the  deduced 
effects  with  the  observed  effects  in  a  variety  of  instances.  If 
the  two  precisely  tally,  the  deductive  machinery  is  verified  ; 
if  not,  not.  A  want  of  accordance  points  to  a  defect  in  one  or 
other  of  the  circumstances  quoted : — the  causes  or  agents  • -e 


not  fully  taken  account  of;  their  exact  amount  is  not  precisely 
obtamed;  or  the  calculation  of  theii-  united  action  is  not 
perfect.  Sometimes,  the  first  point  is  defective,  there  being  a 
residual  agent.  In  other  cases,  we  know  -the  cause  but  not  its 
exact  numerical  amount;  thus,  in  Astronomy,  we  need  to 
know  the  relative  masses  of  the  sun,  moon,  and  planets, 
together  with  their  mutual  distances.  Finally,  it  may  happen 
that  the  calculations  are  impracticable. 

In  Astronomy,  where  Deduction  has  gained  its  greatest 
trmmphs,  verification  has  also  been  most  thoroughly  worked. 
Upwards  of  fifty  Observatories  are  incessantly"  engaged  in 
watchmg  celestial  phenomena ;  the  observations  have'  been 
the  means  of  perfecting  the  deductive  operation,  and  making 
good  all  its  shortcomings. 

^  The  deductive  theory  of  projectiles  combined  gravity,  pro- 
jectile force,  and  the  air's  resistance  ;  the  experiments  on 
gunnery  are  the  verification. 

The  laws  of  the  strength  of  materials  are  deduced  from 
geometrical  and  mechanical  laws,  involving  the  size,  shape, 
and  position  of  beams,  &c. ;  but  however  certain  the  principles 
may  appear,  they  cannot  dispense  with  actual  trials. 

Wo  have  supposed  the  verifying  tests  to  consist  of  detached 
observations ;  they  may  be  furnished  by  groups  of  observa- 
tions,  summed  up  into  what  are  termed  Empirical  Laws, 
buch  was  the  verification  of  Newton's  planetary  theory 
(founded  on  gravity)  by  Kepler's  Laws.  So,  any  theorv  or 
generalization  of  the  operation  of  refracting  surfaces  on  light, 
must  be  in  consistency  with  Snell's  law  of  the  proportion  of 
the  sines  of  incidence  and  refraction. 

The  formulaB  of  fluid  motions  are  of  themselves  insufficient 
to  predict  the  facts  ;  experiments  on  the  flow  of  rivers  must 
be  conjoined  in  a  matter  of  so  great  complicacy. 

Newton  calculated  deductively  the  velocity  of  sound,  and,  on 
comparing  it  with  the  observed  velocity,  found  a  difference  of 
nearly  twenty  per  cent.  It  is  only  of  late  years,  that  the  dis- 
crepancy has  been  got  over,  by  a  more  complete  view  of  the 
forces  developed  in  the  act  of  propagation.  In  such  a  delicate 
question,  one  verifying  instance  is  too  little.  Newton  himself 
equared  the  results  by  arbitrary  assumptions  (as  the  thickness 
ot  the  air  particles),  which  would  have  required  for  their  con- 
firmation  an  independent  class  of  facts. 

Very  confident  prediccions  have  been  made  to  the  intent 
that  the  Sun  is  cooling  down  in  consequence  of  his  enormous 
radiation  ;  and  that  the  earth's  rotation  must  ultimately  decay 


I 


■atisiUuiM^ 


332 


INDUCTION  AIDED  BY   DEDUCTION. 


IMPORTANCE  OF  SECONDARY  LAWS. 


S3S  . 


throngh  the  friction  of  the  Tides.  The  data  and  the  calcula- 
tions seem  very  secure  in  both  instances ;  yet,  in  order  that 
the  deductions  may  be  fully  established,  we  need  evidence  of 
An  actual  change,  in  past  time,  as  regards  both  these  moment- 
ous facts. 

Combined  Induction  and  Deduction  expresses  the  full  force 
of  scientific  method  for  resolving  the  greatest  complications. 
Induction  alone,  and  Deduction  alone,  are  equally  incompetent 
to  the  great  problems  even  of  the  Inorganic  world  ;  still  more 
so  with  Life,  Mind,  and  Society.  Induction,  exclusively  relied 
on,  is  called  '  empiricism ; '  Deduction,  without  an  adequate 
basis  and  an  adequate  check  in  the  Inductive  Methods,  ex- 
presses the  bad  sense  of  *  theoretical,' 

The  two  following  chapters  will  continue  the  exemplification 
of  the  Deductive  Method,  of  which  they  merely  vary  the 
aspect. 


CHAPTER  XI. 

SECONDABT  LAWS— EMPIRICAL  AND  DERIYATIYB. 

1.  The  importance  of  Secondary  (as  opposed  to  Ulti- 
mate) Laws,  grows  out  of  their  close  adaptation  to  concrete 
realities. 

Speculation  delights  to  attain  ultimate  generalities,  which 
give  the  key  to  a  vast  department  of  nature  ;  as  Gravity, 
Conservation,  and  Relativity.  These  are  highly  satisfactory 
to  the  mind  in  its  craving  after  unity,  simplicity,  *  the  one  in 
the  many.'  A  far  more  important  use  of  these  supreme 
generalities  is  to  perfect  the  statement  of  the  Secondaiy  Laws, 
which  are  the  more  immediate  guides  of  conduct,  and  the 
expression  of  the  phenomena  in  their  actual  or  concrete 
embodiment.  The  generalization  of  gravity  did  not  supersede 
Kepler's  Laws  of  the  Planetary  Motions.  So  long  as  the 
concrete  fact  of  planetary  motion  has  an  interest  for  us,  so 
long  are  we  concerned  with  the  secondary  laws  representing 
that  fact.  The  use  of  the  higher  laws  of  Newton  is  to  render 
these  indispensable  secondary  laws  more  precise. 

The  secondary  laws  are  the  *  media  axiomata'  of  Bacon. 
They  were  viewed  by  him  (too  exclusively)  as  the  steps  for 
ascending  to  the  supreme  laws.      Equally   essential   is   the 


descending  movement  from  the  higher  to  the  middle  generali- 
ties. No  branch  of  knowledge  is  complete  until  it  has 
assembled  all  the  secondary  laws  that  express  the  more  usual 
configurations  of  actual  phenomena,  and  until  these  secondary 
laws  have  attained  all  the  precision  that  induction  and  deduc- 
tion can  give  them. 

We  formerly  had  occasion  to  remark  (p.  79),  with  reference 
to  Propositions,  that,  like  the  notion,  they  vary  in  regard  to 
the  reciprocal  properties — Extension  and  Comprehension.  As 
we  increase  the  extension,  we  lose  comprehension,  and  con- 
versely. Now,  of  the  two  attributes,  the  one  most  important 
for  us  practically  is  Comprehension.  We  have  to  deal  with 
small  classes,  and  with  individuals,  and  our  interest  lies  in 
knowing  the  whole  of  the  specialities  attaching  to  these.  An 
English  statesman  needs  to  know  the  peculiarities  of  English- 
men. A  physician  has  to  deal  with  the  diseases  special  to 
humanity,  and  still  more  those  special  to  his  own  sphere; 
while  even  this  degree  of  generality,  is  but  to  prepare  him  for 
mastering  individual  cases. 

Hence,  the  narrowing  of  a  proposition,  which  may  seem  a 
defect  to  the  theorizing  or  speculative  intellect,  is  the  highest 
merit  in  applications  to  practice :  provided  always  that  the 
limitation  of  extent  is  accompanied  with  a  corresponding  in- 
crease in  amount  of  predication,  that  is,  in  meaning,  connota- 
tion, or  intent.  The  full  enumeration  of  the  properties  special 
to  iron,  as  it  is  found  in  a  certain  district,  is  essential  to  the 
working  of  that  particular  ore ;  the  account  of  the  properties 
common  to  all  metals  would  be  valuable  merely  as  contributing 
a  quota  to  the  highly  specialized  and  exhaustive  knowledge 
relative  to  the  particular  substance. 

It  was  a  frequent  remark  of  Aristotle  that  the  finishing 
stroke  of  knowledge  is  the  tact  that  modifies  all  general  pro- 
positions according  to  the  individual  case.  This  of  course  is 
in  the  more  purely  practical  point  of  view. 

The  secondary  laws  are  either  Empirical  or  Deef^ative. 

2.  An  Empikical  Law  is  a  uniformity  supposed  to  be 
secondary,  that  is,  resolvable  into  some  more  general  uni- 
formities, but  not  yet  resolved. 

That  quinine  cures  a  fit  of  ague  is  an  Empirical  Law.  It 
is  a  uniformity  established  by  experience  j  it  is,  however,  a 
secondary  uniformity;  we  have  reason  to  believe  that  it  is 


3U 


SECONDARY   LAWS. 


capable  of  being  resolved  into  higher  uniformities.  The  pre- 
sent inabilify  to  resolve  it  is  a  disadvantage,  not  merely  in  a 
theoretical  or  speculative  point  of  view,  but  as  regards  the 
application  of  the  law  in  practice. 

8.  When  what  was  an  Empirical  Law  has  been  resolved 
into  more  general  uniformities,  or  into  highest  laws,  it  is 
termed  a  JJekivative  Law. 

The  occurrence  of  snow  on  high  mountains  was  at  one  time 
an  empirical  uniformity.  It  was  established  as  an  induction 
from  experience,  but  was  not  susceptible  of  being  referred  to 
any  higher  generalizations.  We  can  now  resolve  it  into  the 
laws  connected  with  radiant  heat  passing  through  the  atmos- 
phere. These  may  not  themselves  be  the  highest  attainable 
generalities  ;  still  they  are  much  more  general  than  the  induc- 
tion connecting  snow  with  hei^fht. 

The  converting  of  an  Empirical  Law  into  a  Derivative 
Law  is  a  step  gained  both  in  scientific  explanation,  and  in 
practical  facilities.  The  defects  inherent  in  an  Empirical  Law 
do  not  inhere  to  the  same  degree  in  a  Derivative  Law. 

4.  Empirical  Laws  are  of  various  kinds.  Their  charac- 
ters are  judged  from  their  appearance  after  being  resolved, 
that  is,  made  derivative. 

I.  Many  are  obviously  made  up  of  the  combination  of 
higher  uniformities  under  definite  arrangements  or  collo- 
cations. 

We  see  this  class  largely  exemplified  in  the  explained  oi 
derived  laws.  The  law  of  a  projectile,  Kepler's  laws,  the  tides, 
the  laws  of  wind  and  rain,  the  laws  of  geological  action  (igne- 
ous and  sedimentary),  combustion,  the  nourishment  of  living 
bodies — being  formerly  empirical  laws,  and  now  derived — we 
can,  from  them,  presume  the  character  of  those  that  are  still 
empirical. 

These  combinations  have  been  already  discussed  under  the 
Deductiv3  Method.  They  suppose  certain  ultimate  laws,  con- 
curring in  their  operation,  and  also  a  certain  definite  arrange- 
ment and  amount  of  the  concrete  agencies  or  forces  that  the 
laws  refer  to, 

5.  IL  Some  secondary  laws  take  the  form  of  laws  of 
succession  between  effects  and  remote  causes ;  they  stiD, 
however,  possess  the  character  last  named. 


VARIOUS  KINDS   OF  SECONDARY  LAWS. 


335 


When  a  sudden  shower  disperses  a  crowd,  the  shower  is  a 
very  remote  cause  of  the  effect ;  a  number  of  intermediate 
nnks  of  causation  are  assignable.  The  taking  of  food  is  re- 
moved by  a  good  many  stages  from  the  renewal  of  the  muscu- 
Jar  strength.  The  sowing  of  a  seed  is  followed  at  a  lon<r 
interval  with  the  maturing  of  an  oak. 

This  is  merely  a  superficial  variety  of  the  first  case— com- 
bination of  agents,  in  definite  collocation.  Each  one  of  the 
links  IS  a  distinct  law  of  causation  or  coincidence,  requiring  to 
be  embodied  m  a  definite  collocation  ;  and  the  combination  of 
the  whole,  in  a  suitable  arrangement,  is   necessary  to  the 

6.  IIL  Some  are  laws  of  Co-existence  or  of  Succession 
between  effects  of  the  same  cause. 

Such  are  the  phases  of  the  Tides,  the  flow  of  the  Seasons. 
iJay  and  Night.  Here  also  there  is  the  same  constant  circum' 
stance--a  conjunction  of  agents  and  collocations.  In  every 
case  of  a  secondary  law,  there  is,  from  the  nature  of  the  case, 
more  than  one  power  at  work.  Only. ultimate  laws  express 
agents  m  isolation,  purity,  or  abstractness. 

In  any  complicated  structure,  a  new  agent  produces  a 
variety  of  changes.  The  taking  of  food  leads  to  concurring 
alterations  m  almost  every  organ  in  the  body.  Every  disease 
has  concurrmg  symptoms.  A  country  engaging  in  war  has 
Its  economy  simultaneously  disturbed  in  many  different  ways  • 
hence  there  are  numerous  empirical  statements  applicable  t^ 
the  condition  of  war,  which  are  co-effects  of  the  one  general 
situation.  ° 

7.  The  aggregation  of  properties  in  a  natural  kind— a 
mineral,  plant,  or  animal— has  something  in  common  with 
±impirical  Laws. 

^  As  there  may  be  uniformities  of  co-existence,  not  resolvable 
mto  cause  and  effect,  such  uniformities  stand  solely  on  their 
own  inductive  evidence,  like  empirical  laws.  They  are  proved 
by  the  method  of  Agreement  alone,  and  the  proof  extends  no 
tarther  than  the  cases  observed. 

8.  The  criteria  of  an  Empirical  Law  are  principally 
vuese  j^— 

If  a  uniformity  is  established  only  by  Agreement,  it  is 
not  shewn  to  be  a  law  of  causation  ;  and  (if  not  an  ulti- 
mate law  of  co-existence)  it  is  an  empirical  law. 


836 


SECONDARY  LAWS. 


Agreement  does  not  single  out  a  cause  when  there  is  plurality. 
It  is  at  fault,  besides,  in  discriminating  cause  and  effect  from 
effects  of  the  same  cause.  Moreover,  unless  the  variation  of 
the  circumstances  has  been  thorough  and  complete,  there  is 
an  uncertainty  even  in  cases  where  there  is  but  a  single  cause, 
and  where  the  antecedents  contain  that  cause. 

The  Method  of  Difference  does  not  at  once  lead  to  ultimate 
laws.  The  swallowing  of  alcohol  is  followed  by  a  certain 
sensation  ;  this  is  proved  by  the  Method  of  Difference  to  be 
cause  and  effect,  yet  it  is  not  an  ultimate  sequence  ;  it  is  an 
empirical  uniformity. 

9.  The  other  criteria  arise  out  of  the  characters  already 
mentioned. 

Thus,  when  phenomena  are  obviously  complicated,  and 
when  there  are  intermediate  links  of  operation,  the  laws  of 
such  phenomena  are  not  ultimate  but  secondary  ;  they  are 
empirical,  or,  if  resolved,  derivative. 

The  law  that  connects  the  fall  of  the  barometer  with  wind 
or  rain  is  plainly  empiiical.  We  can  see  that  many  different 
agencies  enter  into  the  sequence ;  and,  also,  that  there  are 
many  intermediate  steps  between  the  antecedent  and  the 
consequent. 

We  presume  the  action  of  a  drug  to  be  an  empirical  law, 
because  we  know,  from  the  complication  of  the  human  body 
and  the  plurality  of  attributes  of  natural  kinds,  that  there 
must  be  many  concurring  processes,  each  one  governed  by  its 
own  law  or  laws  of  causation. 

LIMITED  APPLICATION   OF  DERIVATIVE  AND  EMPIRICAL  LAWS. 

10.  A  Derivative  Law,  and  still  more  an  Empirical  Law 
must  not  be  extended  beyond  narrow  limits  of  Time,  Place 
and  Circumstance. 

It  being  supposed  that  such  laws  are  established  by  all  the 
evidence  that  the  case  admits  of,  still  they  are  applicable  only 
a  certain  way  beyond  the  narrow  sphere  where  they  have  been 
observed  to  operate. 

The  reasons  are  those  already  stated  under  the  Deductive 
Method.  A  uniformity  depending  on  several  higher  uniformi- 
ties, and  on  a  definite  collocation  of  agents,  that  is,  on  certain 
special  co-efficients,  must  fail,  first,  if  any  of  the  concurring 
uniformities  be  counteracted,  and  secondly,  if  the  proper  ad- 
justment of  the  agencies  is  departed  from.      The  elliptic 


APPLICATION   TO  ADJACENT  CASES. 


337 


motion  of  the  planets  would  be  defeated,  if  some  great  dig- 
turbmg  body  were  sufficiently  near  to  counteract  solar 
attraction,  or  if  the  tangential  force  were  made  different  from 
what  it  is.  Hence  we  cannot  extend  the  law  of  the  ellipse  to 
every  body  that  may  now  or  at  any  future  time  revolve  about 
the  sun. 

This  limit  to  the  extension  of  secondary  laws— whether 
Empirical  or  Derivative— is  the  all-important  fact  respecting 
them,  m  the  logical  point  of  view.  A  large  number  of  pre- 
vailing errors  might  be  described  as  the  undue  extension  of 
Himpirical  Laws.  We  shall  present  a  few  examples  of  secondary 
laws,  calling  attention  to  the  difference  of  our  position  in 
re^rd  to  them,  according  as  they  are  Empirical  or  Derivative. 

The  rise  of  water  in  pumps  was  an  empirical  law,  previous 
to  the  discovery  of  the  pressure  of  the  atmosphere.  The 
application  of  the  Method  of  Agreement  in  different  countries, 
and  with  pumps  of  different  bore,  proved  that  no  pumps  could 
draw  water  beyond  about  33  feet.  The  law  could  be  relied  on 
within  the  wide  limits  of  place  and  circumstance  where  it  had 
been  tried.  It  could  not  have  been  extended  to  other  planets  ; 
but  it  might  be  extended,  with  apparent  safety  to  any  part  of 
the  earth.  "^  ^ 

Since  the  law  became  derivative,  the  limits  of  its  operation 

are  precisely  defined  ;  we  can  tell  exactly  where  it  would  have 

failed.    We  know  that  on  the  tops  of  high  mountains  the 

maximum  height  would  have  been  much  below  33  feet ;  that 

the  exact  height  would  not  be  the  same  at  all  times  ;  that 

other  liquids,  as  alcohol,  sulphuric  acid,  solutions  of  salts, 

mercury,  vary  in  the  height  attained.    Now,  probably  none 

of  all  these  limitations  had  been  actually  discovered  in  the 

empirical  stage  ;  they  might  have  been  obtained  by  sufficiently 

wide  and  careful  experiments  ;  the  derivation  superseded  the 

laborious  task,  which  was  probably  beyond  the  competence  of 

an  unscientific  age. 

It  is  an  empirical  law  that  the  temperature  of  the  earth 
increases,  as  we  descend,  al  a  nearly  uniform  rate  of  V  of 
Fahrenheit  to  50  feet  of  descent.  This  law  has  been  verified 
by  observations  down  to  almost  a  mile.  We  might  extend  the 
law  inferentially  to  the  adjacent  depths,  as  far  perhaps  as 
several  miles ;  but  wo  are  not  at  liberty  to  extend  it  to  the 
centre  of  the  globe.  We  do  not  know  that  the  requisite  col- 
locations extend  so  far. 

Yet  this  law  ip  not  wholly   empirical.      It  Ip  a  derivative 
iniformity.      It  is  connected  with  the  known  facte— that  the 


f  ■i' 


838 


SECONDARY  LAWS. 


earth  has  a  high  temperature  in  the  interior,  and  is  cooled  at 
the  surface  by  radiation  in  space.  Knowing  these,  we  are  yet 
unable  to  deduce  the  law  of  decrease  from  the  higher  laws 
concerned,  because  we  are  ignorant  of  the  degree  of  central 
heat,  and  imperfectly  acquainted  with  the  laws  of  its  conducr 
tion  through  the  unknown  materials  of  the  globe.  We  under- 
stand the  general  situation,  but  do  not  possess  the  numerical 
and  other  data  requisite  for  computing  the  effects. 

That  air-breathing  animals  are  hot-blooded,  is  a  law  formerly 
empirical,  now  derivative.  It  comes  under  the  general  law  of 
the  dependence  of  temperature  on  the  oxygenation  of  the  blood, 
and  may  be  extended  widely  on  the  faith  of  that  great 
generality. 

The  Law  of  Continuit}' — *  Natura  non  agit  per  saltum ' — is 
an  Empirical  Law.  In  the  continuity  of  Vegetable  and  Animal 
Life,  there  would  be,  under  the  Doctrine  of  Development,  a 
reason  for  the  fact,  and  it  would  be  in  that  case  Derivative. 
Also,  in  the  transition  from  one  state  of  matter  to  another, — as 
in  melting,  boiling,  and  their  opposites — there  must  be  a 
certain  amount  of  continuity  owing  to  the  greatness  of  the 
transition.  But  except  where  there  is  some  presumption  of 
this  nature,  the  extension  of  the  law  is  wholly  unsafe  ;  we  are 
not  to  expect,  for  example,  that  the  simple  bodies  of  nature 
should  be  arranged  in  series  with  continuous  or  shading  pro- 
perties. We  find  the  greatest  gaps  in  almost  all  the  properties 
of  the  elementary  bodies. 

In  medical  science,  there  is  hardly  such  a  thing  as  a  single 
effect  produced  by  a  simple  cause.  What  is  worse,  there  are 
scarcely  any  great  inductive  generalities  relating  to  the  cure  of 
disease,  except  through  hygienic  or  constitutional  treatment. 
Thus  the  use  of  drugs  is  almost  exclusively  empirical. 

The  limitation  in  this  case  operates  variously.  It  forbids 
our  inferring  that  two  medicines  of  close  kindred  will  have 
the  same  effect ;  thus  bark  and  quinine  are  not  interchange- 
able, although  the  one  is  the  crude  form  and  the  other  the 
essential  extract.  It  also  forbids  our  extending  a  mode  of 
treatment  to  a  closely  allied  ailment,  as  in  reasoning  from 
one  species  of  fever  to  another.  Lastly,  it  forbids  the  applica- 
tion of  the  same  treatment  to  the  same  disease,  in  different 
persons. 

Hence,  medicine  is  of  all  sciences  the  one  most  completely 
tentative.  Experience  gives  a  probability  to  begin  with  ;  but 
until  the  effect  is  tried  in  the  new  case,  we  cannot,  as  a 
general  rule,  rely  on  it. 


EMPIRICAL  LAWS  IN  MEDICINE. 


339 


Until  the  day  arrives  when  the  operation  of  medicines  is 
made  derivative,  the  only  progress  possible  is  to  obtain  through 
multiplied  experience,  a  more  exact  statement  of  the  conditions 
attending  on  the  successful  application  of  certain  modes  of 
treatment ;  as  for  example,  the  constitutional  or  other  circum- 
stances in  the  patient  favourable  or  unfavourable  to  special 
drugs. 

The  treatment  of  tape  worm  by  male  fern  is  of  old  date  iu 
medicine.  In  the  early  period,  the  failures  were  frequent ; 
at  present,  the  oil  of  the  fern  is  extracted  and  given  instead  of  the 
root,  with  an  almost  uniform  success.  This  empirical  unifor- 
mity is  to  a  certain  extent  derived  or  explained  ;  the  substance 
18  a  poison  to  the  parasite.  After  such  an  explanation,  there 
IS  afforded  a  clue  to  other  remedies  for  the  disease ;  previous 
to  the  explanation,  the  uniformity  was  confined  to  the  one 
remedy. 

As  an  empirical  law  in  Medicine,  we  may  instance  Brio-ht's 
discovery  of  the  connexion  between  albuminous  urine,°and 
degeneration  of  the  kidney.  The  law  is  as  yet  unresolved 
into  any  higher  law  of  structure  and  function ;  the  kidney 
degeneration  is  not  associated  with  degeneration  in  any  other 
tissues  of  the  body  ;  and  no  account  is  given  of  the  temporary 
production  of  albumen  without  the  permanent  disease. 

It  is  an  empirical  law  that  about  250  persons  in  a  year 
commit  suicide  in  London. "  This  law  may  be  extended  a  little 
way  into  the  future,  but  it  may  not  be  extended  into  a  remote 
time,  when  moral  habits  may  be  different,  nor  to  other  cities 
and  populations. 

The  Statistics  of  Mortality  show  a  remarkable  doincidence 
between  the  rate  of  mortality  and  the  density  of  the  popula- 
tion. A  high  degree  of  longevity  is  found  in  thinly  peopled 
districts,  notwithstanding  even  the  poverty  that  sometimes 
occurs  in  sterile  tracts ;  and  mortality  reaches  its  maximum 
in  the  most  crowded  parts  of  cities,  'if  we  knew  nothino-  of 
the  causes  of  this  uniformity,  if  it  were  as  empirical  as^'the 
medicinal  action  of  mercury  on  the  system,  we  could  not 
extend  the  law  into  other  countries  and  other  circumstances  of 
the  population.  But  it  is  a  derivative  law,  and  knowing  what 
agents  the  effect  depends  on,  and  what  circumstances  would 
defeat  their  operation,  we  apply  it  without  scruple  to  every 
portion  of  the  human  race.  We  should,  however,  refrain  from 
applying  it  to  animals  very  differently  constituted  from  man 
as  to  the  necessities  of  breathing  pure  air.  All  animals  require 
oxygen,  but  some  need  it  in  smaller  quantity,  and  are  indif« 


340 


SECONDARY  LAWS. 


ferent  to  impure  gases  ;  while  warmth  and  the  opportunities  of 
better  food  mi^ht  more  than  compensate  for  the  close  atmos- 
phere of  a  confined  habitation. 

In  regard  to  the  Human  Mind  and  character,  we  have 
uniformities  that  cannot  be  extended  to  the  race  generally. 
Thus,  the  universality  of  sympathy  or  fellow-feeling  is  liable  to 
exceptions.  Mr.  Samuel  Bailey,  after  quoting,  from  a  travel- 
ler in  Burmah,  the  incident  of  a  drowning  man  being  beheld 
by  a  crowd  as  an  amusing  spectacle,  and  being  allowed  to 
sink  without  an  attempt  at  succour,  makes  the  following 
remarks : — 

'  Incidents  of  this  kind  (and  the  example  might  be  easily 
parallelled  from  other  nations)  serve  to  show  that  when  we 
ascribe  certain  sentiments  to  human  nature  or  to  men  univers- 
ally on  given  occasions,  because  they  exist  amongst  ourselves 
on  those  occasions,  it  is  by  no  means  a  safe  inference ;  we 
cannot  safely  ascribe  them  except  to  men  under  analogous 
circumstances  of  knowledge  and  civilization. 

*  We  may  attribute  with  confidence  to  most  men  and  to  most 
races  of  men,  the  rudimentary  feelings  which  I  have  shown  to 
originate  and  to  constitute  moral  sentiment ;  and  some  of  them 
with  equal  confidence  to  all  men  :  namely,  sensibility  to  cor- 
poreal pleasure  and  pain  ;  liking  the  causes  of  one  and  dis- 
liking the  causes  of  the  other ;  the  propensity  to  reciprocate 
both  good  and  evil ;  the  expectation  of  the  same  reciprocation ; 
and  more  or  less  sympathy  with  other  sensitive  beings ;  but 
the  direction  and  intensity  of  these  emotions  respectively  it  is 
often  difficult  and  even  impossible  to  assign  :  there  are  so 
many  causes  at  work  to  counteract,  or  modify,  or  suppress 
such  of  these  common  susceptibilities  as  can  be  counteracted, 
or  modified,  or  suppressed — to  call  them  forth  or  to  keep 
them  in,  that,  unfurnished  with  precise  knowledge  of  national 
and  social  circumstances,  we  cannot  predict  with  confidence 
how  they  will  manifest  themselves  on  particular  occasions. 
Without  specific  information  of  this  kind  we  cannot  safely 
pronounce  that  the  people  of  rude  or  distant  and  imperfectly 
explored  countries  would,  under  given  circumstances,  share  in 
those  afiections  and  moi-al  sentiments  which  it  seems  contrary 
to  our  own  very  nature,  under  such  circumstances,  not  to  have/ 

That  *  the  mind  of  man  is  by  nature  conciliated  and  adapted 
to  his  condition '  was  formerly  an  empirical  law.  We  may 
now  consider  it  as  a  deduction  or  derivation  from  the  law  of 
Universal  Relativity.  The  principle  has  been  greatly  abused. 
It  has  been  loosely  extended  far  beyond  the  limits  where  it  is 


POLITICAL  EULESk 


341 


observed  to  hold  true ;  indeed  those  limits  were  never  correctly 
marked  in  its  empirical  state.  As  a  derivative  uniformity,  we 
may  assign  its  limits  with  tolerable  precision. 

The  laws  of  Political  Society  are  all  secondary  laws,  either 
empirical  or  derivative.  Hence  the  necessity  for  limiting  their 
application.  The  politician  is,  like  the  ancient  sailors,  obliged 
to  sail  close  by  the  shore,  rarely  venturing  out  ofsightof  land. 

We  are  not  at  liberty  to  transfer  to  our  own  time  the  maxims 
suitable  to  the  anoient  world,  supposing  even  that  the  ancients 
really  attained  any  political  rules  highly  salutary  in  their  own 
case. 

*  The  distinction  between  ancient  and  modern  history,*  says 
Mommsen,  *  is  no  mere  chronological  convenience.  Modern 
History  is  the  entry  on  a  new  cycle  of  culture,  connected 
at  several  epochs  of  its  development  with  the  perishing  or 
perished  civilization  of  the  Mediterranean  States,  but  destined 
to  traverse  an  orbit  of  its  own.'  It  would  be  a  vicious  extension 
ot  secondary  laws,  to  predict  the  extinction  of  modern  nations 
because  the  great  ancient  empires  are  perished.  ' 

We  cannot  transfer  at  once  the  practice  of  one  nation  to 
another  nation.  Hardly  any  political  device  has  been  so  much 
copied  as  the  British  constitution.  Yet,  its  advantages  being 
not  purely  empirical,  but  to  a  certain  extent  derivative,  it  may 
be  extended  to  adjacent  cases  with  some  confidence. 

It  is  suitable  to  the  complicacy  of  the  political  structure  to 
make  changes  in  the  direction  of  existing  institutions,  and  to 
confade  m  them  only  when  introducing  a  state  of  things  nearly 
adjacent  to  the  present.  After  seeing  the  working  of  a  ten- 
pound  franchise  in  this  country,  the  inference  was  fair  that 
the  lowering  to  eight,  seven,  or  six  pounds  could  not  depart 
very  tar  from  actual  experience. 

The  use  of  precedents  in  Law  and  in  Politics  exemplifies  the 
rule  of  hmitation.  Bacon,  remarking  on  legal  precedents,  lays 
It  down  that  ths  more  recent  are  the  safer,  although,  on  the 
other  hand,  they  have  a  less  weight  of  authority.  *  A  prece> 
dent  18  at  its  maximum  of  proving  force  when  it  is  sufficiently 
near  our  own  time  to  ensure  similarity  of  circumstances,  and 
Bufficiently  distant  to  ensure  the  consolidation  of  practice,  and 
the  experimental    exhibition  of  the   practical  result.'  (G.  C. 

Xj6W1S  )* 

11.  The  rule  may  be  farther  illustrated  under  the  second 
form  of  the  Secondary  Laws —Uniformities  of  remote 
connexion  between  cause  and  effect. 


342 


SECONDARY  LAWS. 


INDUCTION  OF  CAUSE. 


343 


Of  these,  the  most  prominent  examples  are  the  results  of 
Blow  processes  in  the  arts,  protracted  treatment  in  disease,  the 
growth  of  plants,  the  development  of  animals,  the  formation  of 
the  human  character.  That  all  empiricisms  of  this  class  must 
be  precarious  and  liable  to  frequent  defeat  is  apparent.  Even 
when  derivative  to  the  full  extent,  they  are  rendered  uncertain 
by  the  number  and  complication  of  the  agencies. 

12.  Lastly,  with  reference  to  Uniformities  suspected  or 
known  to  be  effects  of  a  common  cause. 

The  principle  of  limitation  is  still  the  same. 

As  an  example,  the  case  is  put — what  reliance  are  we  to 
place  on  the  sun's  rising  to-morrow  ? 

Suppose,  in  the  first  place,  that  this  were  an  empirical 
generality,  we  being  ignorant  of  its  derivation.  Suppose, 
also,  that  we  have  authentic  evidence  tbat  the  sun  has  risen 
daily  for  the  last  five  thousand  years.  How  far  into  the  future 
are  we  at  liberty  to  extend  the  law  ;  to  what  limits  of  time 
should  we  confine  it  ?  The  answer  is,  we  may  count  the  con- 
tinuance in  the  future,  on  the  same  scale  as  the  continuance 
in  the  past ;  we  may  fairly  assume  a  period  counted  by 
thousands  of  years ;  we  may  be  tolerably  certain  for  one 
thousand  years,  and  have  a  considerable  probability,  for  three, 
four,  or  five  thousand  ;  but  we  should  not  be  safe  in  extending 
the  scale  to  tens  of  thousands,  still  less  to  hundreds  of 
thousands.  For  anything  we  should  know,  a  catastrophe  may 
be  preparing  that  will  speedily  interfere  with  the  regularity  of 
day  and  night ;  still,  long  continuance  in  the  past  reduces, 
without  annihilating  the  chances. 

Let  us  next  look  at  the  case  as  a  derivative  uniformity.  We 
know  that  the  phenomenon  will  continue  so  long  as  these 
circumstances  are  conjoined,  namely,  (1)  the  luminosity  of 
the  sun,  (2)  the  earth's  being  within  a  proper  distance  of  the 
sun,  (3)  the  earth's  rotation,  and  (4)  the  negative  condition  of 
the  absence  of  any  intervening  opaque  body  to  act  as  a  screen. 
Now,  we  know  from  past  experience  that  all  these  conditions 
are  likely  to  be  perpetuated  for  a  period  of  time,  to  be  estimated 
by  not  less  than  hundreds  of  thousands  of  years^  The  sun 
may  be  cooling,  but  the  rate,  judging  from  the  past,  is 
extremely  slow ;  the  earth's  rotation  is  believed  to  be  subject 
to  decay,  but  the  rate  of  decay  is  infinitesmally  little;  'the 
removal  of  the  earth  out  of  the  solar  infiuence  is  in  opposition 
to  our  very  best  guarantees  ;  and  the  permanent  intervention  of 
an  echpsmg  body  is  the  most  unlikely  incident  of  all.     Thus, 


then,  while,  as  an  empirical  law,  we  cannot  well  extend  the 
rising  of  the  sun  (or  day  and  night  as  we  now  have  it)  beyond 
thousands  of  years  at  most,  we  may  extend  it,  as  a  derivative 
law,  to  hundreds  of  thousands,  if  not  to  millions. 

EVIDENCE   OF  THE   LAW   OF   CAUSATION. 

13.  It  may  be  shown  that  the  Law  of  Causation,  the  indi- 
spensable  ground  work  of  all  Induction,  itself  reposes  ou 
the  highest  evidence  suitable  to  the  case— uncontradicted 
Agreement  through  all  nature. 

We  have  hitherto  taken  for  granted  that  sufficient  evidence,  • 
ot  the  only  kind  suited  to  the  case,  has  been  obtained  in  favour 
ot  the  ^aw„o^,  Universal  Causation,  on  which  law  have  been 
grounded  all  the  processes  of  experimental  eUmination.      A 
summary  of  this  evidence  will  farther  illustrate  the  logical 
processes  detailed  in  the  foregoing  chapters. 
^    The  uniformity  of  successions '^was  first*  observed  in  easy 
instances,  such  as  the  more  obvious  mechanical  effects.      A 
body  at  rest  was  observed  never  to  move  from  its  place  without 
the  application  of  some  force  to  move  it ;  a  body  in  motion 
was  observed  not  to  stop  abruptly  without  interference  and 
obstruction.     The  fact  of  the  descent  of  unsupported  bodies 
IS  invariable.      So  light  and  heat  display  obvious  regularities 
that  could  be  counted  on.    Even  in  the  instability  of  the  winds 
there  would  be  discovered  circumstances  of  constancy.      The 
most  complicated  of  all  things,  living  bodies,  were  seen  to 
nave  numerous  points  of  striking  uniformity. 

That  change  of  every  kind  whatsoever  follows  on  a  definite 
pnor  change,  could  not  be  affirmed  in  early  times,  except  by 
the  mere  instinct  of  generalization,  which  is  no  proof.  Hende 
m  ancient  philosophy,  there  were  alternative  suppositions. 
Anstotle  allowed  an  element  of  Chance,  along  with  the  reien 
of  Law.  °  ^ 

Modern  science  has  extended  the  search  into  natural  se- 
quences, collecting  new  examples  of  uniformity,  and  removing 
exceptions  and  apparent  contradictions.  Investigations  have 
been  pushed  into  every  department  of  nature ;  and  had  there 
been  any  decisive  instances  where  change  grew  out  of  nothing 
or  where  the  same  agent,  in  the  same  circumstances,  was  not 
toUowed  by  the  same  effect,  such  instances  must  have  been 
brought  to  light. 

14.  In  the   form  of  Persistence  of  Energy,  under  definite 


I 


^1 
'II 


1 


544 


EVIDENCE  OF  THE  LAW   OF  CAUSATION. 


laws  of  Collocation,  the  Law  of  Cause  and  Effect  has  been 
subjected  to  the  most  delicate  experimental  tests. 

By  irrefragable  obscrvatioDS  it  was  shown  that  Matter  is 
indestructible,  which  is  one  element  of  nature's  constancy. 
Farther  observations  have  proved  the  numerical  Persistence 
of  Force  throughout  all  its  transformations,  and  also  the  unifor- 
mity of  the  collocations  or  arrangements  for  transferring  it. 

The  first  contribution  to  this  result  was  the  proof  of  the 
Laws  of  Motion,  as  respects  both  the  continuance  of  motion 
once  begun,  and  the  conservation  of  the  total  moving  force  in 
case  of  transfer  by  impact.  These  mechanical  verities  make 
up  one  department  of  uniform  cause  and  efiect  Next  came 
the  proof  of  the  equivalence  of  mechanical  force  and  beat — 
the  constancy  of  the  amount  of  one  produced  from  a  definite 
amount  of  the  other.  Joule's  mechanical  equivalent  of  Heat 
^stifles  to  nature's  constancy  in  a  very  wide  department. 
Following  on  this  is  the  mumerical  estimate  of  the  heat  of 
Chemical  combinations,  also  admitting  of  numerical  statement, 
from  which  there  is  no  deviation  ;  a  third  great  department 
of  constancy  is  thereby  established. 

If  numerical  equivalence  has  not  been  arrived  at  in  Nerve 
Force,  and  in  Light,  the  subtleties  of  the  phenomena  are 
sufficient  to  account  for  the  deficiency.  We  have  reasonable 
ground  to  presume  that,  according  as  these  phenomena  are 
fully  understood,  they  will  show  the  same  constancy  as  all  the 
rest ;  the  burden  of  proof  lies  upon  any  one  maintaining  the 
contrary. 

^  The  only  exception  usually  claimed  to  the  Law  of  Causation 
IS  the  alleged  Freedom  of  the  Will.  But  whatever  be  the 
mode  of  dealing  with  this  long-standing  enigma,  there  is  a 
statistical  testimony  in  favour  of  the  constancy  of  human 
motives.  The  actions  of  men  have  a  degree  of  regularity 
compatible  only  with  uniform  causation. 

Mr.  Mansel  has  characterised  as  a  *  paralogism '  the  doc- 
toe  that  'the  ground  of  all  Induction  is  itself  an  Induction.' 
He  might  have  called  it  a  paradox  or  an  epigram,  an  apparent 
contradiction  needing  to  be  resolved :  it  is  not  a  paralogism 
unless  it  can  be  made  out  a  self-contradiction. 

If  the  account  given  above  of  the  methods  of  Proof  and 
Elimination  is  sufficiently  intelligible  and  conclusive,  nothing 
farther  is  necessary  to  resolve  the  paradox.  There  is  one  fun- 
damental mode  of  Proof— Agreement  through  all  nature— by 
which  all  ultimate  laws  are  established,  including  Causation 


CAUSATION  BESTS   ON  AGREEMENT  ALONE.  345 

There  are  several  derivative  deductive,  or  dependent  methods 
of   Proof,  the   special  Methods  of   Elimination— Agreement 
(according  to  Mill's  Canon),  Diff-erence,  and  Variations  ;t^ese 
are    called  by   courtesy  Inductive  Methods;  they  are  more 
properly  Deductive  Methods  available  in  Inductive  investie^a! 
tions.     The  special  form  of  Agreement  described  in  the  canon 
IS  not  quite  the  same  as  the  fundamental  method  of  A^ree 
ment,  on  which  alone  repose  all   the  ultimate  generalizations" 
Ihat  canon,  as  supposing  Causation,  would  be  inapplicable  to 
the  proof  of  Causation    The  method  of  Agreement  that  proves 
Causation  is  not  a  method  of  elimination.    It  does  not  proceed 
by    varying    the   circumstances,    and    disproving  successive 
antecedents  ;  it  can  only  find  A  followed  by  a,  wherever  the 
two  occur.     Until  the  law  is  first  proved,  we  cannot  establish 
A  as  the  cause  of  a,  by  omitting  successively  B,  C  D  and  all 
other  accompanying  circumstances,  leaving  nothing  constantly 
joined  save  A  and  a;  even  if  this  were  done,  there  must  still  be 
a  search  through  all  nature  for  A  followed  by  a,  when  the  ques! 
t  on  of  causation  itself  is  at  issue.    Hence  Agreement  for  estab- 
lisbmg  an  nltiinate  law  is  not  the  same  as    the  Method  of 

tyT^r    '  '"^  ^f'  ^^''^S.'  ^^^^st^l^listing  cases  of  causation, 
after  the  general  law  is  sufficiently  guaranteed. 

There  is  a  certain  propriety  in  comparing  the  establishment 

ot  the  Law  of  Causation  (or  any  other  ultimate  law),  with  the 

proof  of  an  Empirical  Uniformity,  which  has  nothing  but  de! 

taxied  Agreement  to  found  upon.      True,  an  Empirical  Uni- 

formity  is  to  be  apphed  only  a  little  way  beyond  the  limits  of 

time,   place    and   circumstances.      But,   now,   as  Mr.    MiU 

remarks,     if  we  suppose  the  subject  matter  of  any  ^eneraliza- 

tion  to  be  so  widely  difi^used,  that  there  is  no  tim^e,^no  Xc^ 

and   no  combination   of  circumstances,  but  must  afford  an 

example  either  of  its  truth  or  its  falsity,  and  if  it  be  never 

found  otherwise  than  true,  its  truth  cannot  depend  on  any 

l^Tt'T  7^?^/^^  ^  e^i«*  ^t  all  times  and^laces ;  nor 
can  it  be  frustrated  by  any  counteracting  agencies,  unless  bv 
such  as  never  actually  occur.     It  is,   therefore,  an  em2ica^ 

Ihl' ^?:r^*  r'^V!' ^ '^^  ^^^"^  experience;  at  which  V'n 
the   distinction   between  empirical  laws  and  laws  of  nature 
vanishes,  and  the  proposition  t^^es  its  place  among  the  most 
firmly  established,  as  well  as  largest   truths  accessible  to 
Bciouce* 


'41 


CHAPTER  XH 


EXPLANATION  OF  NATURE. 


1.  The  laws  arrived  at  by  Induction  and  Deduction  ai« 
the  proper  Explanation  of  natural  phenomena. 

Explanation  has  various  meanings.  These  all  agree  in 
affording  us  a  certain  satisfaction  or  relief  when  oppressed 
with  the  difficulty,  obscurity,  perplexity,  contradiction,  mys- 
tery, of  natural  facts.  But  the  human  mind  has  at  different 
times  been  satisfied  in  different  ways  ;  and  individuals  still 
vary  as  to  the  kind  of  explanation  that  satisfies  them. 

When  all  Nature  was  peopled  with  deities,  and  the  various 
phenomena  partitioned  among  them,  a  sufficient  explanation 
of  anything  was  that  a  certain  god  or  goddess  willed  it.  The 
intervention  of  Neptune  was  a  satisfying  account  of  why  a 
storm  arose.  The  wrath  of  Apollo  was  the  explanation  of  the 
plague  that  broke  out  among  the  Greeks  at  the  siege  of  Troy.* 

There  is  a  special  and  every-day  form  of  explanation  that 
consists  in  assigning  the  agency  in  a  particular  occurrence ; 
as  when  we  ask —  what  stops  the  way  ?  who  wrote  Junius  ? 
who  discovered  gunpowder  ?  These  questions  belong  to  our 
practical  wants  and  urgencies,  but  the  answer  does  not  involve 
the  process  of  scientific  explanation.  If,  however,  we  proceed 
from  the  *  who '  or  *  what '  to  the  *  why  : — why  does  A's 
carriage  stop  the  way  ?  why  did  the  author  of  Junius  write 
so  bitterly  ? — there  is  an  opening  for  the  higher  scientific 
process. 

2.  The  basis  of  all  scientific  explanation  consists  in 
assimilating  a  fact  to  some  other  fact  or  facts.  It  is 
identical  with  the  generalizing  process,  that  is,  with  In- 
duction and  Deduction. 

Our  only  progress  from  the  obscure  to  the  plain,  from  the 
mysterious  to  the  intelligible,  is  to  find  out  resemblances  among 
facts,  to  make  different  phenomena,  as  it  were,  fraternize. 
We  cannot  pass  out  of  the  phenomena  themselves.  We  can 
explain  a  motion  by  comparing  it  with  some  other  motion,  a 

•  See  Grote's  Plato  (Phadon)  fr  r  the  views  of  the  ancient  philosopheri 
with  regard  to  Explanation,  or  the  Jd«  a  of  Cause. 


EXPLANATION  IS   GENERALIZATION. 


347 


pleasure  by  reference  to  some  other  pleasure.  We  do  not 
change  the  groundwork  of  our  conception  of  things,  we 
merely  assimilate,  classify,  generalize,  concentrate,  or  reduce 
to  unity,  a  variety  of  seemingly  different  things. 

The  phenomenon  of  combustion  was  considered  to  have 
been  explained  when  Priestley  showed  it  to  be  the  combina- 
tion ot  oxygen  with  carbon  or  other  substance ;  in  short,  he 
assimilated  the  fact  to  cases  of  oxidation,  as  the  formation  of 
the  red  precipitate  of  mercury,  the  rusting  of  iron,  &o. 
l^ightning  was  explained  by  Franklin's  assimilating  it  with 
electricity.  The  polarity  of  the  needle  was  explained  by 
assimilating  the  entire  globe  to  a  magnet  or  loadstone. 

-bixplanation  thus  steadily  proceeds  side  by  side  with 
assimilation,  generalization.  Combustion  was  explained  by 
oxidation  ;  oxidation  is  explained  by  the  higher  generality-- 
chemical  combination  ;  chemical  combination  is  swallowed  op 
in  the  Conservation  of  Energy. 

3.  Mr.  Mill  distinguishes  three  forms  of  the  explanation 
01  tacts  and  laws. 

I.  Explaining  a  joint  effect,  by  assigning  the  la-^vs  of 
the  separate  causes,  as  in  the  ordinary  Deductive  operation. 

The  Deduction  of  a  complex  effect,  by  computing  the  sum 
ot  the  separate  elements,  is  also  the  explanation  of  that  effect 
By  combinmg  gravity  with  projectile  impulse,  we  explain 
the  niotions  of  the  planets.  This  deduction  once  verified,  is 
oflered  as  the  explanation  of  the  planetary  motions.  In  other 
words,  the  showing  that  these  motions  are  made  up  of  the 
two  causes -gravity  and  tangential  force— is  the  explaining 
or  their  motions.  ^  ° 

In  such  cases,  the  explanation  points  out  the  simple  causes 
concurring,  m  the  shape  of  forces  or  agencies,  and  also  indi- 
cates their  amount  and  their  due  concurrence.  Jupiter's 
orbit  depends  on  the  mass  of  the  sun,  on  the  tangential  force 
ot  the  planet,  and  on  its  mean  distance  from  the  sun  These 
are,  m  the  language  of  Astronomy,  the  coefficients,  which  must 
be  given  in  order  to  our  assigning  the  result  of  the  operation 
ot  the  laws,  A  mere  law,  such  as  the  law  of  gravity,  is  not 
an  explanation  until  it  is  clothed  in  the  concrete  statement  of 
two  or  more  gravitating  masses,  with  a  given  amount  and  a 
given  distance  from  each  other.  These  numerical  statements, 
the  coefficients  of  Astronomy,  are  also  said  to  determine  the 
CL'llocati(yns  of  the  agents  concerned. 


1*1 


9/1 


348 


EXPLANATION   OF  NATURE. 


To  explain  the  rise  of  a  balloon,  is  to  give  the  laws  of 
gravity,  of  buoyancy,  and  of  gaseous  elasticity,  and  to  state 
the  exact  weight  and  elasticity  of  our  atmosphere,  and  the 
specific  gravity  of  the  mass  of  the  balloon. 

To  explain  genius  is  to  refer  it  to  general  laws  of  the  mind, 
or  to  certain  elementary  powers— intellectual  and  emotional — 
whose  higher  or  lower  degrees  and  modes  of  combination 
produce  the  kind  of  intellectual  superiority  so  named. 

To  explain  the  rise  of  free  governments  is  to  state  the 
general  principles  of  human  action,  and  the  definite  collocation 
of  circumstances  calculated  to  produce  the  efiect. 

The  separate  laws  are  obviously  more  general  than  the  laws 
of  the  conjoint  effect.  Gravity  has  a  much  wider  sweep  than 
planetary  motions ;  the  law  of  the  perseverance  of  moving 
bodies  in  a  straight  line  is  far  more  comprehensive  than 
tangential  impulse. 

4  II  Explanation  may  assume  the  form  of  discovering 
an  intermediate  link,  or  links,  between  an  antecedent  and 
a  consequent. 

What  seems  at  first  sight  the  direct  or  immediate  cause  of  a 
phenomenon  may,  by  the  progress  of  assimilation,  turn  ou6 
the  remote  antecedent.  The  drawing  the  trigger  of  a  musket 
is  followed  by  the  propulsion  of  a  ball.  The  why  of  this 
phenomenon  is  given  by  disclosing  a  series  of  intermediate 
sequences,  each  of  which  is  assimilated  with  some  known 
sequence.  The  trigger  by  concussion  evolves  heat;  the'  heat 
ignites  the  gunpowder ;  the  gunpowder  is  a  mass  adapted  for 
very  rapid  combustion ;  the  combustion  evolve  gases  which 
being  confined  in  a  small  space,  have  a  very  high  expansive 
force  ;  the  expansive  force  propels  the  ball. 

Again,  the  contact  of  sugar  with  the  tongue  is  the  precursor 
of  a  feeling  of  the  mind,  the  sensation  called  sweetness.  The 
explanation,  so  far  as  hitherto  attained,  supplies  the  following 
series  of  closer  links.  The  sugar  is  absorbed  by  the  mucus 
membrane  of  the  tongue,  and  comes  in  contact  with  the  fila- 
ments of  the  gustatory  nerve ;  there  ensues  a  chemical  or 
some  other  molecular  action  on  tho  nerve.  This  action  is 
of  a  kind  that  can  be  propagated  along  the  course  of  the  nerve 
to  the  nerve  centres,  or  the  brain  ;  whence  are  diffused  a  multi- 
tude of  nervous  currents  ending  in  muscular  movements.  To 
the  cerebral  agitation  attaches  the  mental  state  called  the  sensa- 
tion of  sweetness. 


i  \ 


njTEBMEDUTE  LINKS. 


349 


rl^  nn.e3fpl«ined  phenomena  connected  with  the  Law  of 
Conservatjon  refer  to  the  intermediate  links,  or  tmnsitions,  in 
*^«  interchange  of  the  mechanical  and  the  molecular  for;,s, 

cesses  m  the  conversion  of  mechanical  energy  into  hpat  heat 
into  electricity,  chemical  force  into  muscular  power  and 
nervous  power.-are  not  accounted  for:   and  we^selonlv  a 

beWn^'n^^Tr  '"*fr''J>'«  '^Ses,  each  susceptible  of 
being  assigned  and  brought  under  some  general  law  of  cansa. 

than*th»*!rt.'^'^^  ^'''''^'  °'  ^^^"^"ces,  are  each  one  moregeneral 
Th«  ah«  ''°"?''««'l  sequence.  Take  the  case  of  a  sweet  taste. 
The  absorptive  power  of  the  animal  membranes  for  vaXw 
substences  (the  crystalloids  of  Graham)  is  a  general  kw    of 

TnH'^n         ^^"'e'i"'^'-  disturbance  from  the  contact  of  nerve 
Th«o!f^*'  ^'  *r°T   °'  chemical  or  molecular  affinity, 
co^eni-       .*  ^'*'°^u^  *''f  "^'■'^^  ^°"^  "  »  "-"ited  instance  of 
the  wLr  r'  ''    ^^^  ''"?"''^'  ^""^  «^Wbit  other  cases, 
vLv     It   ^.e'P«,<=<»"P>-ehei.sible   under    some   higher   law 
wi?h   be*^"  iTi^  that  rektes  the  physical  actions  of  Ae  brain 
riati  1.  f  1      5'"'  ^'°?^  *°  ^'""^  ^ider  statement  that 
A^Xr    i'^^Tu*^""^'""^  *°  ^^^''  P^y'^^  concomitants. 
n.it  ??Tr  '  '°  *''*'  P"^"""'  "'"^P**'-'  i'  «  incident  to  such 
many-lmked  sequences,  to  be  more  frequently  frustrated  than 

coLt^r""  ^^l"^'"^^^  *'>!''  "^ke  them.      A   circumstance 

whn^!^T  ^^  """^  °"r^  ""^  ^^^  °'''««'-  ""ks  counteracts  the 
whole  phenomenon.  If  the  lock  of  the  musket  makes  an  in- 
suffioiont  concussion  of  the  explosive  substance;  if  the  ffuu- 

^Zf  hnL'f?^^'"'"^  incombustible  by  damp;  if  the  expanding 
gases  burst  the  piece  :-m  any  one  of  these  contingencies,  thi 
ball  is  not  propelled.  ^  ' 

5,  III.  The  third  mode  of  Explanation  is  termed  the 
Subsumptton  of  one  law  into  another ;  or  the  gathering  up 
ll^         laws  in  one  more  general  and  all-compieheading 

This  represents  the  upward  march  of  generalization,  pure 
and  simple.  We  have  attained  a  certain  number  of  inferior 
generalities  by  assimilating  individual  cases  in  ordinary  in- 
duction. We  have  assimilated  the  kindling  of  fires  for  heat 
and  for  light  and  for  the  disintegration  of  compounds,  under 
one  bead,  called  combustion ;  we  have  assimilated  the  tarnish- 


fir 


350 


EXPLANATION  OF  NATURE. 


ing  and  corrosion  of  metallic  surfaces  under  another  head ; 
we  subsume  both  under  the  higher  law  of  oxidation,  which 
both  exemplify.  We  have  also  assimilated  the  action  of  acids 
upon  alkalies  under  a  general  head :  we  find  that  this  case 
can  fraternize  with  the  foregoing  and  with  many  other 
phenomena,  under  a  still  higher,  or  more  general  aspect^ 
signified  by  chemical  comhiiiafion. 

So,  again,  terrestrial  gravity  and  celestial  attraction,  each 
the  result  of  separate  assimilations,  being  found  to  agree,  are 
subsumed  into  the  illustrious  unity  of  Universal  Gravitation. 

Magnetism,  Common  Electricity,  Voltaic  Electricity, 
Electro-Magnetism,  &c.,  are  all  strung  upon  the  common 
thread  of  Electrical  Polarity. 

Capillary  attraction,  solution,  alloys  (not  chemical),  cements, 
&c.,  are  subsumed  under  the  general  law  of  molecular  attrac- 
tion (not  chemical)  between  difiereut  substances,  named 
heterogeneous  or  alien  attraction. 

Numerous  laws  of  smaller  compass  arc  subsumed  under 
Relativity.  The  pleasures  of  variety  and  novelty,  the  neces- 
sity of  contrast  in  works  of  art,  antithesis  in  rhetoric,  the 
statement  of  the  obverse  or  counter  proposition  in  science, — are 
minor  laws  generalized,  but  not  superseded,  by  the  higher 
law. 

.  When  minor  laws  are  thus  merged  in  a  greater  law,  the 
mind  feels  a  peculiar  and  genuine  satisfaction — the  satisfaction 
of  having  burst  a  boundary  to  expatiate  over  a  wider  field. 
We  rise  from  a  statement  bearing  upon  a  small  group  of  facts 
to  a  statement  comprehending  a  much  larger  group ;  from  a 
ten-fold  condensation,  we  reach  a  thousand-fold  condensation. 
The  intellect,  oppressed  with  the  variety  and  multiplicity  of 
facts,  is  joyfully  relieved  by  the  simplification  and  the  unity  of 
a  great  principle. 

The  charm  of  resolving  many  facts  into  one  fact  was  acutely 
felt  by  the  speculative  minds  of  antiquity.  It  took  a  power- 
ful hold  of  the  earliest  Greek  philosophers  ;  and  made  them 
almost  unanimous  in  imagining  that  all  phenomena  whatso- 
ever are  at  bottom  one,  or  are  susceptible  of  being  represented 
in  some  single  expression,  being  merely  the  many-sidedness  of 
some  single  central  power,  substance,  agent,  or  cause.  Such 
unity  was,  according  to  Thales,  Water ;  according  to  Anaxi- 
mander,  an  Indeterminate  Substance  ;  according  to  Anaxi- 
menes,  Air ;  according  to  Pythagoras,  Number. 


T7LIMATE  PHENOMENA. 


351 


LIMITS   OF  EXPLANATION. 

6.  Scientific  explaDation  and  inductive  generalization 
Deing  the  same  thing,  the  liviiis  of  Explanation  are  the 
limits  ot  Induction. 

Wherever  Induction  (extended  by  Deduction)  can  go,  there 
legitimate  scientific  Explanation  can  go,  they  being  the  same 
process  difierently  named.  ^  7       j  ^  ux» 

7.  The  limits  to  inductive  generalization  are  the  limits 
to  the  agreement  or  community  of  facts. 

Induction  supposes  similarity  among  phenomena,  and  when 
such  similarity  is  discovered,  it  reduces  the  phenomena  under 
a  common  statement.  The  similarity  of  terrestrial  gravity 
to  celestial  attraction  enables  the  two  to  be  expressed  as  one 
phenomenon.  The  similarity  between  capillary  attraction 
solution  the  operation  of  cements,  &c.,  leads  to  their  being 
regarded  not  as  a  plurality,  but  as  a  unity,  a  single  causative 
luik,  the  operation  of  a  single  agency. 

^  So  remarkable  have  been  the  achievements  of  modern  times, 
m  the  direction  of  lofty  generalities,  that  some  countenance 
seems  to  be  lent  to  the  ancient  dream  of  attaining  an  ultimate 
centralized  unity  in  the  midst  of  the  seeming  boundless 
diversity  of  nature. 

It    depends   purely   on   actual   investigation,    how  far  all 
phenomena  are  resolvable  into  one  or  into  several  ultimate 
laws  ;  whether  inductive  finality  leaves  us  with  one  principle 
with  two,  or  with  twenty  principles.  ' 

^    Thus,  if  it  be  asked  whether  we  can  merge  graviiy  itself 
m  some  still  higher  law,  the  answer  must  depend  upon  the  facts. 
Are   there   any  other  forces,   at  present  held  distinct  from 
gravity,  that  we  may  hope  to  make  fraternize  with  it,  so  as  to 
join  m  constituting  a  higher  unity  ?     Gravity  is  an  attractive 
lorce  ;  and  another  great  attractive  force  is  cohesion,  or  the 
force  that  binds  together  the  atoms  of  solid  matter.      Might 
we  then  join  these  two  in  a  still  higher  unity,  expressed  under 
a  more  comprehensive  law  ?      Certainly  we  might,  but  not 
to  any  advantage.     The  two  kinds  of  force  agree  in  the    one 
pomt—attraction,  but  they  agree  in  no  other ;  indeed,  in  the 
manner  of  the  attraction  they  differ  widely ;  so  widely  that 
we  should  have  to  state  totally  distinct  laws  for  each.  Gravity 
is  common  to  all  matter,  and  equal  in  amount  in  equal  masses 
of  matter  whatever  be  the  kind;  it  follows  the  law  uf  the 

10 


352 


EXPLANATION  OF  NATtJEE. 


ULTIMATE  FEELINGS   OF  THE   MIND. 


353 


diffnsion  of  space  from  a  point  (the  inverse  square  of  the 
distance)  ;  it  extends  to  distances  unlimited  ;  it  is  indestruc- 
tible and  invariable.  Cohesion  is  special  for  each  separate 
substance ;  it  decreases  according  to  distance  much  more 
rapidly  than  the  inverse  square,  vanishing  entirely  at  very 
small  distances.  Two  such  forces  have  not  sufficient  kindred 
to  be  generalized  into  one  force ;  the  generalization  is  only 
illusory  ;  the  statement  of  the  difference  would  still  make  two 
forces  ;  while  the  consideration  of  one  would  not  in  any  way 
simplify  the  phenomena  of  the  other,  as  happened  in  the 
generalization  of  gravity  itself. 

Again,  gravity,  considered  as  a  power  to  put  masses  in 
motion,  to  generate  visible  or  moving  force,  may  be 
compared,  by  way  of  an  attempt  at  assimilation,  with  the 
equally  familiar  mode  of  begetting  motion  by  impact,  or  the 
stroke  of  a  mass  already  in  motion  ;  as  in  propelling  a  ball  by 
a  mallet.  Here  too,  however,  we  have,  with  similarity  of 
result,  a  total  contrast  in  the  mode.  Gravity  draws  bodies 
together  from  a  distance ;  impact  must  be  supposed  to  urge 
them  through  their  atomic  repulsions.  When  the  expanding 
gases  of  kindled  gunpowder  blow  a  bullet  through  the  air, 
there  is  no  actual  contact  of  the  parts ;  there  is  merely  the 
operation  of  powerful  forces  of  mutual  repulsion,  acting, 
however,  at  very  short  distances,  like  the  cohesion  of  solidity. 
Now,  there  appears  to  be  nothing  in  common  to  gravity  and 
these  atomic  repulsions,  except  the  result.  We  have,  there- 
fore, no  basis  for  assimilation  or  inductive  generalization  in 
such  a  comparison.  The  two  modes  of  action  must  be 
allowed  to  lie  apart  in  physical  science ;  they  must  be  em- 
bodied in  different  statements  or  laws,  with  no  hope  of  being 
ever  brought  together. 

It  is  because  gravity  does  not  assimilate  with  the  propulsion 
of  impact  from  a  blow  or  a  stroke  that  people  have  accounted 
it  mysterious.  In  point  of  fact,  there  is  no  more  mystery  in 
the  one  than  in  the  other.  Attraction,  from  great  distances, 
is  one  form  of  the  production  of  force ;  Repulsion,  at  near 
distances,  is  another  form.  The  last  of  the  two  is,  on  the 
whole,  most  familiar  to  us;  it  is  the  genus  that  our  own 
physical  force  belongs  to  ;  and  we,  by  a  mere  whim,  suppose 
it  a  simpler  and  more  intelligible  mode  of  exerting  power ; 
the  truth  being  that,  in  all  that  regards  simplicity  and  intel- 
legibility,  gravity  has  the  advantage.  It  is  only  by  confining 
ourselves  to  the  superficial  glance  of  bodies  coming  into  close 
contact,  thence  giving  and   receiving  momentum,  that   we 


suppose  this  mode  of  exerting  force  a  simple  one ;  the  inter- 
polated  links  of  molecular  repulsion  are  much  more  compli- 
cated than  gravity. 

A  similar  line  of  remarks  would  apply  to  any  endeavour  to 
assimilate  gravity  with  the  Correlated  Forces  generally.  These 
forces  by  their  nature  counteract  gravity.    The  various  move- 
ments in  nature  are  explicable  by  the  conflict  and    mutual 
action    of    two  great    Powers ;    Gravity,  on    the  one    hand 
and  the  sum  total  of  the  Correlated  Forces,  molar  and  mole- 
cular on  the  other.     The  Correlated  Forces  mostly  appear 
under  the  guise  of  repulsions,  as,  for  example,  heat ;  so  much 
so  that  this  must  be  considered  their  typical  manifestation ; 
the  electrical  and  magnetic  attractions  are  exceptional,  and 
are  probably  mere  superficial  aspects  of  the  deeper  fact  of 
repulsive  separation. 

Three  departments  of  Force  thus  stand  out  so  distinct  as  to 
be  mcapable  of  assimilation  :— Gravity,  the  Correlated  Forces, 
and  Molecular  Adhesion.  This  last  appears  under  two 
terms  ;--the  attraction  between  particles  of  the  same  sub- 
stance—iron for  iron,  water  for  water  ;  and  the  attraction 
between  two  substances— as  iron  for  lead,  water  for  alcohol  or 
for  common  salt.  There  may  be  a  possibility  of  generalizing 
these  two,  or  stating  them  as  a  common  force.  Some  approach 
has  been  made  to  this  in  the  facfc  that  the  second  kind  of 
attraction  holds  between  bodies  nearly  allied— as  metals  with 
metals,  earths  with  earths. 

AX.  ^'  "[^^  ultimate  laws  of  Nature  cannot  be  less  numerous 
than  the  ultimate  feelings  of  the  human  mind. 

This,  as  Mr.  Mill  pointed  out,  is  the  insurmountable  barrier 
to  generalization,  and  consequently  to  explanation.  Whatever 
number  of  distinct  states  of  consciousness,  not  mutually  re- 
solvable, can  be  traced  in  the  mind,  there  must  be  that  number 
ot  ultimate  facts  or  elements  of  knowledge,  and  of  ultimate 
laws  connecting  those  states  with  their  causes  or  concomitants. 
li  the  sensation  of  colour  be  radically  distinct  from  the  feelings 
of  resistance,  of  movement,  of  form,  there  must  be  a  separate 
law  with  reference  to  colour.  The  phenomenon  called  white- 
ness  cannot  be  resolved  into  the  phenomenon  of  form,  or  of 
motion. 

Even  if  we  found  that  the  fact  of  whiteness  is  conditioned 
by  a  certain  molecular  structure,  and  certain  moleculai-  move- 
ments, we  should  not  thereby  resolve  whiteness  into  movement- 
the  facts  would  be  distinct  facts,  although  joined  in  nature 


■SSI 


m 


354 


EXPLANATION   OP  NATUBB. 


^H 


So,  we  are  aware  that  the  sensation  of  sound  is  conditioned  by 
a  vibratory  movement  of  the  particles  of  a  sonnding  body  ; 
bnt  the  vibration  is  not  the  soand ;  all  we  can  say  is  that  a 
law  of  causation  relates  the  vibration  to  the  sound.  Now 
there  must  always  remain  one  law  connecting  the  molecular 
movements  of  bodies  with  the  sensation  of  whiteness,  and 
another  law  connecting  molecular  movements  with  the  sensa- 
•  tion  of  sound. 

In  so  far  as  all  sensations  are  generalized  into  a  common 
fact  of  sensation,  having  similarity  with  diversity,  so  far  may 
we  generalize  the  laws  that  connect  sensation  with  corporeal 
activities.  This  is  a  real  and  important  step  of  genei-alization. 
Yet  it  does  not  supersede  the  necessity  of  other  laws  for  con- 
necting special  and  irresolvable  modes  of  sensation  with  their 
special  seats  of  corporeal  activity.  We  may  have  a  law  of 
pleasure  and  pain  generally ;  yet  we  need  laws  for  the  distinct 
modes  of  pleasure  and  pain— the  pleasures  of  light,  of  sound, 
&c. — inasmuch  as  these  cannot  be  resolved  into  each  other. 

The  great  generalities  relating  to  Force  all  refer  to  one 
sensibiUhj  of  our  nature— the  muscular,  or  the  active  side  ; 
owmg  to  which  fact,  they  may  admit  of  unity  of  law,  or  a 
common  statement.  Likewise,  there  may  be  unity  of  law  as 
regards  Light  and  Colour,  provided  all  the  modes  and  varie- 
ties are  resolvable  into  the  variation  in  degree  of  some  funda- 
mental mode  of  consciousness.  If  there  be  several  fundamental 
modes,  there  must  be  a  law  for  each  ;  thus  there  may  be 
wanted  one  law  for  white  light,  with  its  degrees,  and  one  for 
each  of  the  primary  colours— four  laws  for  the  sense  of  sight. 

We  may  be  able  to  discover  how  Heat  causes  Light  to  the 
extent  of  generalizing  the  molecular  condition  of  luminosity, 
and  connecting  this  with  the  molecular  condition  of  high 
temperature ;  but  that  such  molecular  condition  and  its  ac- 
companiments—radiation, i-efraction,  &c.  —  should  yield  the 
sensation  of  light,  must  always  be  expressed  in  a  distinct  law, 
a  law  uniting  an  objective  with  a  subjective  experience.  Such 
is  the  proper  goal  or  end  of  our  knowledge  in  regard  to  the 
phenomenon. 

FALLACIOUS   AND  ILLUSORY  EXPLANATIONS. 

9.  One  form  of  illnsory  explanation  is  to  repeat  the  fact 
in  different  language,  assigning  no  other  distinct  yet 
parallel  fact. 

This  is  ridiculed  in  Moliere's  physician,  who  gives  as  the 
reason  why  opium  causes  sleep,  that  it  has  a  soporific  virtue. 


ILLUSION   OP   FAMILIARITY. 


355 


Not  much  IS  done  to  explain  the  greenness  of  the  leaf  of 

l^^^u^^  \f  ^'''?  ^^^*  '*  '^  ^'^^  ^^  ^  substance  named  *  chloro- 
phyll. The  only  step  gained  is  the  fact  (if  it  be  a  fact)  that 
greenness  m  all  plants  is  due  to  the  same  substance. 

A  simile  IS  sometimes  offered  for  an  explanation.  Black's 
i^atetit  Heat  was  merely  a  re-statement  of  the  fact :  he  miffht 
have  gone  on  to  call  it  secret,  concealed,  embodied,  shutfup 
Meat ;  all  which  expressions  would  merely  iterate  the  circum- 
stance that  a  certain  amount  of  heat  no  longer  appeared  as 
heat  to  the  sense,  or  to  the  thermometer.  f^H      «u  da 

It  is  with  the  great  ultimate  generalizations,  such  a^  the 
Uniformity  of  Nature,  and  the  Axioms  of  Mathematics,  that 
we  are  most  prone  to  give  as  a  reason,  or  proof,  a   mere 
various   wording  of  the  principle    itself.      *  Why  must   the 
future  resemble  the  past  ?  '     *  Because  Nature  is  Uniform  ' 
L,.n    %  P^'^^j^.^f^?^' ,  sleep,  wa^   referred  by  Whewell  to  a 
law  of  periodicity  m  the  animal  system.      This,  however,  does 
nothmg  but  repeat  the  fact  to  be  explained  ;    there  is  no 
assimilation  with  another  fact,  so  as  to  yield  a  higher  ^ene- 
ff  l^'-^l         would  be  inductive  explanation,  and  nl  reference 
to  a  higher  generality  already  formed,  which  would  be  deduc- 
tive explanation.     A  step  towards  real  explanation  is  made  bv 
companng   it  with  the  repose   or  quiescence  of  the  organs 
after  any  activity  whatsoever.        This  is  to  assimilate  the 
phenomenon  with  another  distinct  phenomenon  ;  the  two  taken 
together  form  a  higher  generality,  which,  so  far  as  it  ffoes,  is 
an  explanation.  °     ^ 

10.  Another  illusion  consists  in  regarding  phenomena 
as  simple  because  they  are  familiar.  «nomena 

ihJZl  ^''°''"^''  f^^'i^'  T"^  *^  '^°^  ^^  ^«  ^eed  of  explanation 
themselves  and  to  be  the  means  of  explaining  whatever  cm 
be  assimilated  to  them.  ^^ 

Thus,  the  boiling  and  evaporation  of  a  liquid  is  supposed  to 
h«t;If7f  Bimple  phenomenon  requiring  no  explanation,  and 
a  satisfactory  medium  of  the  explanation  of  rarer  phenomena. 

3to  IvW  n  °M  ^"^  uP  "•  *°  *''^  ""instructed  mind,  a  thing 
wholly  mt^lhgible;  whereas,  to  the  man  acquainted  with 
Physical  science  the  liquid  state  is  anomalous  and  inexplicable. 
The  I'gttmg  of  a  fire,  by  contact  with  a  flame,  is  a  great 
scientific  difficulty;    yet  few   people   think   it   sa      A  soap 

™Vrn*  f°°^?'  f  unexplained  phenomena.  Volnntai> 
action,  from  famihanty,  has  long  been  reckoned  so  simple  in 


•1*1 

-m 


356 


EXPLANATION   OF  NATURE. 


IJ: 


'%'.', 


\i.k 


itself  as  to  have  provided  a  satisfactory  explanation  of  all 
other  modes  of  generating  mechanical  force, 

11.  The  greatest  fallacy  of  all  is  the  supposition  that 
something  is  to  be  desired  beyond  the  most  generalized 
conjunctions  or  sequences  of  phenomena. 

It  is  supposed  by  many  that  the  possession  of  a  supreme 
generality  on  any  subject  is  insnflicient ;  the  mind,  it  is  said, 
craves  for  something  deeper,  and  this  craving  (which  can 
never  be  satisfied)  is  considered  to  be  proper  and  legitimate. 
The  genei*alization  of  Gravity  leaves  behind  it  a  sense  of 
mystery  unsolved,  as  if  there  were  something  farther  that  we 
might  arrive  at  if  obstacles  did  not  intervene. 

Newton  seemed  unable  to  acquiesce  in  gravity  as  an  ulti- 
mate fact.  It  was  inconceivable  to  him  that  matter  should 
act  upon  other  matter  at  a  distance,  and  he  therefore  desired 
a  medium  of  operation,  whereby  gravity  might  be  assimilated 
to  Impact,  But  this  assimilation  has  hitherto  been  impracti- 
cable ;  if  so,  gravity  is  an  ultimate  fact,  and  its  own  sufficing 
and  final  explanation. 

The  acceptance  of  the  law  of  universal  gravitation  as  a  full 
and  final  solution  of  the  problem  of  falling  bodies,  without 
hankering  or  reservation,  is  the  proper  scientific  attitude  of 
mind.  There  seems  no  hope  at  present  of  making  it  fraternize 
with  a  second  force,  and  there  is  no  other  legitimate  outgoing 
of  enquiry  with  reference  to  it. 

In  the  same  way  the  mysteriousness  often  attributed  to 
Heat,  is  partly  resolved  by  the  Theory  of  Correlated  Forces, 
under  which  heat  is  assimilated  to  movement.  The  subjec- 
tive fact  of  heat — the  sensation  of  the  mind  so  described,  is  a 
fact  coming  under  the  general  relationship  of  body  and  mind. 

Light  is  still  a  mystery  in  the  legitimate  sense  ;  it  has  been 
but  imperfectly  generalized  as  regards  its  physical  workings. 
Every  isolated  phenomenon  is,  in  the  proper  acceptation,  a 
mystery. 

Apparent  contradiction  is  something  that  demands  to  be 
explained  ;  investigation  should  never  stop  short  of  the  attain- 
ment of  consistency.  Thus,  the  glacial  period  of  the  earth's 
history,  is  at  variance  with  the  only  hypothesis  yet  framed  as 
to  the  solar  agency — the  slow  but  gradual  cooling  in  the  course 
of  ages. 

The  molecular  aspect  of  the  Correlated  Forces  is  repulsion 
(as  in  Heat),  yet  in  Magnetism  and  in  Friction  Electricity,  it 
appears  as  attraction. 


HI 


MYSTERY  OF  BODY   AND  MIND. 


357 


Free-will  is  often  stated  as  a  hopeless  and  insoluble  contra- 
diction. To  leave  any  problem  in  such  a  condition  is  un- 
Bcientific. 

The  union  of  Body  and  Mind  has  long  been  considered  the 
mystery  by  pre-eminence.     The  prevailing  opinion  has  been 
that  this  connexion  would  for  ever  resist  and  paralyze  explana- 
tion.     Yet,  the  scientific  mode  of  dealing  with  the  case  is 
clear.     The  material  properties  and  the  mental  properties  are 
each  to  be  conceived  according  to  their  own  nature — the  one 
by  the  senses,  the  other  by  self-consciousness.     We  then  en- 
deavour to  assimilate  and  generalize  to  the  utmost  each  class 
of  properties ;  we  generalize  material  properties  into  inertia, 
gravity,  molecular  forces,  &c. ;  we  generalize  mental  proper- 
ties into  pleasures,  pains,  volitions,  and  modes  of  intelhgence. 
We  next  endeavour  to  rise  to  the  most  general  laws  of  the 
union  of  the  two  classes  of  properties  in  the  liuman  and  animal 
organization.     When  we  succeed  in  carrying  this  generalizing 
operation  to  the  utmost  length  that  the  case  appears  to  admit 
of,  we  shall  give  a  scientific  explanation  of  the  relationship  of 
body  and  mind.     Any  farther  explanation  is  as  incompetent^ 
as  it  is  unnecessary  and  unmeaning. 

Such  language  as  the  following  is  unscientific  : — *  Conscious 
sensation  is  a  fact,  in  the  constitution  of  our  corporeal  and 
and  mental  nature,  which  is  absolutely  incapable  of  explana- 
tion.' The  only  meaning  attachable  to  this  is,  that  bodily  facts 
and  mental  facts  are  fundamentally  distinct,  yet  in  close 
aUiance.  So— *To  this  day,  we  are  utterly  ignorant  how 
matter  and  mind  opemte  upon  each  other.*  Properly  speak- 
ing there  is  nothing  to  be  known  but  the  fact,  generalized  to 
the  utmost. 

*  Is  there  *  says  Hume  *  any  principle  in  all  nature  more 
mysterious  than  the  union  of  soul  and  body  ;  by  which  a 
supposed  spiritual  substance  acquires  such  influence  over  a 
material  one,  that  the  most  refined  thought  is  able  to  actuate 
the  grossest  matter  ?  ' 

Again,  *we  know  nothing  of  the  objects  themselves  which 
compose  the  universe  ;  our  observation  of  external  nature  is 
limited  to  the  mutual  action  of  material  objects  on  one  another.* 
What  is  the  good  of  talking  of  a  supposable,  and  yet  impos- 
sible, knowledge  ?  * 

•  See  Febeier's  Remains  (vol.  II.  p.  436),  for  some  pertinent  lemarkt 
on  the  nature  of  Explanation. 


CHAPTER  XIIL 


HYPOTHESES. 


■1  \ 


■■■!    I 


1.  Vanons  meanings  belong  to  tlie  word  Hypothesis. 

I.  It  means  the  suppositions,  suggestions,  or  guesses,  as 
to  any  matter  unknown,  leading  to  experimental  or  other 
operations,  for  proof  or  disproof. 

In  the  course  of  a  research,  many  suppositions  are  made, 
and  rejected  or  admitted  according  to  the  evidence.  Kepler 
made  an  incredible  number  of  guesses  as  to  the  planetary 
relations  before  he  discovered  the  actual  laws.  Davy  sup- 
posed the  alkalies  to  be  compounds  before  he  established  the 
fact  by  decomposing  them. 

In  the  Inductive  operation  of  arriving  at  general  laws,  the 
supposition  made  is  some  law  that  appears  likely  to  explain 
the  fact,  as  Kepler's  Third  Law  (of  periodic  times  and  mean  dis- 
tances). Such  suggested  laws  have  to  be  duly  verified 
according  to  the  Experimental  Methods. 

In  the  properly  Deductive  operation  of  carrying  out  a  law 
by  bringing  cases  under  it,  the  supposition  is  an  identity^  as  in 
the  examples  already  given  under  the  Deductive  Method. 
The  hypothesis  of  a  man's  being  guilty  of  a  certain  crime  is  of 
this  nature ;  the  proof  consists  in  the  tallying  or  fitting  of  the 
circumstances  of  the  accused  with  the  circumstances  of  the 
crime  (commonly  called  *  circumstantial  evidence*).  Of  the 
same  nature  is  *the  hypothesis  of  Wolfe  with  respect  to  the 
origin  of  the  Homeric  poems  ;  the  hypothesis  of  Niebuhr, 
with  respect  to  the  derivation  of  portions  of  the  early  Roman 
history  from  ballads  or  epic  poems  ;  the  hypotheses  of  Eich- 
horn.  Marsh,  and  others,  with  respect  to  the  origin  of  the  text 
of  the  four  gospels ;  the  hypothesis  of  Horace  Walpole,  with 
respect  to  the  character  of  Richard  the  Third,  and  vai'ious 
hypotheses  with  respect  to  the  Man  in  the  Iron  Mask.  So 
there  are  hypotheses,  in  literary  history,  as  to  the  authorship 
of  certain  works,  as  the  Aristotelian  CEcmiomics^  the  treatise 
De  Imitatione  Christie  the  Letters  of  Junius.  In  each  of  these 
cases  a  supposition  is  made,  the  truth  of  which  is  tried  by 
combining  it  with  all  the  cuxumstances  of  the  case.* 


A  HYPOTHESIS  DEFINED.  359 

These  cases  contain  no  matters  for  lo^cal  (iWox^^^\r.r.     m. 

2.  The  definition  of  a  Hypothesis  (accordino'  to  Miin  i, 

a"  eement  with  Zl  ?  °1''  ^  ^""^""^  conclusions  in 
0?  the  h'JoXsi^"^  '""^  '  *'^  ^^■^^'"^'^^  ''^^"o  '^^  proof 

The    only   resource    then,   is   to    comr^^r^   111  ^      ^' 

with  what  would  result  U  ^heTvS  modes'TS' 
If  these  appearances  are  consistent  with  one  modfi  nnl^  tk 

givt  ta:SnTe:kTtri;Lr':fr'  "°"t  - » 

the  n.an's  conduct  is  exactlfw^ttaTLlr ITd  fc 
The  soundness  of  the  criterion  depends  annn  tw    u  • 

i^/eSif  -  --'-^''-  °^  -«- "'-  wt[^  ^:x 

3.  It  is  manifestly  desirable,  in  assumptions  'elatina  t» 
natural  agencies  that  these  should  be  known  to  exi  t  |ht 
Hypothesis  IS  then  limited  to  such  points  ^Itheir  pre! 
sence.  their  amount,  and  the  law  of  their  operation!      ^ 

electric^y  to  „agn^etisn.,  to^^SuTes't'bll  ZnC '  ^^ 
crowded  dwelLngs,  or  to  some  combination  of  these  ^Th^ 
agencies  are  real ;  every  one  of  them  is  whTt  Newto^Wm.! 
a  vera  causa.    What  is  hypothetical  is  the  t t„7p-e^r  <J 


.  !. 


I 


360 


HYPOTHESES. 


li? » 


one  or  other,  tlie  mode  of  operation,  and  the  sufficiency  to 
prodnce  the  effect.  If  all  these  could  be  established  m  favour 
of  one,  the  point  would  be  proved.  If  the  presence  cannot  be 
proved  (the  difficulty  in  past  effects),  there  must  be  shown  an 
exclusive  fitness  in  some  one  to  account  for  the  appearance.^ 

The  illustrious  example  of  Gravity  may  be  quoted  in  its 
bearing  on  Hypotheses.  Newton's  suggestion  was,  that  celes- 
tial attraction  is  the  same  force  as  terrestrial  gravity.  He 
thus  proceeded  upon  a  real  or  known  cause  ;  the  hypothetical 
element  was  the  extension  of  gravity  to  the  snn  and  planets. 

The  preliminary  difficulty  to  be  got  over  was  the  rate  of 
decrease  of  the  force  according  to  distance.  From  Kepler's 
laws,  it  was  proved  that  celestial  attraction  diminishes  as  the 
square  of  the  distance  increases.  Was  this  true  of  the  earth's 
gravity  ?  The  fall  of  the  moon  was  ihe  criterion,  and  exactly 
coincided  with  that  supposition.  Thus,  then,  the  law  of  the 
sun's  attraction  and  the  law  of  the  earth's  attraction  are  the 
same.  The  earth's  attraction  extends  to  the  moon  ;  may  li 
not  extend  to  the  sun,  and  may  not  the  sun  reciprocate  the 
very  same  attraction  ?  .  .      ,  . 

The  wonderful  amount  of  tallying  or  coincidence  in  this 
case  was  sufficient  in  the  minds  of  all  men  to  justify  the 
assumption  that  the  two  attractions  are  the  same.  The 
hypothesis  was  proved  by  its  consequences.  And,  as  no  rival 
supposition  has  ever  stood  the  same  tests,  the  Newtonian 
theory  is  considered  as  beyond  the  reach  of  challenge. 

The  rival  hypothesis  to  gravity,  in  the  explanation  of  the 
celestial  motions,  was  the  Cartesian  vortices,  or  whirlpools  of 
ether,  which  floated  the  planets  round,  as  a  chip  revolves  in 
an  eddy  of  a  stream. 

The  identity  here  assumed  is  between  the  circular  motion 
of  the  planets,  in  what  is  commonly  supposed  to  be  empty 
space,  and  the  circular  motion  of  a  whirlpool  of  water  or  of 

air. 

The  first  obvious  disparity  respects  the  fluid  medium,  in 
the  whirlpool  of  water  we  have  a  liquid  mass  with  density 
sufficient  to  buoy  up  wood,  and  mechanical  momentum  suffi- 
cient to  propel  it  in  the  direction  of  the  stream.  No  such 
fluid  mass  is  known  to  be  present  in  the  celestial  spaces ;  the 
very  supposition  is  hostile  to  all  familiar  appearances.  A 
fluid  sufficient  to  move  the  planets  at  the  rate  they  move  in 
would  have  numerous  other  consequences  that  could  not 
escape  detection.  It  would  mix  with  our  atmosphere  as  an 
active  element  and  produce  disturbances  on  the  earth's  surface. 


ASSUMPTION  OF  A  NEW  AGENT. 


361 


In  this  vital  circumstance,  therefore,  the  Comparison  fails ;  the 
assimilation  is  incompetent. 

A  second  disparity  was  brought  to  light  in  Newton's  criti- 
cism of  the  scheme.  The  laws  of  a  whirlpool  are  not  the  laws 
of  the  planetary  orbits  ;  a  whirlpool  is  incompatible  with  the 
laws  of  Kepler.  Now,  we  cannot  assimilate  two  mechanical 
phenomena,  two  attractions,  for  example,  unless  they  follow 
the  same  law  of  force.  This  is  a  vital  point  in  a  mechanical 
comparison.  The  following  of  the  same  dynamical  law  was 
the  crowning  circumstance  of  the  likeness  between  gravity  and 
solar  force. 

It  would  be  said,  therefore,  that  the  Cartesian  scheme  did 
not  assign  a  vera  causa.  It  assigned,  no  doubt,  a  mode  of 
action  quite  familiar  to  us  ;  whirlpools  are  a  real  fact.  But 
it  assumed  a  material  substance  unlike  anything  hitherto  dis- 
covered ;  water  we  know,  and  air  we  know,  but  the  entity 
demanded  for  the  vortices  is  entirely  foreign  to  all  our  experi- 
ence of  material  things. 

4.  As  it  would  seem  irrational  to  affirm  that  we  already 
know  all  existing  causes,  permission  must  be  given  to 
assume,  if  need  be,  an  entirely  new  agent.  The  conditions 
of  proof  are,  in  this  case,  more  stringent. 

The  chief  example  of  this  kind  of  Hypothesis  is  the 
Undulatory  Theory  of  Light. 

The  supposition  of  an  etherial  substance  pervading  all  space, 
and  by  its  undulations  propagating  Light  and  Heat^as  the  air 
propagates  sound,  is  in  accordance  with  many  of  the  facts  of 
Light,  more  especially  what  is  called  the  Interference  of  Light, 
a  generalization  of  many  distinct  appearances.  The  hypothesis 
also  served  to  discover  new  facts  of  luminous  agency. 

Assuming  what  is  not  strictly  accurate  as  yet,  that  the 
undulatory  hypothesis  accounts  for  all  the  facts,  we  are  called 
on  to  decide  whether  the  existence  of  an  undulating  ether  is 
thereby  proved. 

We  cannot  positively  affirm  that  no  other  supposition  will 
explain  the  facts  ;  what  we  can  say  is,  that  of  all  the  hypotheses 
hitherto  suggested,  this  approaches  the  nearest  to  an  exact 
explanation.  Newton's  corpuscular  hypothesis  is  admitted  to 
have  broken  down  on  Interference ;  and  there  is  at  the  present 
day,  no  rival. 

Still,  it  is  extremely  desirable  in  all  such  hypotheses,  to  find 
some  collateral  confirmation,  some  evidence  aliunde,  of  the 
supposed  ether.     This  is  supplied  in  part  by  the  observationi 


362 


HYPOTHESES. 


on  the  comet  of  Eucke.  If  the  retardation  of  that  comet,  and 
other  observations  of  a  like  nature,  establish  the  fact  of  a 
resisting  or  inert  medium,  there  will  remain,  as  hypothetical, 
the  properties  of  that  medium,  namely,  tlie  peculiar  mode  of 
elasticity  fitted  for  transmitting  luminous  and  other  emana- 
tions. 

There  is  farther  to  be  urged,  in  support  of  the  hypothesis, 
its  constancy  with  the  other  hypothesis  that  regards  Radiant 
Heat  and  Light  as  the  propagation  of  molecular  movements 
from  hot  and  luminous  bodies.  The  transmission  of  these 
influences  through  space,  by  the  communication  of  molecular 
impulse,  is  in  harmony  with  their  character  as  motions  in  the 
molecules  of  the  masses  of  ordinary  matter. 

An  additional  confirmation  is  supplied  in  the  remarkable 
fact  that  bodies,  when  cold,  absorb  the  same  rays  (of  the  solar 
spectrum)  that  they  give  out  when  hot.  This  is  precisely 
analogous  to  the  law  of  musical  strings,  namely,  that,  of  the 
notes  sounded  by  another  instrument  in  their  neighbourhood, 
they  assume  each  its  own  note. 

5.  Some  Hypotheses  consist  of  assumptions  as  to  the 
minute  structure  and  operations  of  bodies.  From  the 
nature  of  the  case,  these  assumptions  can  never  be  proved 
by  direct  means.  Their  only  merit  is  their  suitability  to 
express  the  phenomena.     They  are  Representative  Fictions. 

All  assertions  as  to  the  ultimate  structure  of  the  particles  of 
matter  are,  and  ever  must  be,  hypothetical.  Yet  we  must  not 
discard  them  because  they  cannot  be  proved  ;  the  proper  cri- 
terion for  judging  of  their  value  is  their  aptness  to  represent 
the  phenomena.  That  Heat  consists  of  motions  of  the  atoms 
can  never  be  directly  shown  ;  but  if  the  supposition  is  in  con- 
sistency with  all  the  appearances,  and  if  it  helps  us  to  connect 
the  appearances  together  in  a  general  statement,  it  serves 
an  important  intellectual  function. 

The  phenomena  of  the  solid,  liquid,  and  gaseous  state  of 
matter  can  be  represented  by  the  opposiug  play  of  two  sets  of 
forces — the  attraction  of  cohesion  inherent  in  the  atoms  of 
each  substance,  and  the  repulsive  energy  generated  by  the 
heat  motions.  In  crystals,  the  heat  motions  are  at  a  minimum, 
and  in  that  case,  the  cohesion  assumes  a  polar  character,  or  is 
concentrated  at  particular  points,  whose  difference  of  relative 
situation  makes  difference  of  crystalline  form. 

The  Undulatory  hypothesis  of  Light,  even  although  it  may 
never  be  fully  established  as  fact,  will  have  a  permanent  value 


REPRESENTATIVE  FICTIONS. 


363 


as  a  Representative  summary  of  the  facts  of  Light ;  and  may 
be  gradually  carried  to  perfection  in  this  character. 

In  a  paper  by  Graham,  on  the  *  Molecular  Mobility  of  Gases,' 
published  in  the  Transactions  of  the  Royal  Society,  1863, 
there  is  put  forward  a  hypothesis  of  the  Constitution  of 
Matter.     The  assumptions  are  these  : — 

(1)  The  various  kinds  of  matter  may  consist  of  one  species 
of  Atom  or  molecule,  having  a  different  kind  of  movement  in 
each  substance.  This  is  in  harmony  with  the  equal  action  of 
gravity  upon  all  bodies. 

^  (2)  The  greater  the  energy  or  swing  of  the  primordial  and 
inalienable  movements  of  the  ultimate  atoms,  the  lighter  the 
mass.  The  leading  fact  named  Density  or  specific  gravity  is 
represented  by  this  assumption. 

(3)  These  ultimate  molecules,  whose  primitive  movement 
gives  specific  gravity,  are  supposed  to  be  made  up  in  groups, 
each  group  having  a  farther  movement,  vibratory  or  other ; 
which  second  superinduced  movement  represents  the  gaseous 
molecule  affected  by  Heat,  and  leading  to  gaseous  expansion. 
This  Graham  also  calls  the  diffusive  molecule. 

(4)  Equal  volumes  of  two  forms  of  gaseous  matter,  irre- 
spective of  weight,  have  a  facility  of  combining  ;  this  is 
Chemical  Combination.  It  is  a  hypothetical  expression  of  the 
law  connecting  Atomic  Weight  with  Gaseous  Volume.  The 
gaseous  state  is  expressed  by  Graham  as  the  typical  state  of 
matter ;  '  the  gas  exhibits  only  a  few  grand  and  simple  fea- 
tures.* 

The  special  point  of  the  hypothesis  consists  in  assuming 
motions  within  motions,  like  primary  and  secondary  planets. 
There  is  no  limit  to  the  successive  groupings  and  their  charac- 
teristic movements.  For  still  more  complex  properties,  new 
groupings  may  be  assumed. 

A  somewhat  different  hypothesis  of  Molecular  Motions  has 
been  given  by  Mr.  Clark  Maxwell  (Phil.  Trans.  1866).  It 
might  be  superadded  to  Graham's. 

Under  the  methods  of  Chemistry,  we  shall  advert  to  the 
hypothesis  named  The  Atomic  Theory  ;  and  under  the  methods 
of  Biology,  there  will  occur  other  examples  of  celebrated 
hypotheses.  Also,  in  the  Logic  of  Medicine,  the  representa- 
tive conceptions  are  brought  under  review. 

The  political  fiction  as  to  a  Social  Contract,  determining 
the  rights  of  sovertignty,  is  not  entitled  to  the  dignity  of  a 
Hypothesis.     It  is  a  pure  fabrication  to  serve  a  political,  op 


$ 


M 


364 


HYPOTHESES. 


i. 


eTen  a  party  purpose  ;  and  ranks  with  the  legends  in  the 
ancient  Grecian  states,  relied  on  as  g.vm-  validity  to  the 
title  of  a  tribe  to  its  territory,  or  of  a  family  to  the  sovereign 
power. 

6  It  has  been  said  (by  Dugald  Stewart  and  others) 
that  the  reasonings  of  Geometry  are  bnilt  upon  hjpotheses. 
The  meaning  is,  tliat  the  figures  assumed  are  abstractions, 
or  ideals,  and  do  not  correspond  to  any  real  things. 

The  word  *  hypothesis/  is  here  employed  in  a  somewhat 
peculiar  sense.  It  is  identical  in  meaning  with  *  Abstract  as 
opposed  to  actual  or  *  Concrete '  objects.  The  impoi^ant 
truth  intended  to  be  conveyed  would  probably  be  given  much 
better  by  avoiding  the  use  of  *  hypothesis. 

In  Geometry,  as  in  all  Abstract  Rpasonmg,  the  essence  of 
the  operation  is  to  view  the  things  in  one  exclusive  aspect  or 
with  reference  to  one  single  property,  although,  m  point  of 
fact,  no  object  exists  possessing  tiiat  property  m  pure  isola- 
tion  The  geometrical  Point  is  a  mark  of  position  ;  we  reason 
upon  it  solely  as  marking  position.  Every  real  point,  and 
even  the  point  that  we  conceive  in  the  mind,  possesses  at  the 
same  time  a  certain  magnitude,  a  certain  colour,  and  certain 
material  substance.  We,  however,  make  abstraction  ot  all 
these  features;  we  do  not  assume  them  m  any  degree;^ we 
drop  them  entirely  out  of  view  ;  we  consider  position,  in 
so  far  m  *  position,'  and  make  affirmations  on  that  special 
assumption.  When  we  come  to  deal  practically  with  an 
actual  point,  we  must  re-admit  all  these  properties  helonging 
to  it  in  its  concreteness ;  we  most  allow  for  the  fact  that  no 
actual  point  can  determine  an  abstract  position  ;  it  covers  an 
area,  and  therefore  does  not  fix  position  except  by  an  approxi- 

™^In^Mechanic8,  there  are  convenient  fictions  that  subserve 
the  abstraxjt  reasonings  of  the  sciences ;  as,  for  example,  the 
supposition  that  the  whole  mass  of  an  irregular  body  is  con- 
densed into  its  Centre  of  Gravity-an  operation  impossible  in 
fact,  but  having  a  practical  convenience  m  mechanical  demon- 
Btrations.  It  is  desirable,  for  certain  purposes,  that  we  should 
make  abstraction  of  the  form  and  size  of  a  mass  and  view 
only  its  weight  and  its  relative  position  to  some  other  mass  ; 
and  one  way  of  compassing  \h^  end  is  to  imagine  the  form  and 
the  size  non-exist^nt,  or  that  the  mass  exists  in  a  mathe- 
matical  point  We  say  there  is  a  certain  definite  position  in 
the  Ulterior  of  the  earth,  wherein,  if  the  whole  mass  were 


EXPERIMENTUM   CRUCIS. 


365 


concentrated,  the  earth's  attraction  for  the  sun  and  the  moon 
would  be  the  same  as  it  actually  is.  This  is  merely  a  verbal 
aid  to  the  process  of  reasoning  in  the  Abstract.  The  remark 
is  applicable  to  all  the  other  abstract  centres — oscillation, 
suspension,  gyration,  &c. 

7.  A  fact  that  decides  between  two  opposing  Hypotheses 
was  called  by  Bacon  an  experimentum  cruets. 

The  *  Instantia  Cracis '  of  Bacon  does  not  properly  belong 
to  the  Experimental  Methods  of  Induction.     It  is  the  decisive 
instance  between  two  contending  hypotheses.      Thus,  when 
the  Copernican  system  was  brought  forward  in  opposition  to 
the  Ptolemaic,  not  only  was  there  a  necessity  for  showing  that 
the  new  system  corresponded  with  all  the  facts ;   there  was 
farther  required  the  production  of  some  facts  that  it  alone 
could  conciliate.     The  first  fact  of  this  decisive  character  was 
the  Aberration  of  Light,  a  fact  incompatible  with  the  earth's 
being  at  rest.     Another  fact,  equally  decisive,  is  furnished  by 
the  recent  pendulum  experiments  of  Foucanlt  with  regard  to 
the  motion  of  the   earth.      Bacon  himself,  who  never  fully 
accepted  the  Copernican  system,  desiderated  an  *  experimen- 
tum crucis '  of  this  nature,  namely,  a  fact  to  show  that  the 
velocities  of  bodies  appearing  to  move  round  the  earth  are 
in  proportion  to  their  distance ;  which,  he  says,  would  be  a 
proof  that  the  earth  stands  still,  and  that  the  apparent  daily 
motion  of  the  stars  is  real. 

The  entire  absence  of  mechanical  ener^ry  in  the  rays  of 
light  is  regarded  as  decisive  against  Newton's  Emission 
Hypothesis.  The  most  delicate  experiments  fail  to  show  any 
moving  energy  in  the  concentrated  rays  of  the  sun ;  which 
failure  is  inconsistent  with  a  stream  of  particles  of  inert  matter. 


CHAPTER  XIV. 


APPEOXIMATE  GENEEALIZATIONS  AND  PEOBABLE 

EVIDENCE. 

1.  Probable  Inference   is   inference  from  a  proposition 
only  approximately  true. 

Every  certain  inference  supposes  that  the  major  is  a  pro- 
position universally  true,  as  *  all  men  are  mortal,'  *  all  matter 


866 


APPROXIMATE  GENERALIZATIONS. 


gravitates.*  When  a  minor  is  supplied  to  such  propositiong, 
the  conclusion  is  certainly  true. 

From  a  proposition  true  only  in  the  majority  of  instances, 
the  inference  drawn  is  not  certain,  but  only  probable.  *  Most 
(not  all)  phenogamous  plants  have  green  leaves  ;'  hence  it  is 
probable  that  any  given  class  of  these  plants  has  green  leaves. 

The  word  for  such  generalities  is  '  most ; '  the  synonyms  are 
*  many,*  *  usually,'  *  commonly,'  *  generally,'  *  for  the  most 
part,'  *  in  the  majority  of  instances.' 

2.  If  we  know  the  exact  proportion  of  cases  in  an  ap- 
proximate generalization,  we  can  state  numerically  the 
degree  of  probability  of  an  inference  drawn  from  it. 

It  being  known  that  a  certain  thiug  happens  in  nine  in- 
stances out  of  ten,  the  probability,  in  a  particular  case,  is  nine 
to  one,  or  nine- tenths.  All  the  metals,  except  copper  and 
gold,  are  devoid  of  colour,  (being  either  white  or  some  shade 
of  grey).  The  probabiUty  that  a  new  metal  is  white  or  grey 
is  as  fifty-two  to  two. 

On  the  supposition  that  the  majority  of  drunkards  are  never 
reformed,  the  probability  is  against  the  reform  of  any  indivi- 
dual drunkard.  The  strength  of  the  probability  depends  upon 
our  estimate  of  the  comparative  numbers.  If  this  estimate  is 
vague  and  uncertain, — if  we  cannot  say  whether  the  reformed 
drunkards  number  one  fiftieth,  one  twentieth,  or  one-fourth  of 
the  whole, — our  estimate  of  the  probability  in  the  given  in- 
stance is  correspondingly  vague. 

What  Hobbes  says  of  Charles  II — 

Nam  tunc  adoloscens 
Credidit  ille,  quibus  credidit  ante  Pater-— 

is  true  of  the  vast  majority  of  men  even  in  the  most  enlightened 
countries.  Hence  a  strong  probability  that  any  given  indi- 
vidual has  never  exercised  any  independent  judgment  in 
politics  or  in  religion.  A  hundred  to  one  is  a  safe  estimate  of 
such  a  probability. 

It  is  an  approximate  generalization  that  both  intelligence 
and  independent  thought  are  most  frequent  in  the  middle 
ranks  of  society.  The  generalization  has  in  its  favour  deduc- 
tive as  well  as  inductive  evidence.  We  know  the  circum- 
stances adverse  to  those  qualities  in  the  highest,  and  also  in 
the  lowest,  ranks.  Still,  it  is  but  approximate,  and  yields 
only  probability  in  every  given  application.  Like  all  proba- 
bilities, however,  if  applied  to  masses,  it  gives  certainty.    The 


PROBABLE  INFERENCES. 


367 


OoUective  action  of  a  middle  class  body  would  be  more  intelli- 
gent and  independent  than  the  action  of  the  other  classes. 

The  proposition  is  approximately  true  that  the  wealthy  are 
more  virtuous  than  the  indigent.  There  are  numerous  excep- 
tions, but  the  evidence  is  sufficient  to  prove  the  rule  as  an 
approximate  generalization.  The  only  dispute  is  as  to  the 
extent  of  it.  Direct  statistics  on  the  great  scale  are  wantino* ; 
and  the  deductive  argument  consists  in  comparing  the  tend- 
encies for  and  against  virtue  in  the  wealthy,  as  compared 
with  the  poorer  class — a  comparison  where,  Irom  the  vao-ue 
nature  of  all  estimates  of  human  conduct,  a  certain  latitude  of 
expression  must  be  allowed. 

The  characters  of  men  are  described  by  such  general  terms 
as  energetic,  timid,  teuder-hearted,  irascible,  truthful,  intel- 
lectual, and  so  on.  Even  when  most  carefully  generalized, 
these  characters  are  only  approximate ;  they  represent  prevail- 
ing tendencies,  liable  to  be  defeated  in  the  comphcacy  of 
human  motives.  So  with  classes,  professions,  and  nations. 
All  the  current  generalities  respecting  the  characteristics  of 
sex  and  of  age  are  mere  approximations.  Literary  and  Art 
criticism,  as  expressing  the  style  and  manner  of  authors  or 
artists,  is  of  a  like  nature. 

The  operation  of  laws  and  institutions  is  at  best  but 
approximate.  We  cannot  affirm  that  the  general  good  con- 
sequences follow  in  every  instance.  The  tendency  of  severe 
punishments  is  to  deter  from  crime  ;  they  may  do  so  in  nine 
cases  out  of  ten,  or  ninety-nine  out  of  a  hundred.  It  is  the 
duty  of  the  state  to  seek  out  the  mode  that  approximates 
most  to  the  desired  end.  In  such  a  case,  statistics  give  a  kind 
of  numerical  precision  to  the  general  tendency,  and  a  corres- 
ponding exactness  to  the  inference  of  probability. 

The  very  best  institutions  have  to  be  defended  on  the 
ground  of  superior  good,  not  of  absolute  or  unexceptional 
good.  This  is  all  that  can  be  said  for  liberty  as  against  re- 
straints, for  responsible  government  as  against  despotism. 

Proverbial  sayings  are  for  the  most  part  but  rude  approxi- 
mations to  truth.  Many  of  them  can  hardly  be  said  to  have 
a  preponderance  of  cases  on  their  side.  *  The  more  haste,  the 
less  speed  '  is  not  true  in  the  majority  of  instances ;  its  merit 
IS  chiefly  as  an  epigrammatic  denial  of  the  universality  of  the 
rule  that  activity  succeeds  in  its  object.  We  often  take  delight 
in  parading  the  exceptions  to  approximate  generalities ;  and 
not  a  few  of  our  proverbs  are  occupied  with  the  representation 
of  minorities.     Tallyrand's  *  No  zeal '  is  incorrect  as  a  rule  • 


n 


;  4S 


368 


APPROXIMATE   GENERALIZATIONS. 


the  mle  that  it  crosses,  however,  is  bat  approximate,  and  haa 
exceptions  ;  the  point  of  the  saying  lies  in  suggesting  these. 

3.  It  is  a  legitimate  effort  to  endeavour  to  make  the 
approximation  of  a  rule  as  close  as  possible,  before  apply- 
ing it  to  cases.     This  can  be  done  in  various  ways. 

(1)  An  approximate  generalization  is  rendered  absolutely 
certain  in  its  scope,  when  all  the  exceptions  can  be  enumer- 
ated ;  as  in  grammar  rules,  and  in  Acts  of  Parliament  contain- 
ing schedules  of  exceptions. 

(2)  A  very  near  approximation  can  be  made  if  we  know  the 
exact  occasions  and  circumstances  where  the  rule  holds.  Thus 
that  *  Honesty  is  the  best  policy  *  is  in  the  abstract  only  a 
rough  generalization ;  it  is  far  from  the  exact  truth.  But  we 
are  able  to  assign  the  specific  circumstances  where  it  holds 
good  more  nearly.  The  *  honesty  '  should  exactly  correspond 
to  the  standard  of  the  time,  not  rising  above,  and  not  falling 
below  the  established  code.  It  should  be  apparent  and  not 
concealed  from  view.  It  should  contribute  something  to  the 
advantage  of  persons  of  weight  and  influence.  Thus  limited 
and  quaUfied,  the  approximation  is  very  near  the  truth ;  yet 
not  altogether  true.  The  dishonest  successful  men  are  still 
sufficiently  numerous  to  constitute  a  standing  exception  to  the 

maxim.  . 

The  Proposition  *  Knowledge  is  virtue  '  was  maintained  in 
the  Socratic  school.  It  is  an  ap^proximate  generalization, 
giving  a  certain  small  probability  in  its  applications.  That  it 
has  the  truth  on  its  side  is  proved  by  the  statistics  of  crime  ; 
the  majority  of  criminals  coming  from  the  least  instructed 
part  of  the  population.  Still,  the  exceptions  are  numerous. 
We  know  from  deductive  considerations  that  virtue  does  not 
spring  directly  from  the  knowing  faculties  ;  the  filiation  is  in- 
direct or  circuitous.  The  best  application  of  so  slight  a  pro- 
bability is  to  take  it  with  concurring  probabilities.  The 
conditions  of  a  virtuous  character  can  be  stated  with  consider- 
able precision,  while  intellectual  culture  also  is  an  element 
whose  value  can  be  assigned.  Hence,  in  applying  the  rule  to 
a  known  case,  we  can  infer  with  a  far  higher  probability,  than 
could  be  given  by  any  one  approximate  generality,  as  to  the 
virtuous  tendencies  of  knowledge,  of  parentage,  of  occupation, 
and  other  circumstances.  We  can  unite  all  the  presumptions 
into  one  still  stronger. 

It  is  a  usual  defect  of  empirical  generalities  that  the  sub- 
ject of  them  is  badly  defined,  or  that  the  circumstances  where 


INCREASED  APPROXIMATIONS. 


369 


the  predicate  holds  cannot  be  exactly  specified.  This  is  a 
common  defect  in  the  practice  of  medicine.  A  drug  has  a 
certain  efficacy  in  the  majority  of  instances,  and  is  therefore 
only  probable  in  its  consequences.  A  higher  knowledge 
would  give  the  exact  conditions  wherein  it  succeeds,  which 
would  be  to  convert  the  approximation  into  certainty. 

So  in  Politics.  Certain  institutions,  as  for  example  Free 
Government,  are  good  for  nations  generally.  In  some  cases, 
they  fail.  It  is  for  political  science  to  specify  accurately  the 
circumstances  where  they  are  suitable,  and  those  where  they 
are  unsuitable  ;  by  which  means  we  may  attain  to  rules  of  a 
certain,  or  nearly  certain  character. 

It  is  commonly  said  that  being  educated  at  a  public  school 
developes  particular  manly  virtues,  as  self-reHauce,  courage, 
&c.  This  is  but  an  approximate  generalization.  If  we  had 
the  comparative  numbers  of  the  successes  and  the  failures,  we 
could  assign  the  probability  in  a  given  instance.  Still  better, 
however,  would  be  the  enquiry,  what  are  the  circumstances 
wherein  the  eifect  would  arise  ;  what  kind  of  youths  would  be 
operated  on  in  the  salutary  way  ? 

It  is  an  approximate  generalization  that  absolute  sovereigns 
abuse  their  power  ;  it  is  true,  in  a  large  majority  of  instances, 
but  not  in  all  instances.  It  can  be  converted  into  a  still  closer 
approximation,  if  we  can  assign  the  particular  situation  of  an 
individual  sovereign — the  motives  operating  upon  him  person- 
ally, either  as  encouraging  or  as  checking  the  despotic  vices. 
Hence,  by  a  series  of  provisos  (as  Mr.  Mill  remarks)  we  may 

render  an  approximate  rule,   an   almost  certain  rule  : An 

absolute  monarch  will  abuse  his  power,  unless  his  position 
makes  him  dependent  on  the  good  opinion  of  his  subjects,  or 
unless  he  is  a  person  of  unusual  rectitude  and  resolution,  or 
unless  he  throws  himself  into  the  hands  of  a  minister  posses- 
sing these  qualities.* 

4.  Approximate  generalizations  give  an  opening  to  the 
bias  of  the  feelings,  and  to  the  arts  of  a  sophistical  reasoner. 

It  is  impossible  to  deal  fairly  with  an  approximate  genera- 
lization, except  by  forming  some  estimate,  the  best  that  can 
be  had,  of  the  instances  on  one  side  and  on  the  other.  This 
is  often  difficult  even  to  the  most  candid  and  painstakiatr 
truth-seeker.  Nothing  then  is  easier  than  to  turn  away  the 
mind  from  a  part  of  the  instances,  and  to  decide  upon  the 
remainder.  Any  strong  feeling  has  this  blinding  efficacy. 
For  example,  our  Patent  Law  has  raised  a  certain  number  of 


'i 


t 


i 


370 


ANALOGY. 


persons  to  wealth  ;   it  lias   stimulated  a  certain  number  to 
inventions,  whether  profitable  or  not  to  the  inventors ;    it  has 
induced  a  certain  number  to  waste  their  lives  in  unproductive 
and  hopeless  enterprises  :  it  has  obstructed,  in  certain  instances, 
the  introduction   of  improvements.       Whether  the  law  has 
been  good  or  evil  on  the  whole,  depends  upon  the  relative 
number  of  these  various  instances.      Now,  it  would  be  most 
difficult  to  attain  an  exact  comparative  estimate  in  such  a  ques- 
tion.    How  easy  then  for  any  one  to  incline  to  the  instances 
favouring  a  preconceived  theory,  and  to  pay  no  heed  to  the  rest  ? 
The  arts  of  the  pleader  suit  themselves  to  this  situation. 
By  dwelling  upon  and  magnifying  the  instances  in  one  side, 
by  ignoring  and  explaining  away  those  in  the  other,  a  skilled 
advocate  reverses  the  state  of  the  numbers  in  the  approximate 
generalization,  making  the  minority  seem  the  majority.      The 
reply  needs  to  be  conducted  so  as  to  redress  the  distorted 
estimate.     (For  the  practical  applications  of  Probability  to 
Testimony  and  other  Evidence,  see  Appendix  I.). 


CHAPTER  XV. 

ANALOGY. 

1.  The  foundation  and  ju:,tification  of  all  inference  ia 
Similarity.  The  similarity  may  exist  in  various  forms 
and  degrees,  and  the  validity  of  the  inferences  will  be 
modified  accordingly. 

When  two  situations  are  exactly  the  same,  the  uniformity 
of  nature  leads  to  the  same  consequences.  Place  equal  weights 
in  a  balance  so  as  to  make  an  exact  equipoise.  Shift  the 
centre  of  motion  to  one  end,  and  that  end  will  rise  and  the 
other  fall,  every  time  that  the  change  is  made.  A  great  deal 
of  variety  may  be  introduced  into  the  experiment,  with  the 
same  result.  The  rod  may  vary  in  length,  and  in  material, 
and  the  weights  may  be  small  or  great :  so  that  we  may  have 
sameness  in  the  result  without  sameness  of  the  antecedents. 

Again,  having  seen  a  great  many  animals  die,  we  infer  that 
other  animals  living  and  to  be  born  will  die :  the  resemblance, 
together  with  nature's  uniformity,  being  the  justification. 
But  there  are  often  wide  disparities  between  the  instance* 
observed  and  the  instances  inferred. 


IITDUCTION   IN   DIFFERENCE   OF   SUBJECT. 


371 


It  was,  however,  the  object  of  the  experimental  methods  to 
eliminate  the  essential  parts  of  a  causal  situation  from  the 
non-essential  parts.  In  the  midst  of  all  the  various  forms  of 
the  experiment  with  the  balance,  we  find,  by  the  use  of  the 
methods,  that  the  one  circumstance  that  disturbs  the  equipoise 
is  to  remove  the  point  of  suspension  from  its  central  position 
in  the  beam ;  that  the  size  and  material  of  the  beam,  the  size 
and  material  of  the  weights,  are  unessential  circumstances.  So 
with  animal  life  ;  the  fact  called  organized  life  is  the  fact  ac- 
companied with  mortality ;  the  forms  and  sizes  of  animals, 
their  being  vertebrate  or  invertebrate,  are  inductively  elimin- 
ated as  unessential. 

An  inductive  inference  is  thus  an  inference  from  sameness  in 
certain  particulars,  shown  by  induction  to  be  the  particulars 
always  present  when  some  consequence  or  collateral  is  pre- 
sent.    This  is  an  inference  by  identity,  a  perfect  induction. 

2.  There  may  be  a  radical  difference  in  the  subjects  of 
two  compared  phenomena  witluut  preventing  a  strict  In- 
ductive inference.  The  sole  condition  is  that  the  same- 
ness apply  to  the  attribute  found  by  induction  to  bear  the 
consequence  assigned. 

To  say  *  there  is  a  tide  in  the  affairs  of  men  *  is  to  use  a 
mere  metaphor,  the  subjects  compared  being  totally  distinct. 
Now,  to  reason  from  one  subject  to  another  of  a  different  kind, 
might  be  called   reasoning   by  Analogy;  yet,   the  inference 
might  be  such  as  to  deserve  the  name  of  induction.     Great 
as  is  the  difference  between  the  march  of  human  history,  and 
the  flow  of  the  tides,  still,  if  the  two  phenomena  exactly  re- 
sembled in  the  single  feature  of  ebbing  and  flowing,  and  if  no 
inference  were  drawn,  except  what  this  feature  involved,  the 
argument  would  be  a  sound  and  strict  induction.     If  human 
affairs  in  any  way  are  truly  describable  as  ebbing  and  flowing, 
we  are  entitled  from  one  movement  to  predict  the  following. 
If  periods  of  great   public   excitement  in  special  topics  as 
Liberty,  Religion,  aggressive  War,  are  followed  by  periods  of 
apathy,  there  is  a  species  of  tidal  movement,  and  the  laws  of 
the  tides  may  so  far  be  applied  to  the  case,  by  a  legitimate 
induction,  or  else  by  a  deduction  founded  on  an  induction. 

The  Chinese  profess  to  found  their  government  on  the 
paternal  principle,  and  to  justify  their  peculiar  form  of  despot- 
ism on  the  similarity  of  the  state  to  a  family.  The  argument 
is  not  inductive ;  there  is  a  failure  in  essential  points.  It  is  a 
crude  metaphor.      There  is  a  certain   important  similarity, 


372 


i^NALOGY. 


namely,  tbe  fact  of  government,  involving  authority,  superior- 
ity,  and  punishment ;  and  any  inferences  drawn  upon  this 
single  circumstance  would  be  valid.  Certain  of  the  merits 
and  of  the  demerits  of  government  are  identical  m  bptH 
instances :  the  graduation  of  punishment  to  ofTence,  consist- 
ency and  fairness  on  the  part  of  the  ruler  to  the  ruled,  are 
equally  required  in  the  family  and  in  the  state.  But  it  is  not 
an  inductive  inference  to  say  that  because  the  parent  is 
despotical,  so  should  the  state.  The  two  cases  do  not  agree 
in  the  point  whence  the  despotical  relation  flows ;  in  the 
family,  the  subjects  of  government  are  children ;  in  the  state, 
the  subjects  are  grown  men,  on  a  level  with  the  rulers.  The 
inference  would  require  the  case  of  a  very  ignorant  and 
degraded  community  ruled  by  a  wise  and  high-minded  caste^ 
To  whatever  degree  a  nation  approximates  to  this  state  ot 
things,  there  is  an  identity  between  it  and  the  family  relation- 

plato's  comparison  of  the  state  to  an  individual  man  is  not 
an  analogy  in  the  proper  sense  of  the  terra.  It  is  one  of  those 
figurative  resemblances  where  the  points  of  agreement  and  of 
disacrreement  are  perfectly  ascertainable,  and  where  there  is 
no  efement  unknown.  Any  one  can  tell  whether  the  inferences 
drawn  from  the  comparison  follow  from  the  points  of  agree- 
ment. That  there  should  be  a  three-fold  classification  of 
citizens  in  the  state,  cannot  be  inferred  or  confirmed  by  an 
analysis  of  the  mind  into  three  leading  functions.  The  con- 
stitution of  a  state  has  nothing  in  common  with  the  divisions 
of  the  mental  powers  of  an  individual  man. 

The  same  remark  is  applicable  to  another  favourite  com- 
parison of  Plato's— virtue  to  health.  The  resemblance  is 
exceedingly  slight ;  yet,  if  nothing  were  inferred  but  what 
grew  out  of  that  resemblance,  we  could  not  object  to  the  use 
of  the  comparison.  But  Plato's  theory  of  punishment  derived 
from  it  supposes  a  likeness  that  does  not  hold ;  and  the  theory 
is  refuted  by  exposing  the  dissimilarity. 

The  Ancient  Philosophy  was  full  of  these  misapplied  com- 
parisons, improperly  termed  analogies. 

Speaking  with  reference  to  the  early  growth  of  Law,  Mr. 
Mayne  observes :  —  *  Analogy,  the  most  valuable  of  instru- 
ment's in  the  maturity  of  jurisprudence,  is  the  most  dangerous 
of  snares  in  its  infancy.  Prohibitions  and  ordinances,  ori- 
ginally confined,  for  good  reasons,  to  a  single  description  of 
acts,  are  made  to  apply  to  all  acts  of  the  same  class,  l)ecause 
a  man  menaced  with  the  anger  of  the  gods  for  doing  one 


PROPER  MEANING   OF   ANALOGY. 


OiO 


thing,  feels  a  natural  terror  in  doing  any  other  thing  remotely 
connected  with  it.  After  one  kind  of  food  has  been  interdicted 
for  sanitary  reasons,  the  prohibition  is  extended  to  all  food 
resembling  it,  though  the  resemblance  occasionally  depends  on 
analogies  the  most  fanciful.  So,  again,  a  wise  provision  for 
insuring  general  cleanliness  dictates  in  time  long  routines  of 
ceremonial  ablution  ;  and  that  division  into  classes  which  at  a 
particular  crisis  of  social  history  is  necessary  for  the  main- 
tenance of  national  existence  degenerates  into  the  most  disas- 
trous and  blighting  of  all  human  institutions — Caste.' 

Analogy  has  been  often  defined  *  resemblance  in  relations  : ' 
as  when  a  wave  of  water  is  said  to  be  analogous  to  an  undu- 
lation of  air,  or  of  ether ;  or  a  magnet  is  compared  to  a 
charged  Leyden  jar  because  of  the  common  polar  condition. 
This  definition  is  objectionable  chiefly  on  the  ground  of 
vagueness.  The  word  '  relation '  is  too  general  for  a  precise 
statement  of  the  case.  What  truth  or  fitness  there  is  in  the 
expression  can  be  given  in  other  ways. 

^  3  Analogy,  as  different  from  Induction,  and  as  a  dis- 
tinct form  of  inference,  supposes  that  two  things  from 
resembling  in  a  number  of  points,  may  resemble  in  some 
other  point,  which  other  point  is  not  known  to  be  con- 
nected with  the  agreeing  points  by  a  law  of  causation  or 
of  co-existence. 

If  two  substances  agree  in  seven  leading  properties,  and 
differ  in  three,  the  probability  of  their  agreeing  in  some 
eleventh  property  (not  known  to  be  connected  with  any  of  the 
ten)  is,  with  reference  to  the  known  properties,  seven  to  three. 
But  this  rule  would  be  modified  by  the  consideration  of  the 
number  of  properties  still  remaining  to  be  discovered,  a  cir- 
cumstance necessarily  indefinite.  If  we  had  reason  to  suppose 
that  a  large  number  of  properties  still  remained  undiscovered, 
the  probability  could  not  be  stated  with  the  same  fixity  or 
confidence. 

4.  A.n  argument  from  Analogy  is  only  Probable.  The 
probability  is  measured  by  comparing  the  number  (and 
importance)  of  the  points  of  agreement  with  the  number 
and  importance  of  the  points  of  difference  ;  having  respect 
also  to  the  extent  of  the  unknown  properties  as  compared 
with  the  known. 

No  Analogy  can  amount  to  full  proof ;  very  few  give  even 
a  high  probability.     *  It  may  afibrd,'  says  Reid,  *  a  greater  or 


374 


ANALOGY. 


M.' 


1688  degree  of  probability  according  as  the  things  compared 
are  more  or  less  similar  in  their  nature ;  but  it  can  afford 
only  probable  evidence  at  the  best.  i.„„:«oi 

The  natural  Kinds  afford  the  best  examples  of  the  typical 
case  of  Analogy.  They  have  numerous  properties,  known 
and  unknownf  extensive  agreements  prevail  among  groups 
of  them,  together  with  differences  more  or  less  numerous. 
Thus,  sodium  and  potassium  have  nunoerous  points  of  agree- 
ment and  a  few  points  of  difference.  There  would,  tberefore^ 
be  a  certain  amount  of  probability  that  any  effect  due  to 
Bodium,  or  a  given  compound  of  sodium,  might  arise  from 
potassium,  or  the  same  compound  of  potassiuin.  ,      ,  .  , 

^  The  celebrated  guess  of  Newton,  as  to  the  Diamond,  which 
was  afterwards  verified  by  experiment,  was  not  an  analogical 
inference  in  the  strict  sense.  Had  the  inference  been  from  a 
Binffle  body,  as  an  oil,  to  the  diamond  (the  point  of  agreement 
between  them  being  nnusual  refracting  power),  the  resem- 
blance would  have  been  too  limited  even  for  a  guess.  iho 
application  to  the  Diamond  was  the  carrying  out  ot  an 
Empirical  Law,  partially,  if  not  wholly  proved.  The  circum- 
stance  that  arrested  Newton's  attention  was  that  the  refracting 
power  of  bodies  is  very  neariy  as  their  densities  excepting  that 
unctuous  and.  sulphireous  bodies  refract  more  than  others  of  the 
same  density.  Having  obtained  measures  of  the  refractive 
powers  of  the  densities  of  twenty-two  substances  varying  m 
density  between  air  and  diamond,  he  found  that  they  tell  into 
two  classes.  In  one  class,  were  topaz,  selemte,  rock-crystal, 
Iceland-spar,  common  glass,  glass  of  antimony,  common  air  :  in 
all  which,  the  refracting  powers  are  almost  exactly  as  the 
densities,  excepting  that  the  refraction  of  Iceland-spar  is  a 
little  more  than  the  proportion.  In  the  second  class  were 
camphor,  olive  oil,  linseed  ail,  spirit  of  turpentine,  amber  ^hich 
are,  *  he  said,'  *  fat,  sulphureous,  unctuous  bod.es,  aiid  diamond 
which  *  probably  is  an  unctuous  substance  coagulated  ;  all 
these,  compared  together,  have  their  refractive  powers  almost 
exactly  proportioned  to  their  densities.  But  now,  when  the 
two  classes  are  compared,  the  refractive  powers  of  toe  second 
class  (the  unctuous  substances)  are  twice  or  thrice  as  great, 
in  proportion  to  their  densities,  as  the  refractive  powers  of  the 
first  class.  Water  has  a  middle  position  between  the  two 
classes ;  salts  of  vitriol  may  stand  between  the  earthy  sut> 
stances  and  water ;  and  spirit  of  wine  between  water  and  the 
oils.  The  suggestion  as  to  the  diamond  thus  arose  from  its 
position  among  a  number  of   highly  refracting  bodies  that 


EXAMPLES    OF  ANALOGY. 


375 


agreed  in  being  of  an  inflammable  or  combustible  nature. 
The  concurrence  of  high  refracting  power  with  inflammabS 
was   an   empirical   law  ;    and   Newton    perceiving  the  law 
extended  It  1^  the  adjacent  case  of  the  diamond,     f  he  remai  k 

powers' of^th^r^''^''"'  '"'  .^^"^^^  ^—  the  reSive 
CI       r  fl  ^^i^^T^ls  greenockite  and    octohedrite,  he  would 

oi^vZ  ^r^P^^  <>f  Analogy  proper  let  us  suppose  the  Balsam 
ot    Fern  to  possess  certain  properties,   med  cinal    or    other 

proper<I;s^^^O^  '"'  >•  '^"  ^^^f '^"'  ^^  unimportant 

^n^?/     ti  ^  proposition,  we   should  ground   a  very 

considerable  presumption,  that  the  one  might  replace  the  olher 
m  new  and  untried  applications  in  Pharmacy. 

AnWl  «  *'^*'''''a°''^^^  ^^  extended  to  Vegetable  and  to 
Anmial  species  A  quadruped  resembles  a  human  bein..  in 
yeiy  many  points  of  structure  and  function,  but  also  dVrs 

propertLf  r^^^^  '  ^'^^^  *^^^'^  -^^  ^^  undiscovered 

properties   in    both.     This    reduces    to   a   weak    probabilitv 

food'  ST  f?  ^"^  ''  ^'^  ^^^^'^  -  '^  '^^  suiUe  kS 
food,  liability  to  disease,  or  medical  treatment.     Experiments 

lirT^tT^  ''^.'  ^'^^'  ^^  *^^  ^^^^^  «»bject,  proS  we 

in  b^th  fs  nX^^^  r  --t-oted  Laiiy  ahle 

d^^elon^  r  *^^.°^7^^t^^'  ^^  *?^  "^^^'^^^^  *^«  breathing,  the 
digestion,  (fee.     The  function  of  the  saliva  and  of  the  o-a^trie 

ra^tntLVoflSe'^  '^''^^T  ^^  ^^^^^^  ^  '-st 

werVr^erit^d  :lrcCsrb  t  trtatrtTT'  r?" 

It  18  interesting  to  determine  whether  onr  inferenn^  fi-n™ 

ness,  IS  am  induction  or  only  an  ana  ogy.     We  beheve  thaf  ;„ 
human  bemga,  consciousness  is  alwavi  assoLtPrt  wi^tl  3  • 
eternal  manifestations,  called  the  sSnTof  feeler td  ';^;h 

thern'-t^l'tisn^^^^^^^ 

brutes,  some  approximating  more,  and  some  less  closSv  to 

the  human  type.^  It  would  seem,  therefore,  that  by'iudutL^ 


f 


3Y5  ANALOGY. 

and  not  by  analogy,  we  are  to  infer  the  existence  of  conscious 
ness  in  the  animals,  with  modifications  of  degree  only. 

Mind  and  Body  are  of  opposite  natnre  ;  they  are  the  greatest 
of  all  contrasts.  Yet  there  are  points  of  analogy  that  have 
been  made  use  of  to  furnish  language  and  illustration  from 
the  one  to  the  other.  As  in  material  phenomena,  we  may 
have  a  plurality  of  forces  conspiring  or  opposmg  each  other, 
the  resultant  being  arithmetically  computable,  so  in  mmd  we 
have  motives  uniting  or  opposing  their  strength,  the  effect 
being  computable  (although  not  with  numerical  exactness)  by 
adding  together  those  on  each  side,  and  noting  which  is  the 
larger  amount.  Reid  has  objected  to  this  companson,  re- 
marking that  *the  analogy  between  a  balance  and  a  man 
deliberating,  though  one  of  the  strongest  that  can  be  found 
between  matter  and  mind,  is  too  weak  to  support  any  argu- 
ment.'  Yet,  if  the  analogy  is  trusted  only  to  the  extent  of  the 
similarity,  there  is  no  good  objection  to  making  an  inference 
from  it.  Now,  the  similarity  is  complete  as  far  as  regards  the 
cumulative  effect  of  concurring  motives,  and  the  neutralizing 
or  frustrating  effect  of  opposing  motives.  Whatever  power  a 
given  motive  adds  to  a  man^s  volition  when  it  concurs,  it 
must  subtract  or  withdraw  when  it  opposes. 

The  intrusion,  by  Aristotle  and  by  Kant,  of  phraseology 
derived  from  the  intellect,  into  the  domain  of  the  feelings  and 
the  will,  may  be  pronounced  an  improper  identification,  or  an 
abuse  of  analogy.  Aristotle's  syllogism  of  the  Will,  and 
Kant's  categorical  Imperative,  point  to  no  real  resemblance ; 
a  syllogism  expresses  an  argument  conducted  by  the  reason- 
ing faculty  ;  it  has  no  relevance  or  suitabibty  to  express  the 

decisions  of  the  will.  .,1.  -rr  i     x  

Reflex  Actions  may  be  profitably  compared  with  Yoluntary 
Actions,  if  we  confine  ourselves  to  the  points  of  similanty. 
The  Reflex  is  the  voluntary  with  consciousness  suppressed  or 
made  unessential ;  on  the  corporeal  side,  there  is  a  consid^ji- 
able  amount  of  resemblance,  or  still  better,  a  gradation  or 

continuity.  ,        _  ,  ,     . 

Until  recently,  the  sun  was  considered  to  be  only  analogi- 
callv  compared  to  terrestrial  fires.  The  points  of  agreement, 
in  giving  forth  radiant  heat  with  Ught,  are  of  the  most  essential 
kind ;  but  there  was  supposed  to  be  a  disparity  also  vital.  It 
wafi  conceived  that  the  sun  gave  forth  its  vast  flood  of 
radiance,  with  no  diminution  of  intensity.  Now,  every  hot 
body  on  the  earth  cools  by  radiation.  Until  this  senous  dis. 
parity  was  got  over,  scientific  men  felt  that  all  inferences  from 


ANALOGICAL  HYPOTHESES. 


377 


terrestrial  bodies  to  the  composition  of  the  sun  were  rash  and 
unauthorized. 

Much  speculation  has  been  expended  on  the  question — Are 
the  planets  inhabited  ?  The  argument  is  at  best  analogical ; 
and  there  is  not  even  the  force  of  analogy  except  with  refer- 
ence to  a  small  number.  Bodies,  like  the  moon,  possessing  no 
water  and  no  atmosphere,  must  be  dismissed  at  once.  The 
planets  generally  appear  to  possess  atmospheres. 

We  seem  justified,  however,  in  making  a  summary  exclusion 
of  the  near  and  theremote  planets,  on  the  ground  of  temperature. 
All  organized  life  known  to  us,  is  possible  only  within  narrow 
nmits  of  temperature  ;  no  animal  or  plant  can  exist  either  in 
freezing  water  or  in  boiling  water.     Now,  the  temperature  of 
Mercury  must  in  all  likelihood  be  above  the  boiling  point, 
even  at  the  poles,  and  the  temperature  of  Uranus,  and  of 
Saturn,  below  freezing  at  the  equator.     The  constituent  ele- 
ments being  now  shown  to  be  the  same  throughout  the  solar 
system— Carbon,  Oxygen,  Hydrogen,  &c.,  we  are  not  to  pre- 
sume any  such  departure  from  our  own  type  of  organized  liie  as 
would  be  implied  by  animals  and  plants  subsisting  in  these 
extremes  of  temperature.     On  the  supposition  that  the  sun's 
temperature  has  steadily  decreased,  and  is  still  decreasing,  by 
radiation,  the  day  of  living  beings  is  past  for  Uranus  and 
Saturn,  and  perhaps  for  Jupiter  ;  it  is  not  begun  for  Mercury. 
Confining  ourselves,  therefore,  to  the  neighbouring  planets, 
and  referring  to  the  others  only  for  the  periods,  past  or  future, 
when  the  capital  circumstance  of  temperature  is  suitable,  we 
have  an  analogical  argument  as  follows.     Venus  and  Mars  are 
gravitating  masses  like  the  earth,  containing,  we  may  now  say 
with  certainty,  the  same  materials  as  this  globe— solid,  liquid, 
and  gaseous.     But  we  cannot  tell  the  precise  arrangement  of 
the  constituent  substances  ;  and,  seeing  that  with  ourselves  so 
much  depends  upon  the  mere  collocation  and  amount  of  such 
elements  as  oxygen  and  cai'bon,  we  may  consider  that  the  un- 
known properties  of  the  supposed  planets  are  considerable  in 
number,  and  serious  in  character.     The  probability  arising  out 
of  the  points  of  agreement,  if  not  greatly  affected  by  known  dif- 
ferences, is  reduced  by  this  large  element  of  the  unknown. 

Many  Hypotheses  are  of  the  nature  of  analogies  or  compari- 
sons, the  degree  and  value  of  the  resemblance  being  more  or 
less  uncertain.  Thus,  to  refer  to  the  undulatory  hypothesis 
of  Light.  When  Newton  explained  the  waves  of  water,  and  the 
vibrations  of  the  air  in  sound,  by  the  oscillations  of  a  pendu- 
lum,  he  was  assimilating  phenomena  of  the  same  mechanical 


378 


CREDIBILITY  AND   INCREDIBILITY. 


character,  and  reasoning  only  from  the  points  of  similarity'. 

But  when  we  reason  from  the  sonorous  vibrations  of  the   air 

to  the  vibrations  of  an  ether  assumed  as  occupying  space,  and 

conveying  light  and  heat,  we  work  by  analogy.      It  would, 

therefore,  not  be  irrelevant  to  apply  the  rule  of  analogy,  and 

estimate  the  points  of  agreement,  as  compared  with  the  points 

of  disagreement,  and  conclude  accordingly.      On  this  view, 

the  hypothesis  would  have  but  a  small  intrinsic  probability  ; 

it  would  be  left  in  a  great  measure  dependent  on  the  kind  of 

evidence  already  quoted  in  its  favour,  the  tallying  with  the 

special  facts  of  the  operation  of  light. 

The  first  attempt  to  penetrate  the  mystery  of  nervous  action 
was  Hartley's  hypothesis  of  vibratory  propagation,  based  on 
the  analogy  of  sound.  The  comparison  was  crude  and  un- 
satisfactory ;  but  there  was  a  certain  amount  of  likeness,  and 
the  inferences  founded  on  that  were  admissible.  It  realized 
the  fact  of  influence  conveyed  inwards  from  the  nerves  to  the 
brain,  and  outwards  from  the  brain  to  the  muscles,  thus 
suggesting  a  circle  of  action,  which  circumstance  alone  is 
pregnant  with  valuable  conclusions,  as  appeared  after  the 
discovery  of  Bell  gave  new  vigour  to  the  conception.  The 
vibratory  mode  of  communication  had  no  relevance,  and  any 
conclusions  drawn  from  it  were  unsound.  Next  came  the 
analogy  to  the  electric  current,  which  was  much  closer  to  the 
facts,  more  fertile  in  suggestions,  and  less  charged  with  mis- 
leading circumstances.  By  taking  liberties  with  current 
action,  something  like  the  liberties  taken  with  the  ether  in 
adapting  it  for  light,  we  are  able  to  shape  a  view  of  nerve 
force  that  fits  the  actual  phenomena  with  remarkable  close- 
ness. A  third  mode  of  representing  the  action  has  been 
advanced  by  Mr.  Herbert  Spencer,  which  departs  from  electri- 
cal and  chemical  action  and  reposes  upon  the  physical  property 
called  allotropism. 


CHAPTER  XYL 

OEEDIBILITY  AND  INCREDIBILITY. 

1.  There  are  propositions  supported  by  a  certain  amount 
of  evidence,  that  are  nevertheless  disbelieved.     Froni  some 


CONSISTENCY   WITH  ESTABLISHED   INDUCTIONS.        379 

circumstance  connected  with  them,  they  are  pronounced 
Incbedible. 

Irrespective  of  the  evidence  specifically  adduced  in  favour 
of  a  certain  fact,  we  often  pronounce  it  credible  or  incredible  ; 
in  the  one  case  we  believe,  and  in  the  other  disbelieve,  under 
the  same  amount  of  positive  testimony.  We  believe,  on  a 
slight  report,  that  a  fishing  boat  foundered  in  a  heavy  gale  ; 
we  do  not  believe,  without  much  stronger  testimony,  that  a 
fully  equipped  man-of-war  was  wrecked.  It  was  lately 
rumoured  that  the  Eddystone  lighthouse  was  blown  down ; 
every  one  felt  that  the  rumour  required  confirmation. 

2.  The  circumstance  that  renders  a  fact  Credible  or 
Incredible  is  its  being  consistent  or  inconsistent  with 
well-established  inductions. 

In  simple  cases,  this  is  apparent.  That  a  child  initiated  in 
crime  by  its  parents  should  become  a  criminal,  is  credible,  be- 
cause it  is  highly  probable,  being  the  result  of  a  well-grounded 
induction  of  the  human  mind.  That  such  a  child  should  turn 
out  a  paragon  of  virtue,  as  is  sometimes  described  in  romance 
we  pronounce  improbable  and  therefore  incredible.  In  the 
one  case  we  are  satisfied  with  a  small  amount  of  testimony 
in  the  other  case,  we  demand  very  strong  evidence. 

We  are  thus  often  led  to  reject  evidence  at  once  on  the 
score  of  antecedent  improbability.  We  may  be  in  the  posi- 
tion of  refusing  a  large  amount  of  positive  evidence ;  as  when 
a  number  of  respectable  witnesses  testify  that  a  man  after 
being  immersed  in  the  water  for  an  hour  has  been  resuscitated. 
It  is  to  be  remarked,  however,  that  in  all  such  cases  the  evi- 
dence tendered  is  only  probable  ;  it  may  have  a  very  high 
degree  of  probability,  it  may  be  500  to  1,  yet  it  does  not 
amount  to  certainty.  It  fails  once  in  five-hundred-and-one 
times,  and  is  therefore,  in  certain  circumstances,  not  safe  from 
rejection. 

3.  Such  well-established  scientific  inductions,  as  the 
Law  of  Gravity  and  the  Law  of 'Causation,  render  wholly  in- 
credible any  assertion  that  contradicts  them. 

That  [Mahomet's  coffin  hung  suspended  in  middle  air,  that 
a  table  of  its  own  accord  mounted  to  the  ceiling  of  a  room, 
are  facts  to  be  wholly  disbelieved. 

All  the  alleged  discoveries  of  a  perpetual  motion,  or  the 
rise  of  force  out  of  nothing,  are  incredible ;  they  are  opposed 


^=li 


,isi 


380 


CREDIBILITY   AND   INCREDIBILITY. 


to  Causation  as  expressed  tinder  the  Correlation  or  Persistence 
of  Energy.  All  supposed  modes  of  deriving  motive  power, 
otherwise  than  from  solar,  heat  past  or  present,  are  incredible. 
That  any  medium  of  force  more  economical  than  the  combus- 
tion of  coal  remains  to  be  discovered  is  all  but  incredible. 

If  any  one  affirms  that  some  change  has  happened  without 
a  cause,  we  refuse  to  listen  to  it.  An  exception  to  this  rule  is 
sometimes  claimed  in  the  case  of  the  human  will ;  but  that 
exception  has  never  yet  been  established  upon  evidence  suffi- 
cient to  cope  with  the  evidence  in  favour  of  the  law  of  causa- 
tion. 

The  principle  laid  down  by  Hume,  that  nothing  is  credible 
that  contradicts  experience,  or  is  at  variance  with  the  laws  of 
nature,  is  strictly  applicable  to  these  completely  proved  indue- 
tions.  We  cannot  receive  any  counter  evidence  in  their  case, 
unless  of  a  kind  so  strong  as  to  reverse  our  former  judgment 
and  make  them  out  to  be  mistakes.  No  mere  probability  is 
equal  to  this  task  in  regard  to  the  axioms  of  mathematics,  the 
law  of  causation,  the  law  of  gi:avity,  and  many  others. 

That  every  living  thing  proceeds  from  a  previous  living 
thing,  or  as  expressed  by  Harvey — omne  vivum  ex  ovo,  is  an 
induction  verified  by  simple  agreement,  through  a  very  wide 
experience  ;  rendering  spontaneous  generation,  for  the  present, 
incredible.  It  is  an  empirical  law,  true  within  all  the  limits 
of  human  observation  hitherto,  although  we  may  not  be  able 
to  extend  it  over  an  indefinite  period  of  time. 

Among  facts  antecedently  incredible,  we  must  rank  the 
spontaneous  combustion  of  a  human  being,  which  is  totally 
inconsistent  with  the  constitution  of  the  animal  body. 

It  has  been  alleged  by  witnesses  that  the  mummy  corn  of 
the  Egyptian  pyramids  has  been  sown  and  been  productive. 
To  a  botanist,  the  assertion  is  wholly  incredible.  Seeds  two 
centuries  old  are  so  completely  changed  as  to  lose  their 
fertility. 

There  appears  to  be  unexceptionable  testimony  to  tho  prac- 
tice of  the  Indian  Fakeers,  in  allowing  themselves  to  be  buried 
for  a  number  of  days,  after  which  they  are  dug  out  alive. 
This  would  be  wholly  incredible,  but  for  the  knowledge  that 
we  have  of  such  states  as  trance,  or  lowered  animation,  which 
dispense  with  food  altogether  for  a  time,  and  require  only  the 
minimum  of  oxygen. 

It  is  alleged  by  travellers  that  certain  tribes  subsist  upon 
earth  as  food.  This  is  admissible,  only  on  the  supposition 
that  the  earth  contains  a  quantity  of  organic  products,  such 


COMPARISON  OF  PROBABILITIEa 


381 


as  starch,  sugar,  albumen,  or  their  equivalents.  That  any 
human  being  or  animal  could  live  upon  the  purely  inorganic 
matters  of  the  soil  is  to  be  wholly  disbelieved. 

The  phenomena  of  clairvoyance  are  all  in  the  position  of 
antecedent  incredibility.  That  any  one  should  see  with  the 
eyes  bandaged  is  at  variance  with  the  conditions  of  vision  as 
established  by  all  the  authentic  experience  of  the  human  race. 
Yet  this  has  been  affirmed  by  multitudes  of  witnesses.  The 
testimony  of  witnesses,  however,  in  such  a  matter  cannot  b© 
received.  The  sole  condition  of  admitting  such  a  fact  would 
be  (what  has  never  yet  been  attempted)  a  rigorous  verifica- 
tion according  to  the  methods  of  experimental  science.  So 
with  the  other  facts  of  the  same  class — prophetic  dreams, 
visions  or  intimations  of  events  at  a  distance.  These  are  all 
opposed  to  well-established  inductions. 

4.  When  a  fact  with  a  certain  amount  of  evidence  in 
its  favour,  is  opposed,  not  to  an  established  induction,  but 
to  an  approximate  generalization  or  probability,  the  case 
is  one  of  computation  of  probabilities. 

"What  is  only  probable,  or  approximately  true,  has  excep- 
tions; an  opposite  assertion,  therefore,  may  be  credited,  if 
supported  by  a  still  higher  probability,  or  by  a  generalization 
approximating  still  more  to  certainty.  A  fact  true  ninety- 
nine  times  in  a  hundred  is  not  to  be  set  aside  by  an  opposing 
testimony  correct  only  nine  times  in  ten. 

In  an  age  when  physical  laws  were  imperfectly  understood, 
when  the  law  of  causation  itself  was  not  fully  verified,  the 
phenomenon  of  witchcraft  stood  between  opposing  probabili- 
ties. There  was  no  inductive  certainty  on  the  one  hand,  to 
controvert  the  mere  probabilities  of  human  testimony  on  the 
other.  The  physical  knowledge  even  of  Bacon  was  not 
enough  to  render  the  testimonies  in  support  of  witchcraft 
wholly  incredible,  although  it  might  have  stamped  these  with 
inferior  weight  and  cogency. 

6.  The  allegations  of  travellers  as  to  new  species  of 
plants,  or  of  animals,  are  credible  or  incredible  accord- 
ing as  they  affirm  what  contradicts,  or  what  does  not  con- 
tradict, laws  of  causation  or  of  co-existence. 

There  are  certain  peculiarities  of  structure  that  are  involved 
as  cause  and  effect  in  the  animal  system.  An  animal  species 
must  have  an  organ  for  receiving  and  digesting  food,  a  respira- 


Iff' 


^kM 


382 


CREDIBILITY  AND  INCKEDIBILITY. 


tory  organ,  a  means  of  reproduction.      Any  contradiction  to 
thfese  must  be  absolutely  rejected. 

Next  in  point  of  evidentiary  force  are  the  typical  peculiarities 
of  the  order,  as  the  four  limbs  in  the  higher  vertebrata.  An 
animal  of  the  higher  tribes,  with  both  wings  and  arms,  would 
present  an  incredible  combination  ;  there  might  not  be  absolute 
incompatibility,  but  there  would  be  such  a  departure  from  the 
type  as  experienced,  that  it  could  not  be  received  on  less 
authority  than  ocular  inspection  fortified  against  every  possi- 
bility of  delusion.  . 

New  combinations  of  compatible  organs  are  improbable 
only  in  proportion  as  they  have  been  hitherto  undiscovered. 
Flying  fish  were  improbable,  but  not  to  the  degree  of  incredi- 
bility.°  The  extension  of  our  knowledge  of  kinds,  by  showing 
new  variations,  reduces  the  improbability  in  favour  of  other 
kinds,  within  the  limits  of  compatibility.  That  a  rummant 
animal  mav  be  found  without  cloven  hoofs  is  incredible,  if 
these  are  cause  and  effect,  or  effects  of  a  common  cause  ,  it  is 
only  improbable  if  they  are  co-existences  without  causation. 
Such  a  co-existence  has  been  widely  verified,  but  not  as  yet 

exhaustively.  ,  ,  .    ■•  .  i 

A  late  distinguished  historian  for  a  long  time  doubted  the 
fact  of  persons  having  lived  more  than  a  hundred  years.  He 
did  not  regard  the  fact  itself  as  absolutely  incredible  ;  but  in 
the  absenc'e  of  authentic  registrations,  and  the  uncertainty  of 
memory  and  tradition  extending  to  events  a  century  old,  he 
considered  that  the  improbability  of  so  great  an  age  had  not 
been  overcome  by  sufficient  counter  probabilities.  At  length 
he  obtained  what  he  deemed  adequate  evidence  in  favour  of 
centenarians. 

,      6.  The  assertion  of  a  fact  wholly  beyond  the  reach  of 
.  evidence,  for  or  against,  is  to  be  held  as  untrue. 

We  are  not  entitled  to  put  the  smallest  stress  upon  a  fact 
without  evidence  in  its  favour,  because,  from  its  being  inacces- 
sible to  observation,  no  evidence  can  be  produced  against  it. 
To  affirm  that  the  centre  of  the  earth  is  occupied  by  gold,  is 
for  all  purposes,  the  same  as  a  falsehood. 

On  the  Great  Postulate  of  Experience,  we  are  to  believe 
that  what  has  uniformly  happened  in  the  past  will  continue  to 
happen  in  the  future ;  we  accept  uncontradicted  experience  as 
true.  But  where  there  has  been  no  experience,  we  can 
believe  nothing.  We  are  not  obliged  to  show  that  a  thing  is 
not ;  the  burden  lies  upon  whoever  maintains  that  the  thing  is. 


BOOK   IV. 

DEFINITION. 

The  processes  having  reference  to  the  class,  notion,  or 
concept,  have  been  already  enumerated.  The  chief  are. 
Classification,  Abstraction,  Naming  (with  a  view  to  gener- 
ahty),  Definition.  ^ 

The  class,  notion,  or  concept  as  already  explained,  is  a 
product  of  generalization.  It  may  be  constituted  by  one 
common  property,  as  resisting,  moving,  white,  bitter ;  or  by 
more  than  one,  as  house,  mind,  man. 

Classification,  in  its  simplest  form,  follows  the  identifica- 
tion  of  hke  things  ;  that  is,  a  class  is  made  up  of  things  brou<rht 
together  by  hkeness.  When  the  mind  attends  more  particu- 
larly to  the  points  of  community,  it  is  said  to  put  forth  the 
power  of  Abstraction.  A  name  applied  to  the  class  in  virtue 
ot  the  class  likeness,  is  a  General  Name.  The  precise  delinea- 
tion ot  the  likeness  by  a  verbal  statement  is  Definition. 

The  three  processes— Classification,  General  Naming,  and 
IJelinition— are  what  we  are  now  to  consider.  The  first- 
named  process.  Classification,  has  a  larger  meaning  than  the 
mere  assemblage  of  things  upon  one  or  more  points  of  likeness : 
it  includes  the  arts  for  systematically  arranging  vast  multi- 
tudes of  related  objects,  under  higher  and  lower  genera,  as  in 
what  are  called  the  three  Kingdoms  of  Nature.  With  a  view 
V  /^r®  S*®^^?""  complication,  we  shall  view  the  whole  subject 
of  Classification  last  of  the  three. 

As  regards  the  generalization  of  the  Class,  or  Notion, 
m  aU  Its  aspects,  the  fundamental  principle  is  stated  as 
follows : — 

Of  the  various  groupings  of  resembling  things,  prefer- 
ence  is  given  to  such  as  have  in  common  the  most  numer- 
ous  and  the  most  important  attributes. 

This  is  the  basis  of  natural  or  philosophical  classifications, 


3S4 


CANONS    OF  DEFINITION. 


in  contrast  to  insignificant  and  nnsnggestive  classifications ; 
as  in  the  distinction  between  the  Natural  and  the  Linneean 
systems  of  Botany.      It  may  be  termed  the  golden  rule  of 

classifying.  ^    r  *t,  • 

We  are  often  disposed  to  prefer  classes  on  account  ot  tneir 
extent,  although  the  common  attributes— the  comprehension 
or  connotation,  may  have  dwindled  down  to  a  limited  and 
nnimportant  resemblance.  Thus,  the  class  *  land  animals '  is 
very  extensive,  with  little  comprehension ;  and  more  insight 
is  imparted  by  breaking  it  up  into  groups,  as  mammalia  and 
birds,  each  having  numerous  and  important  points  of  com- 
munity. The  class  *  adherents  to  a  religious  creed'  is  so 
wide  as  to  impart  very  little  information  respecting  the  indi- 
viduals ;  the  sub-classes  Buddhists,  Mahometans,  Jews,  Roman 
Catholics,  Calvin  ists,  each  connote  a  large  circle  of  peculiari- 
ties. 


\ 


CHAPTER  I. 
CANONS  OF  DEFINITION- 

1.  Definition  consists  in  fixing  by  language  the  precise 
signification — the  Connotation — of  General  Names. 

Defining  does  not  apply  to  the  unmeaning  name.  An  arbi- 
trary name  used  for  a  particular  object  as  *  Sirius '  for  a  star, 
*  Snowdon  *  for  a  mountain,  '  Samson  *  for  a  locomotive,  is  ex- 
plained only  by  showing  or  indicating  the  thing.* 

Nevertheless,  from  the  important  consideration  already 
stated  (Introduction,  p.  6),  that  even  a  singular  is  conceived 
by  the  mind  as  a  conflux  of  generals.  Definition  becomes 
eventually  applicable  to  individual  things.  A  particular  star, 
a  mountain,  a  locomotive  engine,  may  be  represented  and 
marked  ofi"  from  all  other  things  by  a  j-eries  of  descriptive 
names  of  general  signification.  For  snob  an  operation,  how- 
ever, the  name  Description  is  more  appropriate. 

It  has  been  already  explained  (Part  I.,  p.  71)  that  a  perfect 
Definition  is  the  whole  connotation  of  the  name.  Some  notions 
have  one  point  of  community ;  some  two,  three,  or  four ;  some 
a  great  many,  as  the  often-mentioned  Kinds  ;   the  proper  and 

*  Hence  the  maxim  of  the  old  lo^cians,  '  Omnia  intnitiva  notitia  ert 
definitio  * — '  a  view  of  the  thing  itself  is  its  best  definition.' 


FUNDAMENTALS   OF  DEFINITION. 


385 


complete  Definition  must  give  an  account  of  them  all.  The 
singling  out  of  one  or  two  properties,  for  the  mere  purpose  of 
discrimination,  is  not  a  proper  or  perfect  definition. 

2.  From  the  very  nature  of  human  knowledge,  Defini- 
tion appeals  to  the  two  fundamental  principles — Agreement 
and  Difiference,  or  Generality  and  Contrast. 

I.  Every  generality  must  relate  to  particulars. 

II  To  every  real  notion,  as  well  as  to  every  particular 
experience,  there  corresponds  some  opposite,  also  real. 
This  is  simply  the  Law  of  Eelativity  or  Contrast 

As  the  statement  of  what  is  common  to  a  number  of  parti- 
cular things,  Definition  is  essentially  a  process  of  generaliza- 
tion; while  neither  particular  things,  nor  their  agreements, 
have  any  distinct  meaning,  unless  there  be  assignable  a  dis- 
tinct opposite.  The  act  of  Defining,  therefore,  consists  of  a 
generalizing  operation,  rendered  precise  at  every  step  by 
explicit  or  implicit  opposition,  negation,  or  contrast.  If, 
throughout  the  process  of  generalization,  we  avail  ourselves 
of  explicit  contrast,  to  render  precise  both  the  particulars  and 
the  generalities,  that  one  operation  would  be  enough ;  defining 
would  be  generalizing  pure  and  simple,  and  nothing  besides. 
But  there  is  often  a  great  advantage  gained  by  viewing,  in  a 
separate  and  distinct  operation,  the  opposite  or  contrast  of  the 
thing  defined ;  and  hence  we  may  lay  down  two  canons,  or 
two  stages  of  the  process — the  first  the  canon  of  Generalization, 
the  second,  the  canon  of  Contrast  or  Relativity ;  or,  as  Gene- 
ralization must  enter  into  both,  we  may  call  them  the  Positive 
and  Negative  Methods.  Taken  together  they  stow  that 
Defining  is  rendered  thorough-going,  first,  by  generalizing  the 
Particulars  of  the  Notion  propounded,  and  secondly,  by 
generalizing  the  Particulars  of  its  Negative. 

The  method  of  Defining  given  in  the  ordinary  works  on 
Syllogistic  Logic  contains  no  reference  to  a  generalizing  opera- 
tion. The  scholastic  definition  directs  us  to  assign  (1)  a 
higher  genus  of  the  thing  defined,  and  (2)  the  specific  differ- 
ence, or  the  distinction  between  the  thing  and  the  other 
species  of  the  same  genus  {per  geniis  et  differentiam).  No 
mention  is  made  of  the  way  of  obtaining  either  the  characters 
of  the  genus,  or  the  difierential  characters  of  the  species. 
Suppose  we  were  to  define  Chemistry  in  this  way  ;  (genus)  a 
Science,  (differentia)  having  reference  to  a  peculiar  kind  of 
Combination  of  Bodies,  called  chemical  j — it  is  obvious  that 


Jr 


386 


CANONS   OF  DEFINITION. 


GENERALIZATION   OF   POSITIVE   PARTICULAK3. 


387 


to  give  such  a  definition  we  most  scan  the  subjects  ordinarily 
included  in  Chemistry,  and,  by  generalizing  them,  hnd  an 
expression  suitable  to  them  all,  and  to  none  besides.  Mence, 
the  direction  to  assign  the  genus  and  the  difference,  merely 
relates  to  the  form  of  expressing  the  result  of  a  generalizing 

operation.  ,       e  j  n   -       -u^ 

Allusion  is  made,  by  Mr.  Mill,  to  a  mode  of  defining  by 

« Analysis,'  or  by  resolving  a  complex  notion  into  its   con- 

Btifcuent  elementary  notions;  as  when  we  define  Eloquence-- 

*  the  power  of  influencing  men's  conduct  by  means  ot  speech. 
Here,  Eloquence  is  a  complex  property,  resolved  into  the  two 
simpler  properties,  '  exerting  influence  over  men  s  conduct, 
and  *  speech.'  If,  however,  the  enquiry  was  made,  how  do 
we  arrive  at  this  definition,  the  only  answer  would  be,  by 
generalizing  from  the  particular  examples  of  eloquent  address ; 
BO  that,  in  point  of  fact,  this  method,  if  it  be  a  method,  does 
not  supersede  the  processes  of  generalization. 

The  analytic  statement  could,  if  we  please,  be  thrown  into 
the  scholastic  form  ;  we  have  merely  to  adopt  one  of  the  com- 
ponent notions  as  a  *  genus,*  and  call  the  others  *  differentia ; 
influencing  of  men's  conduct  (genus),  use  of  speech ^(ditieren- 
tia).     We  might  even  reverse  the  notions  ;   *  speech    (genus), 

*  for  influencing  human  conduct '  (differentia). 

Thus,  neither  of  these  two  modes  of  defining  can  come  into 
competition  with  the  main  circumstance  insisted  on,  namely, 
that  to  define  is  to  generalize.  On  what  occasions,  the 
generalizing  process  may  be  dispensed  with,  will  be  a  matter 
of  future  consideration. 

Positive  Method, 

3.  Canon.  Assemble  for  comparison  the  Particulars 
coming  under  the  Notion  to  be  defined. 

By  the  Particulars  are  meant,  not  every  individual  instance, 
but  representative  instances  sufficient  to  embrace  the  extreme 

varieties.  .  ,      n    ^  •     j 

To  define  a  species  of  Plants,  the  botanist  collects  recognized 
examples  of  the  species,  including  the  widest  extremes  admitted 
into  it.  He  compares  the  several  specimens,  noting  their 
acrreements,  until  he  finds  what  characters  pervade  the  whole  ; 
these  he  expresses  in  suitable  language,  which  language  is 
henceforth  the  definition  of  the  species.  So,  m  dealing  with 
the  higher  groupings  -genera,  orders,  and  classes— he  toUows 


the  same  obvious  plan.     Likewise,  the  zoologist  and  mineralo- 
gist have,  in  the  last  resort,  no  other  method. 

Further  to  elucidate  defining  by  the  generalization  of 
the  positive  particulars,  we  will  select  examples  such  as  to 
bring  out  the  difficult  situations,  and  will  indicate,  in  the  form 
of  subordinate  canons,  the  modes  of  overcoming  the  difficulties. 

Suppose  we  have  to  define  a  Monarchy.  We  must  begin 
by  assembling  instances  of  every  institution  that  has  ever 
been  called  by  the  name  :  the  kings  of  the  heroic  age  in 
Greece ;  the  Spartan  kings ;  the  Roman  kings  ;  the  Persian, 
Macedonian,  Syrian,  and  Egyptian  kings ;  the  Teutonic 
king;  the  kings  of  modern  European  nations;  the  kings  of 
the  negro  tribes  ;  the  emperors  ;  the  reigning  dukes,  mar- 
graves, counts,  bishops,  &c.  To  these  we  should  have  to  add 
the  king-archon  at  Athens,  and  the  king  of  the  sacrifices  at 
Rome — mere  relics  of  the  ancient  kingly  government  (Sir 
G.  C.  Lewis,  Methods  of  Politics,  I.  8G).  Now,  if  we  confined 
ourselves  to  a  certain  number  of  these,  we  should  find  the 
common  fact  of  absolute  or  despotic  government ;  this,  how- 
ever, fails  to  apply  to  other  instances,  as  our  modern  constitu- 
tional monarchies ;  and,  if  these  are  to  be  included,  the 
common  features  are  greatly  reduced  in  significance,  being,  in 
fact,  little  more  than  (1)  the  highest  dignity  in  the  state,  and 
(2)  a  participation,  greater  or  less,  in  the  sovereign  authority. 
But  again,  if  we  look  to  the  two  last  instances — the  king- 
archon  at  Athens,  and  the  king  of  the  sacrifices  at  Rome — we 
shall  not  be  able  to  apply  to  them  even  the  attenuated  com- 
munity just  given ;  there  would  be  required  a  still  farther 
attenuation,  reducing  the  points  of  agreement  to  utter  insigni- 
cance. 

Now  this  is  one  of  the  most  usual  situations  arising  in 
the  attempt  to  generalize  a  notion  with  a  view  to  definition. 
We  must  be  led  in  the  first  instance,  by  the  popular  denota- 
tion of  the  name  ;  yet,  if  we  abide  by  that,  we  fail  to  obtain 
any  important  community  of  meaning.  It  is  in  such  a  per- 
plexity, thai  the  golden  rule  must  be  called  to  our  aid ;  we 
must  take  some  means  to  form  a  class  upon  a  deep  and  wide 
agreement.  If  need  be,  we  must  depart  from  the  received  deno- 
tation; leaving  out  some  instances,  and  taking  in  others,  until 
we  form  a  class  really  possessing  important  class  attributes. 
Thus,  in  the  case  of  the  monarch,  we  should  cut  off  at  once 
the  mere  relics  of  old  kingly  power.  As  regards  the  rest,  we 
should  divide  the  instances  between  the  absolute  and  the 
limited  monarchies  ;  there  is  a  large  and  important  community 


388 


CANONS  OF  DEFINITION. 


EULE  OF  IMPOKTANT  COMMUNITY. 


389 


of  meaning  in  the  class  termed  *  absolute  monarchies/  and 
this  class  should  be  isolated,  and  should  make  a  distinct  notion 
in  political  science.  The  remaining  individuals  should  be  dealt 
with  apart ;  they  (as  shown  by  Sir  G.  C.  Lewis)  are  far 
better  excluded  from  Monarchies,  and  classed  with  Republics. 
*  By  including  in  monarchies,  and  excluding  from  republics, 
every  government  of  which  a  king  is  the  head,  we  make  every 
true  general  proposition  respecting  monarchies  and  republics 
impossible.*  In  this  state  of  things  an  operation  of  re-classing 
is  the  indispensable  scientific  corrective  of  the  popular  and 
received  generalities. 

The  definition  of  a  Colovy  would  afford  a  case  exactly 
parallel.  Taking  together  all  the  things  that  have  ever  borne 
this  name  in  ancient  or  in  modern  times — the  colonies  of  the 
Phenicians,  Greeks,  Romans,  Italians,  Spnniards,  Portugese, 
Dutch,  French,  English — we  should  find  these  facts  in  common, 
namely,  emigrating  from  the  mother  country,  settling  in  some 
new  spot,  and  displacing  the  previous  government,  if  not  also 
the  population,  of  the  place  occupied.  With  this  small  amount 
of  agreement,  there  are  very  wide  disparities  ,  and  until  we 
narrow  the  instances,  we  do  not  arrive  at  a  large  and  im- 
portant connotation  or  meaning.  If,  however,  discarding  the 
ancient  colonies,  we  make  the  comparison  among  the  modern 
instances,  we  find  the  important  circumstance  of  a  sustained 
political  relationship  with  the  mother  country  ;  which  is 
better  expressed  by  the  word  dependency.  And  by  sub-divid- 
ing the  class,  we  can  obtain  inferior  classes,  with  still  more 
numerous  important  points  of  agreement ;  as,  for  example, 
the  Canadian  and  Australian  colonies  of  this  country,  which 
exercise  the  powers  of  independent  legislation,  under  the 
least  possible  control  by  the  home  government. 

Let  ns  next  endeavour  to  define  Food.  According  to  the 
canon,  we  assemble  representative  examples  of  all  the  sub- 
stances ever  recognized  under  this  name.  We  have  before  us, 
the  flesh  of  animals,  the  esculent  roots,  fruits,  leaves,  &c. 
We  have  also  a  number  of  substances  of  purely  mineral  origin, 
as  water  and  common  salt.  Our  work  lies  in  generalizing 
these,  in  detecting  community  in  the  midst  of  much  difference. 
Were  man  a  purely  carnivorous  feeder,  his  food  might  be 
generalized  as  the  flesh  of  animals  taken  into  .the  mouth,  and 
passed  into  the  stomach,  to  be  there  digested  and  thence  to 
be  applied  to  the  nutrition  and  support  of  the  system.  But 
when  we  include  vegetable  and  mineral  bodies,  we  must  leave 
oat  *  flesh,'  and   substitute   *  animal,  vegetable,  and  mineral 


Bubstances  ; '  the  other  part  of  the  statement  being  applicable. 
Even  as  amended,  however,  the  definition  is  still  tentative,  and 
needs  to  be  verified  by  comparison  in  detail  with  everything 
that  has  ever  been  put  forward  as  food.  We  must  challenge 
all  informed  critics  to  say  where  the  definition  fails.  Thus, 
nourishment  is  afforded  by  substances  absorbed  through  the 
skin,  which  would  exclude  the  medium  of  the  mouth  and 
stomach,  and  narrow  the  definition  to  nourishing  or  supporting 
the  system.  Again,  it  is  doubted,  whether  alcohol,  tea» 
tobacco  (chewed)  really  nourish  the  system.  This  is  a  fer 
more  serious  objection ;  and  the  manner  of  dealing  with  it 
will  illustrate  the  principles  of  defining. 

In  the  first  place,  there  may  be  a  contest  as  to  the  matter  of 
fact.  Could  it  be  shown  that  these  substances  do  give  nourish- 
ment, support,  or  strength  to  the  system,  the  difficulty  is  at 
once  overcome ;  in  that  case,  they  fall  under  the  definition. 
On  the  contrary  supposition — that  they  do  not  nourish  the 
the  system, — two  courses  are  open.  First,  we  may  exclude 
them  from  the  class  *  Food,'  and  retain  the  definition.  Or 
secondly,  we  may  include  them,  and  alter  the  definition.  As 
modified  to  suit  the  extension,  the  definition  would  be  *  sub- 
stances that  either  nourish  or  stimulate  the  system.'  To  de- 
cide between  those  two  courses,  we  must,  as  before,  refer 
to  the  golden  rule  of  classification,  which  recommends  the 
adherence  to  a  smaller  class  founded  on  a  great  and  important 
community,  rather  than  to  a  larger  where  the  community  of 
meaning  is  attenuated  to  comparative  insignificance.  Better, 
therefore,  to  retain  two  groups—Foods  and  Stimulants, — 
each  with  its  own  definition.  In  that  way,  we  shquld  derive 
much  more  information  respecting  any  individual  thing  de- 
signated either  *  Food '  or  *  Stimulant,'  than  if  the  word  *food' 
covered  both.  It  may  be  that  some  substances  combine  both 
functions  J  which  would  entitle  them  to  be  named  in  both 
classes. 

We  may  notice  the  definition  formerly  given  of  '  Axiom  * 
by  way  of  remarking  that  a  definition  is  obviously  spurious 
that  does  not  distinguish  the  given  notion  from  notions 
already  settled.  Thus,  unless  an  Axiom  be  a  real  proposi- 
tion, it  is  not  divided  from  Definitions;  and  unless  it  is 
fundamental  within  the  science,  it  does  not  difter  from  the  great 
body  of  Propositions  so  far  as  employed  to  prove  other  pro- 
positions. The  chai'acters  proposed  are  alone  sufficient  to 
constitute  a  separate  notion  bearing  the  name. 

These    cases    sufficiently  exemplify  the  situation  where  a 


4 


11 


4  'iil 


(J. 


390 


CANONS  OF  DEFINITION. 


MARGIN  OF  TRANSITION. 


391 


f 
I: 


word  is  extended  to  denote  things  that  have  few  or  no  im- 
portant points  of  community.  The  next  example  will  bring  to 
view  a  perplexity  of  another  kind. 

Suppose  we  seek  to  define  a  Solid.     Summoning  to  view,  if 
not  all  the  solids  in  nature,  sufficient  representatives  of  all  the 
varieties  compatible  with  the   name— metals,  rocks,  woods, 
bones,  and  all  the   products  of  vegetable   and   animal  life 
denominated  solid — we  set  to  work  to  compare  them,  and 
note  their  agreement.      There  is  little  apparent  difficulty  in 
this  instance.      We  see  that,  however  various  these  bodies 
may  be,  they  agree  in  resisting  force  applied  to  change  their 
form  ;  so  readily  does  thi»  strike  us  at  first  sight,  that  the  case 
seems  scarcely  worth  producing  to  exemplify  a  logical  formula. 
Let  US,  however,  apply  the  Socratic  test — exposing  the  defini- 
tion to  the  cavil  of  every  objector, — and  we  shall  probably 
soon  be  told   of  a  grave    difficulty.      The    quality,  so   very 
decided   in  the  great  mass  of  instances,  is  found  to   have 
degrees,  to  shade  insensibly  into  the  state  called  'liquid,* 
where  solidity  terminates.     Now,  at  what  point  does  solidity 
end,  and  the  opposite  state  begin  ?     Is  a  paste,  a  glue,  a  jelly, 
solid  or  not  ?     Is  Hamlet  right  in  talking  of  '  this  too,  too 
solid  flesh  V 

We  have  here  not  a  mere  cavil,  but  a  frequent  and  serious  per- 
plexity. Many  couples  of  qualities,  unmistakeably  contrasted  in 
the  greater  number  of  instances  of  them,  pass  into  one  another 
by  insensible  gradations,  rendering  impossible  the  drawing  of 
a  hard  and  fast  line.  Who  shall  say  at  what  moment  day  ends 
and  night  begins  ?  So,  there  has  always  been  a  doubt  as  to 
the  exact  individual  that  ends  the  animal  series,  and  is  neigh- 
bour to  the  beginning  of  the  plant  series.  Sleeping  and 
waking  may  have  an  intermediate  state,  with  difficulty  as- 
signed to  either.  The  great  chemical  sub- division  into  metals 
and  non-metals  has  an  ambiguous  border  in  the  substances 
arsenic  and  tellurium.  In  the  animal  system,  the  voluntary 
shades  insensibly  into  the  involuntary. 

The  Greek  philosophers  displayed  to  the  utmost  the  in- 
genuity that  lights  upon  difficulties ;  and  this  example  did  not 
escape  them.  They  grounded  upon  it  a  puzzle  named  the 
Sorites,  or  heap.  A  certain  heap  was  presented,  which  was 
fairly  designated  small ;  it  was  then  increased  by  very  gradual 
additions ;  and  the  spectator  was  challenged  to  declare  at 
what  point  it  ceased  to  be  small,  and  deserved  to  be  accounted 
large. 

There  is  but  one  solution  of  the  riddle.     A  certain  margin 


must  be  allowed  as  indeierminedy  and  as  open  to  difference  of 
opinion  ;  and  such  a  margin  of  ambiguity  is  not  to  be  held  as 
invalidating  the  radical  contrast  of  qualities  on  either  side. 
No  one  would  enter  into  a  dispute  as  to  the  moment  when 
day  passed  into  night ;  nor  would  the  uncertainty  as  to  this 
moment  be  admitted  as  a  reason  for  confounding  day  and 
night.  We  must  agree  to  diffiir  upon  the  instants  of  transi- 
tion in  all  such  cases.  While  the  great  body  of  the  non-metals 
can  be  distinctly  marked  off  from  the  metals,  we  refrain  from 
positively  maintaining  arsenic  and  tellurium  to  be  of  either 
class  ;  they  are  transition  individuals,  the  *  frontier  *  instances 
of  Bacon  ;  in  that  position  we  leave  them. 

There  is  a  margin  of  transition  in  the  ethical  distinction  of 
Reward  and  Punishment.  In  the  great  part  of  their  extent, 
these  two  motives  are  amply  contrasted  ;  to  bestow  a  reward 
for  performance,  is  a  diffi3rent  thing  from  inflicting  punish- 
ment for  non-performance  ;  and  the  withholding  of  a  reward 
is  not  confounded  with  punishment  Yet  circumstances  arise 
when  the  one  merges  into  the  other.  A  kind  parent  with- 
holds from  a  child  some  indulgence  originally  meant  as  a 
reward ;  if  the  indulgence  has  been  so  frequent  as  to  become 
a  kind  of  use  and  wont,  the  privation  is  hardly  distinguishable 
from  punishment. 

When  it  is  said,  no  man  is  to  be  punished  for  his  opinions, 
we  are  not  to  infer  that  each  person  is  bound  to  associate 
alike  with  all  persons  of  all  opinions,  because  to  give  a  prefer- 
ence is  to  stigmatize  some  at  the  expense  of  others.  Our  not 
choosing  any  one  as  a  companion  and  friend  is  not  to  be  held 
as  inflicting  a  penalty,  or  as  manifesting  disapprobation. 

We  may  farther  exemplify  the  method  upon  Matter,  As- 
sembling the  various  things  recognized  as  material,  say  solid 
and  liquid  bodies,  and  comparing  them  among  themselves,  we 
find  a  unanimity  in  these  points,  namely,  resistance  to  motioa 
or  force  applied  to  them,  and  exercising  power  or  force  when 
in  motion.  All  solids  and  all  liquids  agree  in  these  features. 
They  farther  agree  in  being  visible  and  tangible.  We  must 
next  bring  into  comparison  the  gaseous  bodies.  Do  these 
possess  the  same  quality  as  to  resistance  and  moving  power  ? 
The  identity  is  not  at  first  sight  apparent,  but  becomes  so  on 
a  closer  inspection ;  airs  resist  motion,  and  constitute  moving 
power,  although  in  a  comparatively  less  degree  than  solids 
and  liquids.  They  are  not,  however,  as  a  class,  visible  and 
tangible ;  consequently,  either  these  qualities  must  be  dropt, 
OT  gaseous  bodies  must  be  excluded ;    we  must  make  our 


392 


CAi^ONS   OF  DEFINITION. 


CONTEAST. 


393 


1   i 

Ml 


choice.  The  decision  is  not  difficult.  So  exceedingly  import- 
ant  is  the  material  property  of  Resistance  and  Momentum 
(given  in  one  word — Inertia),  that  we  are  justified  in  making 
it  the  foundation  of  a  class,  even  although  we  associate 
together  tbiugs  visible  and  tangible,  and.  things  invisible  and 
intangible. 

The  next  enquiry  relates  to  the  Eiher,  or  etherial  medium, 
occupying  all  space.  Shall  this  be  included  in  the  class 
*  Matter  ?  '  If  the  property  of  Inertness  can  be  proved  to 
belong  to  the  supposed  Ether,  we  must  include  it.  On  the 
contrary  supposition,  we  are  in  the  alternative  position  already 
exemplified  ;  we  must  either  exclude  the  instance  or  attenuate 
the  defining  properties.  Now,  the  only  community  that 
could  exist  between  an  unresisting  Ether  and  Matter  would 
be  this  very  general  circumstance,  namely,  being  an  extended 
medium  for  the  operation  of  forces.  The  supposed  ether  con- 
veys light  and  heat,  and  is  therefore  a  transitory  embodiment 
of  molecular  force,  as  solids,  liquids,  and  gases,  are  of  force, 
both  molar  and  molecular.  Better,  however,  on  this  extreme 
supposition,  not  to  class  the  Ether  with  Matter,  but  to  leave, 
as  the  defining  property  of  Matter,  the  all-important  fact  des- 
cribed by  Inertia. 

The  foregoing  instances  under  the  Positive  Canon  are 
enough  to  show  Definition  in  its  primary  character  as  a  general- 
izing operation,  and  also  to  bring  out  the  leading  difficulties  of 
the  process— the  adjustment  of  the  particulars  to  comply  with 
the  golden  precept,  and  the  allowance  ofa  doubtful  margin  in 
cases  where  opposites  pass  insensibly  into  each  other. 

Negative  Method. 

4.  Canon. — Assemble  for  coraparison  the  particulars  of 
the  Opposed,  or  contrasting  Notion. 

This  amounts  to  saying  that,  with  the  given  Notion,  we 
shall  also  define,  by  the  same  generalizing  method,  the  oppos- 
ing Notion.  As  it  is  impossible  for  anything  to  be  prjcisely 
defined,  unless  its  opposite  is  known,  and  defined  with  equal 
precision,  we  must  in  substance  perform  the  two-fold  opera- 
tion, whether  or  not  we  formally  separate  the  opposing  aspects. 
The  cases  where  the  formal  separation  is  expedient  will  be 
made  manifest  by  a  few  examples. 

It  is  impossible  to  place  the  human  mind  in  a  more  favour- 
able position  for  comprehending  a  generality,  than  by  laying 


out  to  the  view  two  arrays  of  particulars — the  one  represent- 
ing the  given  notion,  the  other  its  negative.  The  notion  of 
Straightness,  for  example,  is  thoroughly  set  forth  by  placing 
a  series  of  straight  objects  (of  all  varieties  in  other  properties) 
side  by  side  with  a  series  of  bent,  curved,  or  crooked  objects. 
Supposing  the  representation  of  both  sides  to  be  complete,  the 
very  utmost  has  been  done  to  put  the  learner  in  possession  of 
the  notion,  idea,  or  concept,  called  *  straight.* 

Let  us  apply  the  method  to  the  definition  of  a  Solid.  The 
positive  generalization  leads  to  the  expression  of  the  common 
attribute  thus ; — '  Solids  resist  force  applied  to  change  their 
form.'  Try  next  the  negative  plan,  by  generalizing  liquids 
(and  gases).  On  an  adequate  comparison  of  these  non-solids, 
we  are  able  to  say,  *  liquids  and  gases  yield  to  the  slightest 
pressure,  and  have  no  fixed  form,  except  as  given  by  solid 
enclosures ; '  which  is  the  exact  obverse,  and,  therefore,  the 
confirmation  of  the  prior  statement  with  reference  to  solids. 

Reverting  now  to  the  definition  of  Matter,  already  worked 
out  on  the  positive  side,  let  us  seek  for  a  negative  generaliza- 
tion. But  what  is  the  negative  of  Matter  ?  Most  persons 
would  answer  *  Mind ; '  which  is  true,  but  not  the  whole  truth. 
Matter  is  indeed  opposed  to  Mind  ;  but  it  is  also  opposed  to 
Space  unoccupied  (except  by  the  supposed  Ether).  The  com- 
plete opposition  to  Mind  is  Extension^  whether  as  resisting 
Matter  or  unresisting  Space.  We  have  therefore  to  oppose 
Matter  to  Sj)ace,  and  ask  the  definition  of  Space.  Now,  on 
comparing  all  our  experiences  of  what  we  term,  empty  or  un- 
occupied space,  we  find  this  common  fact,  freedom  to  movey  or 
scope  for  movement ;  a  definition  the  exact  obverse  of  the 
definition  of  matter,  or  of  the  fact  called  B/esistance  or  Inert- 
ness. 

Matter  is  sometimes  opposed  to  Force.  An  argument  for 
the  immateriality  of  mind  is  founded  on  this  opposition. 
Thus  Hartley  says,  matter  which  is  inert,  cannot  be  the  sub. 
stance  of  mind,  which  is  active,  or  a  source  of  power.  This 
is  a  pure  mistake  and  confusion  of  ideas.  It  takes  up  one 
aspect  of  Matter — resistance,  and  drops  the  other  aspect — 
moving  force.  The  two  aspects  ai-e  inseparable;  force  is 
moving  matter  ;  without  matter  there  is  no  force. 

.  The  method  of  Opposites  will  be  seen  to  advantage  in  de- 
fining Chemical  Combi^iation,  the  subject  matter  of  the  science 
of  Chemistry.     By  the  positive  canon,  we  have  to  assemble, 
numerous  instances  of  the  so-called  Chemical   unions — the"^ 
onion  of  oxygen  and  hydrogen  to  form  water,  oxygen  and 


I 


394 


CANONS   OF   DEFINITION. 


COMPLEX  NOTIONS. 


395 


|a> 


carbon  in  carbonic  acid,  <fec.  The  operation  would  tarn  out  a 
very  laborious  one,  from  the  great  multitude  of  the- particulars 
to  be  examined  even  for  adequacy  of  representation.  We 
shall,  however,  suppose  that  there  has  been  obtained  a  general 
statement  of  the  points  of  community;  namely,  change  of 
properties,  definite  proportions,  and  heat. 

We  next  ask  what  is  Chemical  Combination  opposed  to  ? 
Of  the  genus — Combination,  what,  are  the  species  not  chemical  ? 
The  answer  is  Mechanical  mixture  and  Solution  (in  its  broad 
phase  of  molecular  adhesion).  We  should  then  have  to  gene- 
ralize these  two,  and  confront  the  points  of  agreement  with 
those  above  given.  Now,  we  may  dispense  with  drawing  a 
formal  contrast  between  Chemical  union  and  Mechanical 
mixture  ;  for  this  reason,  that  the  two  are  so  prominently 
di«»tinct  as  not  to  be  in  danger  of  being  confounded.  The 
profitable  contrast  is  with  Solution.  Generalizing  the  instances 
of  solvent  attraction — in  common  solutions,  in  alloys,  &c., — 
we  see  that  although  the  solidity  of  a  body  may  be  broken 
up,  or  its  state  changed,  it  retains  the  greater  number  of  its 
characteristic  properties  ;  salt  and  sugar,  when  dissolved,  are 
the  same  for  most  purposes  ;  the  change  is  comparatively 
insignificant.  Again,  solution  may  be  in  all  degrees  up  to 
saturation.  Finally,  solution  is  usually  a  cooling  operation. 
These  are  the  precise  opposites  of  Chemical  union.  We  may 
draw  up  a  pointedly  contrasting  definition  in  this  form  : — 

Combination  Solution 

Characters  of  the  Compounds 

Merged  Retained 

Proportion  of  Combining 

Definite  Indefinite 

Resulting  change  of  Temperature 

Heat  Cold. 

In  the  above  instance,  the  Negative  generalization  is  the 
easier  of  the  two ;  the  field  of  instances  being  sooner  over- 
taken. The  same  advantage  belongs  to  the  defining  of  Mind 
by  the  opposite.  The  particulars  constituting  Mind  are 
numerous,  various,  and  complicated  ;  the  particulars  consti- 
tuting Extension,  the  property  opposed  to  mind,  are  much 
sooner  gathered  up  into  a  general  notion,  and  that  notion  is 
much  more  distinct  and  familiar  than  the  properties  of  mind  : 
moreover,  the  community  of  Extension  is  single  ;  of  mind, 
plural. 

Opposing  notions,  having  between  them  a  border  of  ambigu- 
ous instances,  are  best  cleared  up  by  the  method  of  Negation, 


with  pointed  contrast.  We  formerly  had  to  notice  the  subtlety 
of  the  line  that,  on  some  occasions,  divides  the  Notion  from 
the  Proposition ;  the  definition  of  a  complex  notion  being 
often  very  difficult  to  distinguish  from  a  Proposition. 

Appetite  is  not  sufficiently  defined  un'ess  pointedly  opposed 
to  the  notion  most  nearly  allied  with  it — Desire. 

The  principle  of  Utility^  as  the  moral  standard,  is  opposed  by 
Bentham,  to  the  two  principles — Asceticism,  and  Sympathy 
OP  Antipathy  (Sentiment). 

The  Plant  or  Vegetable  is  defined  by  a  parallel  array  of 
contrasts  with  the  Animal ;  and  conversely. 

Deductive  Definiiions 

6.  When  Complex  Notions  are  foimed  by  conipound- 
ing  simpler  notions,  as  in  the  Deductive  Sciences,  they 
may  be  defined  by  stating  their  composition. 

In  the  Deductive  Sciences,  as  Mathematics,  notions  as  well 
as  propositions  are  formed  by  artificial  composition  or  deduc- 
tion. "Given  the  notion  *  triangle,'  and  the  various  notions 
*  right  angle,*  *  equality,'  &c.,  we  can  construct  the  complex 
notions  *  right-angled  triangle,'  equilateral  triangle,'  *  isosceles 
triangle.*  No  reference  to  particulars  is  needed  for  defining 
such  notions ;  we  merely  recite  the  elements  used  in  com- 
pounding them ;  *  a  right-angled  triangle  is  a  triangle  with 
one  right  angle.* 

Having  the  notion  *  attractive  force,*  and  the  various  numeri- 
cal notions,  squares,  cubes,  &c.,  we  constitute  the  artificial 
compounds,  *  force  as  the  square  of  the  distance,  the  cube  of 
the  distance,*  and  so  on. 

This  is  the  one  grand  exception  to  the  principle  of  defining 
by  the  generalization  of  Particulars.  From  the  magnitude  of 
our  Deductive  Sciences,  there  is  a  very  large  number  of  such 
notions  ;  and  they  have  been  the  means  of  withdrawing  atten- 
tion from  the  fundamental  process  of  Defining  through  the 
comparison  of  instances  in  the  concrete. 

We  make  artificial  compounds,  not  merely  for  scientific 
ends,  as  in  the  Deductive  Sciences,  but  also  in  the  exercise  of 
Imagination,  as  when  we  feign  gods,  demi-gods,  demons,  dra- 
gons, and  ideal  personages  and  scenes  in  poetry.  The  defini- 
tion of  these  notions  also  is  tlie  statement  of  their  composition. 

Tlie  Language  of  Definition. 
6.  The  Language  of  Definition  consists  in  assigning  the 
constituents  of  a  Complex  Notion. 


iw 


M 


15 


396 


CANONS  OF  DEFINITION. 


The  dictionary  definitions  by  synomjms  have  an  inci- 
dental value,  but  are  not  proper  dedaitions. 

The  generalizing  operation  terminates  in  the  seizing  of  com- 
mon features,  which  have  to  be  embodied  in  language.  Now, 
the  language  used  must  express  some  more  elementary  notions, 
whose  combination  gives  the  required  notion.  '  A  solid  resists 
force  applied  to  change  its  form  * — is  an  expression  substitu- 
ting for  the  word  *  solid  '  a  coalition  of  more  elementary  and 
general  names — *  resistance,'  *  force,*  *  change,'  *  form.'  The 
definition  of  Property  is — *  the  right  of  each  person  to  dispose 
of  whatever  things  of  value  they  have  either  acquired  by  their 
own  labour,  or  obtained  by  free  gift  or  by  fair  agreement  from 
those  that  have  so  acquired  it.'  Here  the  constituent  notions 
are'  right,'  'disposal,'  *  value,'  'acquisition,'  'labour,'  'gift,' 

*  agreement.* 

Liberty  is  definable  as  the  power  of  using  one's  faculties  at 
will,  subject  (if  Civil  Liberty  be  meant)  to  not  interfering 
with  the  like  use  in  others  ;  implicating  '  power,'  '  faculties,* 

*  will.* 

Thus  the  so-called  method  of  '  Analysis  *  is  the  method  of 
expressing  every  proper  Definition.  Whether  the  source  of 
the  definition  be  the  generalization  of  particulars,  or  whether 
it  be  deductive  as  just  explained,  the  wording  of  it  is  analytic. 

The  use  of  synonyms  in  defining  depends  upon  the  circum- 
stance that  almost  every  notion  or  thing  has  a  plurality  of 
names,  and  may  be  better  known  by  some  of  these  than  by 
others.  TheriB  are  many  names  for  the  fact  called  *  pleasure  :* 
joy,  enjoyment,  delight,  happiness,  felicity,  delectation,  rapture, 
ecstacy.  The  less  familiar  of  these  names  are  explained  by 
the  help  of  the  more  familiar ;  but  this  is  not  scientific  defining. 

7.  The  scholastic  formula  of  defining — "per  genus  et 
differentiam — like  Analysis,  belongs  to  the  expression, 
rather  than  to  the  discovery  of  the  meaning  of  a  notion. 

Each  of  the  constituent  notions  expressing  a  complex  notion 
is  necessarily   more  general  than  the  compound.     '  Three,* 

*  side,*  and  '  figure  *  are  each  more  general  than   the  notion 

*  triangle,'  which  they  express  by  their  combination.  We 
may,  therefore,  take  any  one  of  these  and  call  it  generic  or  the 
genus — say  '  figure  : '  *  triangle  '  is  then  a  species  of  figure  ;  and 
its  differentia  or  specific  marks  discriminating  it  from  other 
figures  are  given  in  the  remaining  characters  '  three  *  and 
'  side,'    combined  into    '  three-sided.*      So,  if    eloquence  bo 


GENUS  ANT*  DIFFERENCE. 


397 


defined,  analytically,  as  *  the  influencing  of  men*s  feelings  and 
conduct  by  means  of  speech,*  we  might  call  *  influencing 
men*s  conduct,'  the  genus,  and  '  the  employment  of  speech,' 
the  specific  difference.  We  might,  also,  invert  the  terms 
and  make  *  speech '  the  genus,  and  '  influencing  men  *  the 
difference. 

This  latitude,  however,  is  usually  restrained  by  the  circum- 
stance that  one  of  the  constituent  properties  is  the  basis  of  a 
recognized  class,  already  existing.  Thus,  in  defining  a  circle, 
*  line  *  is  the  recognized  genus,  and  *  equal  distance  from  a 
point,*  the  specifying  attribute.  A  great  number  of  classes 
and  class  notions  fall  under  some  superior  class,  or  notion,  on 
some  one  or  more  of  their  attributes.  Not  to  mention  the 
systematic  classifications  of  Natural  History,  we  may  point  to 
such  cases  as  Painting  (genus  Fine  Art),  Mathematics  (genus 
Science),  Prudence  (genus  Virtue),  Planet  (genus  Heavenly 
Body),  Gold  (genus  Metal),  Whiteness  (genus  Colour), 
Cathedral  (genus  Building). 

Instead  of  presenting  an  exhaustive  analysis  of  a  notion,  or 
class  connotation,  this  method  supposes  that  generic  properties 
are  already  known,  that  people  are,  as  it  were,  educated  up 
to  the  point  of  comprehending  the  genus,  and  need  only  to 
have  the  genus  mentioned,  and  the  specific  differences  stated. 
Thus  Mathematics  is  the  Science  (genus)  of  quantity  (differ- 
ence). Ethics  is  the  Science  (genus)  of  men*s  duties  (differ- 
ence). Painting  is  the  Fine  Art  (genus)  that  works  by  colour 
(difference).  Poetry  is  a  Fine  Art  employing  the  instrument 
of  language.  Prudence  is  a  Virtue  (genus)  having  reference 
to  the  welfare  of  the  individual  agent  (difference).  Justice  is 
a  Virtue,  involving  an  equal  and  impartial  distribution  of  ad- 
vantages, according  to  a  received  scale  or  standard.  Polite- 
ness is  Benevolence  in  trifles.  B/cligion  is  Government 
(genus)  by  a  Supernatural  power  (difference).  Wonder,  Fear, 
Love,  Anger,  are  of  the  genus  '  Emotion,'  each  having  a 
specific  difference.  Sight  is  of  the  genus  '  Sensation  ;  *  dif- 
ference, '  by  the  Eye.* 

Locke's  remarks  on  the  scholastic  type  are  very  much  in  point. 
They  are  in  substance  these  : — When,  in  defining,  we  make  use  of 
the  genus,  or  next  general  word,  it  is  not  out  of  necessity,  but 
only  to  save  the  labour  of  enumerating  the  several  simple  ideas 
that  such  general  word  already  expresses,  (or  perhaps  the  shame 
of  not  being  able  to  give  the  full  enumeration).  Detinition  being 
nothing  but  making  any  one  understand  by  words  what  idea  the 
given  word  stands  for,  it  is  best  made  by  giving  all  the  simple 
ideas  combined  in  the  signiflcation  of  the  term ;  and  if  people 


398 


CANONS   OF  DEFINITION. 


have  been  accustomed,  instead  of  the  full  enumeration,  to  use  the 
next  general  term,  it  is  neither  from  necessity  nor  for  greater  clear- 
ness, but  for  quickness  and  despatch.    (Essay.  Book  III.  Chap.  II.) 

Ultimate  Notions, 

8.  For  simple  or  Ultimate  Notions,  the  generalization 
from  Particulars  still  holds,  but  verbal  expression  neces- 
sarily fails. 

For  attaining  the  notion  *  whiteness  '  we  gather  particular 
examples  of  white  colour,  and  of  colours  not-white.  The 
conjunct  impression  of  the  positive  and  the  negative  particu- 
lars does  everything  that  can  be  done  to  master  or  to  convey 
the  notion ;  we  may  then  attach  a  name  to  enable  it  to  be 
spoken  upon,  but  we  cannot  give  a  verbal  definition  of  it; 
there  are  no  notions,  more  elementary,  whose  combination 
would  give  the  notion  *  white.*  So  we  cannot  by  any  form  of 
words  convey  the  idea  of  *  resisting ;  *  as  an  ultimate  fact  it 
can  be  known  only  in  the  actual  experience  of  a  comparison 
of  resisting  things. 

We  may  define  Equality  by  Coincidence,  but  we  can  give 
no  definition  of  Coincidence,  we  must  show  it.  Any  attempt 
at  verbal  expression,  by  such  synomyms  as^  agreeing  in  size/ 
*  exactly  fitting,'  would  be  illusory. 

Succession  and  Co-existence  are  an  ultimate  contrasted 
couple,  definable  only  by  reference  to  examples. 

Unity  and  its  opposite.  Plurality,  are  indefinable.  We 
must  produce  an  array  of  objects  with  the  common  attribute, 
singleness,  and  another  array  of  groups,  and  the  comparison 
of  the  two  arrays  by  the  observer  is  the  only  possible  mode  of 
attaining  the  conception. 

A  Mathematical  point  is  indefinable.  The  definition  given 
in  books  in  geometry,  *  position  without  magnitude  *  is  not 
more  elementary  but  more  complex,  than  the  thing  defined. 
The  correct  mode  of  defining  a  point  for  geometrical  purposes 
£eems  to  be  to  indicate  to  the  eye  positions  or  landmarks 
where  we  begin  or  end  a  measurement,  or  make  a  division. 
The  knowledge  of  a  point  or  a  position  is  obtained  in  the  same 
concrete  examination  that  gives  length  and  space  dimensions. 

A  line  is  not  definable  ;  as  just  noticed,  it  is  an  abstraction 
derived  from  comparing  extended  bodies. 

An  angle  is  not  definable ;  *  inclination  *  is  merely  another 
name  for  the  entire  notion,  it  is  not  a  simpler  or  more  elemen- 
tary conception.  Actual  examples  must  be  shown.  There  is 
a  mutual  implication  of  a  circle  with  an  angle,  so  that  if  we 


INDEFINABLE   NOTIONa 


399 


were  made  to  master  a  circle  in  the  first  instance,  we  mio-ht 
then  learn  an  angle  by  definition  ;  but  in  the  process  of  know- 
ing the  circle  w©  conld  not  avoid  knowing  an  angle.* 

*  Complex  ideas,'  says  Hume,  *  may,  perhaps  be  well  known  by 
definition,  which  is  nothing  but  an  enumeration  of  those  parts  or 

•  Our  sensibilities  in  general  give  us  the  experiences  of  Difference  and 
Agreement ;  Quantity,  amount  or  degree  ,  Number,  or  discrete  quantity  ; 
and  Time  (Succession  is  not  fully  given  until  we  have  the  special  experi- 
ence of  the  simultaneous,  an  acquired  and  complex  notion). 

The  Muscular  sensibilities,  in  particular,  give  Resistance  and  Motion ; 
which,  by  the  farther  help  of  sense  experiences,  are  unfolded  into  Space 
ond  Co-existence: 

Every  one  of  the  Senses  contains  one  or  more  ultimate  experiences ;  no 
one  sense  can  enable  us  to  conceive  what  belongs  to  another.  What 
number  of  independent  or  underivable  sensations  should  be  attributed  to 
each  sense,  we  cannot  easily  sav  ;  whiteness,  and  the  simple  colours  must 
be  conceived  as  ultimate;  while  even  the  compounds  and  shades  of 
colour  are  probably  for  the  most  part  beyond  our  power  to  conceive  by 
any  mere  constructive  effort,  or  apart  from  actual  experience  ,  a  circum- 
stance that  would  make  the  ultimate  notions  of  sight  very  numerous. 
Similar  remarks  may  be  extended  to  Sounds,  Touches,  Smells,  and 
Tastes ;  under  every  one  of  these  classes  of  sensations,  there  must  be  a 
considerable  number  that  cannot  be  referred  by  derivation  to  others,  and 
must  be  separately  experienced.  Our  Organic  Sensiblities,  in  like  man- 
ner, contain  numerous  characteristic  and  independent  modes;  hunger, 
thirst,  repletion,  suffocation,  headache,  rheumatism,  &c.,  are  all  indefin- 
able by  analysis,  because  they  are  ultimate  modes  of  sensibility.  Even 
although  many  of  them  have  a  common  character,  pain,  they  have  a 
apeciality  which  can  be  understood  only  by  being  felt. 

In  the  higher  Emotions,  as  Wonder,  Fear,  Love,  Anger,  Pride, 
Curiosity,  we  have  many  compound  states.  The  aesthetic  pleasures  are  a 
combination  of  simpler  modes.  Still,  a  certain  number  of  emotions  are 
to  appearance  ultimate,  as  Wonder,  Fear,  Tenderness,  Power;  while 
there  is  an  absolute  certainty  that  they  could  not  be  conceived  without 
being  actually  felt.  Moreover,  many  emotions  that  the  Psychologist  is 
able  to  analyze  could  yet  be  constructed  only  with  very  great  difficulty  by 
the  help  of  the  elements  alone.  A  person  that  never  experienced  the 
sentiment  of  veneration  could  scarcely  arrive  at  it  by  merely  being  told 
what  are  its  constituents. 

The  elementary  experiences  of  the  mind  are,  therefore,  very  numerous, 
and  so,  therefore,  are  the  indefinable  notions.  The  varied  situations 
of  human  life  give  birth  to  notions  practically  indefinable;  the  idea 
of  a  Political  Society  could  not  be  communicated  to  any  one  that  had 
never  been  a  member  of  some  actual  society.  Hence,  in  our  attempts  to 
define  Government,  Law,  Authority,  we  must  make  an  appeal  to  the  con- 
crete experiences  of  the  listener. 

When  all  such  cases  are  taken  into  account,  the  notions  that  are  of  an 
indefinable  and  ultimate  nature  must  be  reckoned  by  hundreds.  Diction- 
ary makers  have  hitherto  overlooked  this  circumstance  ;  and  hence  their 
pretended  definitions  revolve  in  a  circle  of  words,  where  there  should  be 
a  reference  to  actual  things.  How  vain  is  a  verbal  definition  of  such 
words  as  light,  heat,  motion,  large,  up,  fragrance,  pain,  wonder ' 
18 


400 


CANONS  OF  DEFINITION. 


simple  ideas,  that  compose  them.  But  when  we  have  pushed  up 
definitions  to  the  most  simple  ideas,  and  find  stiU  some  ambigmty 
and  obscurity ;  what  resource  are  we  then  possessed  of  ?  13y  what 
invention  can  we  throw  light  upon  these  ideas,  and  render  them 
altogether  precise  and  determinate  to  our  intellectual  view  ?  Pro- 
duce the  impressions  or  original  sentiments,  from  which  the  ideas 

Are  cor)ied 

Locke  considershimselftohave  been  the  first  to  remark  that  Simple 

Ideas  are  indefinable.  By  Eeid  and  by  Stewart,  the  merit  of  fir<=t 
stating  the  fact  is  ascribed  to  Descartes.  Hamilton  would  trace 
it  back  to  Aristotle  (Keid's  Works,  p.  220)  :  but  Mr.  Mansel 
questions  the  interpretation  put  by  Hamilton  upon  the  passage 
apparently  relied  on  (Aldrich,  Appendix,  Definition),  and  quotes  » 
remarkable  passage  from  Occam,  approachmg  closely  to  Locke  s 
position  concerning  Simple  Ideas.  Aristotle,  says  Mansel,  may  be 
cited  as  an  authority  for  Umiting  the  indefinable  to  Summa  Genera 
and  to  Individuals.  .  ,       j  v 

Aristotle's  general  theory  of  Definition  is  much  perplexed  by 
being  treated  as  an  investigation  of  Cause,  and  by  keeping  up  the 
distinction  of  Substance  and  Attribute.  But,  in  regard  to  *  hunt- 
ing  for,'  as  he  expressed  the  search  after,  a  definition,  he  allows 
the  method  of  generalization  from  particulars,  as  well  as  the  deduc- 
tive method,  by  working  down  from  a  higher  genus.  He  also 
gives  an  intelligible  distinction  between  Nominal  and  Eeal  Defin- 
uig.  The  Nominal  definition  applies  *  where  there  is  no  evidence 
of  the  existence  of  the  objects,'  as  when  we  define  a  purely  ima- 
ginary being,  such  as  a  centaur.  This  of  course  could  only  be  a 
deductive  definition.  Eeal  definition  applies  to  things  known  to 
exist  and  would  be  most  completely  exemplified  in  definmg  by  a 
generalization  of  particulars.  ,  , 

Mr.  Mill  draws  the  line  between  Nominal  and  Eeal  Definitions 
—Definitions  of  Names  and  Definitions  of  Things— by  remarking 
that  the  last-named  kind,  along  with  the  meaning  of  a  term, 
covertly  asserts  a  matter  of  fact.  (Book  I.,  Chap.  VIII.).  The 
Beal  Definition  postulates  the  real  existence  of  the  thing  defined. 
In  another  place,  however  (Book  III.,  Chap.  V.),  while  discussing 
the  hypothetical  character  of  the  Definitions  of  Geometry,  Mr. 
Mill  remarks  tnily  that  in  order  to  reason  out  facts  we  must  shape 
our  hypotheses  to  facts  ;  imaginary  assumptions  could  bear 
imaginary  consequences,  but  we  need  real  assumptions  in  order  to 
give  real  conse^uencei. 


CHAPTER  11 
GENEEAL    NAMES. 

1.  General  Names  may  not  be  absolutely  indispensable 
to  general  notions,  but,  besides  being  necessary  to  com- 
munication, they  aid  the  memory  in  remembering  genera- 
lities, while  without  them,  we  could  not  combine  a  number 
of  distinct  notions  into  propositions  and  reasonings. 

We  might  discover  similarities  in  nature,  and  might  remem- 
ber and  act  upon  such  discoveries,  without  the  use  of  language. 
We  could  not,  however,  impart  such  discoveries  to  others. 
We  might,  indeed,  in  some  instances,  put  the  resembling 
things  side  by  side,  which  would  make  the  identifying  opera- 
tion somewhat  easier  to  those  that  came  after  us.  By  a 
similar  device,  we  might  indicate  a  natural  conjunction,  in 
certain  very  limited  circumstances.  The  powers  of  fire  might 
be  expressed  by  putting  on  one  side  of  a  fire,  a  pile  of  wood,  and 
on  the  other  a  heap  of  ashes ;  even  this  would  not  be  intelligible 
without  pantomime.  But  beyond  the  simplest  cases,  the 
attempt  at  expressing  general  laws  would  utterly  break  down. 

Our  own  recollection  of  discoveries  of  identity  is  vastly 
lightened  by  the  use  of  names.  The  employment  of  the  same 
nanae  to  the  resembling  things,  both  expresses  the  things  as 
individuals  and  declares  their  community  or  likeness ;  this 
mode  of  signifying  likeness  being  of  all  others  the  least  bur- 
densome to  the  memory.  The  complex  and  many-sided  like- 
ness in  difference,  characteristic  of  natural  objects  —  the 
possibility  of  including  the  same  object,  an  orange  for  exam- 
ple, in  a  great  number  of  classes — renders  this  easy  mode  of 
keeping  the  various  communities  before  the  mind,  of  inesti- 
mable value.  By  the  use  of  a  few  terms — round,  yellow,  soft, 
sweet,  we  can  compendiously  grasp  all  the  relationships  of  the 
orange,  and  make  them  enter  into  our  reasonings  with  com- 
parative ease.  No  discovery  of  identity  among  objects  is 
secured  against  neglect,  until,  joined  to  a  common  name,  it 
can  be  borne  in  men's  minds  by  means  of  this  gentle  and 
constant  insinuation. 

2.  The  conditions  of  general  Naming  fall  under  two 
heads. 


! 


i 


!| 


402 


GENERAL  NAMES. 


First.  Every  name  should  have  a  meaning  well  defined. 

The  necessity  of  this  is  too  obvious  to  need  enforcement. 
Every  science  should  have  all  its  terms  defined.  The  end  of 
the  Logic  of  Definition  is  to  fix  the  meanings  of  general  names. 

We  find  in  point  of  fact  that  words  often  possess  numerous, 
distracting,  and  incompatible  meanings.  Take  the  familiar 
term  *  stone.'  It  is  applied  to  mineral  and  rocky  materials, 
to  the  kernels  of  fruit,  to  the  accumulations  in  the  gall  bladder, 
and  in  the  kidney ;  while  it  is  refused  to  polished  minerals 
(called  gems),  to  rocks  that  have  the  cleavage  suited  for  roof- 
ing (slates),  and  to  baked  clay  (bricks).  It  occurs  in  the  de- 
signation of  the  magnetic  oxide  of  iron  (loadstone),  and  not 
in  speaking  of  other  metallic  ores.  Such  a  term  is  wholly 
unfit  for  accurate  reasoning,  unless  hedged  round  on  every 
occasion  by  other  phrases  ;  as  building  stone,  precious  stone, 
gall  stone,  &c.  Moreover,  the  methods  of  definition  are 
baffled  for  want  of  sufficient  community  to  ground  upon. 
There  is  no  quality  uniformly  present  in  the  cases  where  it 
is  apphed,  and  uniformly  absent  where  it  is  not  applied  ; 
hence,  the  definer  would  have  to  employ  largely  the  licence 
of  striking  off"  existing  applications  and  taking  in  new  ones. 

3.  The  demand  for  new  names  is  a  cause  of  the  loose 
extension  of  words  already  in  use.  The  processes  of  ex- 
tension are  Similarity,  Composition,  and  Contiguity. 

(1)  The  operation  by  Similarity  is  described  by  the  name. 
A  new  object  is  brought  into  comparison  with  some  one 
already  known,  and  the  name  transferred  accordingly.  Thus, 
on  the  discovery  of  an  additional  coal-field,  all  the  designations 
previously  in  use  in  connexion  with  coal  are  legitimately  ex- 
tended to  the  new  formation.  More  precarious  extensions  by 
similarity  are  often  made.  It  is  enough  to  mention  the  whole 
class  of  metaphors,  wherein,  by  virtue  of  similarity,  accom- 
panied by  serious  diversities,  old  words  are  employed  in  new 
meanings  —  *  light  *  to  signify  knowledge,  *  fire  '  to  denote 
zeal  and  irascibility,  *  birth '  and  *  death  '  to  mean  many  things 
differing  widely  from  the  beginning  and  the  ending  of  life  in 
an  organized  being. 

(2)  The  process  of  Composition  is  shown  in  framing  new 
words,  by  the  union  of  existing  words ;  as  log-book,  mince- 
meat, hail-stones,  far-sighted,  and  by  the  systematic  employ- 
ment of  prefixes  and  suffixes,  prejudge,  undo,  withhold, 
boundless,  wisdom,  bearer,  unnecessary. 


TRANSITIVE  MEANINGS  OF  NAMES. 


403 


The  same  process  is  seen  in  using  a  plurality  of  words  to 
convey  a  single  meaning  :  as  in  the  systematic  designation  by 
genus  and  species,  white  man,  moss  rose ;  and  in  numerous 
many- worded  combinations  and  circumlocutions  —  *  the  last 
surviving  descendant  of  an  ancient  family,'  *  the  father  of 
History.' 

(3)  The  process  of  Contiguity  is  exemplified  in  the  figure 
called  Metonymy — as  in  using  the  *  crown  '  for  royalty,  the 
*  turf '  for  horse-racing.  So  long  as  the  figurative  character 
of  this  operation  is  kept  in  view,  there  is  no  harm  done.  A 
more  dangerous  employment  of  contiguity  is  exemplified  in 
what  is  termed  the  *  Transitive  application  of  words.'  This 
operation  demands  special  notice. 

4.  A  word  originally  applied  to  a  thing,  by  virtue  of  one 
quality,  may  contract  the  additional  meaning  of  some 
associated  quality,  and  thence  be  extended  to  things  pos- 
sessing the  second  quality  siugly. 

This  tendency  was  brought  into  prominence  by  Dugald 
Stewart,  who  gives  the  following  symbolical  elucidation  of  it. 
'  Suppose  that  the  letters  A,  B,  C,  D,  E,  denote  a  series  of 
objects  ;  that  A  possesses  some  one  quality  in  common  with 
B ;  B  a  quality  in  common  with  C  ;  C  a  quality  in  common 
with  D  ;  D  a  quality  in  common  with  E ;  while  at  the  same 
time,  no  quality  can  be  found  which  belongs  in  common  to 
any  three  objects  in  the  series.  Is  it  not  conceivable,  that  the 
affinity  between  A  and  B  may  produce  a  transference  of  the 
name  of  the  first  to  the  second  ;  and  that,  in  consequence  of 
the  other  affinities  which  connect  the  remaining  objects  to- 
gether, the  same  name  may  pass  in  succession  from  B  to  C; 
from  C  to  D  ;  and  from  D  to  E  ?  ' 

The  word  *  damp  '  primarily  signified  moist,  humid,  wet. 
But  the  property  is  often  accompanied  with  the  feeling 
of  cold  or  chilness,  and  hence  the  idea  of  cold  is  strongly 
suggested  by  the  word.  This  is  not  all.  Proceeding  upon 
the  superadded  meaning,  we  speak  of  damping  a  man's 
ardour,  a  metaphor  where  the  cooling  is  the  only  circumstance 
concerned ;  we  go  on  still  farther  to  designate  the  iron  slide 
that  shuts  off"  the  draft  of  a  stove,  *  the  damper,'  the  primary 
meaning  being  now  entirely  dropt.  *  Dry '  in  like  manner, 
through  signifying  the  absence  of  moisture,  water,  or 
liquidity  is  applied  to  sulphuric  acid  containing  no  water, 
although  not  thereby  ceasing  to  be  a  moist,  wet,  or  liquid 
substance. 


404 


GENERAL  NAMES. 


The  word  *  letter'  has  undergone  a  series  of  transitions. 
Originally  applied  to  the  alphabetic  characters,  it  passed  to 
epistolary  correspondence,  to  literature  (letters)  ;  but  in  our 
post-office  system  it  has  strayed  still  wider ;  it  has  come  to 
mean  parcels  made  up  of  jewellery,  soft  goods,  and  miscel- 
laneous wares,  provided  they  are  carried  by  post. 

*  Gas '  is  the  popular  name  for  any  effluvia,  anything  in  the 
air.  Cloud  and  smoke  would  be  called  gaseous  emanations, 
although  they  are  not  properly  aerial  bodies. 

A  *  back  door '  originally  the  door  at  the  back  of  the  house, 
for  servants,  is  applied  to  the  door  for  the  same  purpose  when 
in  front  of  the  house. 

*  Street,'  originally  a  paved  way,  with  or  without  houses, 
has  been  extended  to  roads  lined  with  houses,  whether  paved 
or  unpaved.  ^ 

*  Impertinent '  signified  at  first  irrelevant,  alien  to  the  pur- 
pose in  hand  ;  through  which  it  has  come  to  mean,  meddling, 
intrusive,  unmannerly,  insolent.  So  wide  is  the  difference 
between  the  first  and  last  senses,  that,  in  spite  of  the  apparent 
ease  of  the  transitions,  Mr.  Bailey  suspects  the  influence  of  the 
similarity  in  sound  with  the  epithet  *  pert  *  (Discourses,  p. 
101). 

*  Taste  *  is  transferred  by  similarity,  or  metaphor,  from  the 
feelings  of  the  sense  of  Taste,  to  the  feelings  of  Fine  Art  pro- 
ductions. There  is  also,  in  all  probability,  a  transition  in  the 
double  meaning  of  the  word  in  both  employments,  namely,  to 
signify  the  pleasure  imparted,  and  also  the  discrimination  of 
bodies  by  taste,  and  of  good  and  bad  in  Fine  Art  productions. 

Examples  may  be  quoted  from  the  highest  questions  of 
philosophy.  Thus,  the  epithet  *  beautiful,'  properly  circum- 
scribed by  Fine  Art,  is  often  loosely  applied  to  pleasures  not 
artistic. 

This  misleading  tendency  was  never  adverted  to  by  either 
Plato  or  Aristotle,  who,  in  their  enquries,  counted  on  finding 
under  such  words  as  Beauty,  Cause,  Justice,  some  unity  of 
signification.  The  same  mistake  pervades  Bacon's  inductive 
enquiries. 

The  word  *  gei>tleman '  is  an  example  of  transitions  growing 
out  of  historical  and  political  circumstances.  *  Meaning  origin- 
ally a  man  born  in  a  certain  rank,  it  came  by  degrees  to 
connote  all  such  qualities  or  adventitious  circumstances  as 
were  usually  found  to  belong  to  persons  of  that  rank.  This 
consideration  explains  why  in  one  of  its  vulgar  acceptations  it 
means  any  one  who  lived  without  labour,  in  another  without 


TBANSITIONS  BY  SIMILAEITY. 


405 


manual  labour,  and  in  its  more  elevated  signification  it  has  in 
every  age  signified  the  conduct,  character,-  habits  and  outward 
appearance,  in  whomsoever  found,  which,  according  to  the 
ideas  of  that  age,  beloLged  or  were  expected  to  belong  to 
persons  born  and  educated  in  a  high  social  position.' 

Similar  changes  are  traceable  in  the  words  '  loyalty,*  '  vil- 
lain,' *  pagan.* 

A  '  convict  *  properly  means  one  convicted  or  found  guilty ; 
but  the  signification  most  prominent  is  the  transition  to  the 
state  of  hard  labour  entering  into  the  punisfement  of  convicted 
felons. 

6.  The  derivations  of  terms  frequently  exhibit,  in  con- 
junction with  contiguous  transitions,  an  element  of  simi- 
larity. 

In  an  interesting  chapter  devoted  by  Mr.  Mill  to  *the 
Katural  History  of  the  Variation  of  the  meaning  of  terms,'  he 
notes  two  different  tendencies  to  change  both  grounded  in 
similarity — the  one  a  movement  of  Generalization,  the  other  a 
movement  of  Specialization. 

As  to  the  first,  the  rendering  of  specific  terms  general,  we 
have  such  examples  as  *  salt '  extended  from  sea  salt,  to  the 
class  of  saline  bodies  ;  *  oil  *  from  olive  oils  to  oils  generally ; 

*  squire  '  from  the  owner  of  a  landed  estate  to  other  classes 
supposed  to  be  entitled  to  a  similar  position  ;  *  parson  '  from 
the  incumbent  of  a  parish  to  clergymen  at  large. 

The  Specialization  of  terms  is  apt  to  arise  when  people 
have  occasion  to  think  and  speak  oftener  of  one  member  of 
the  genus  than  of  the  others.  Thus  *  Magazine,'  a  store  or 
receptacle,  has   been   narrowed  to   a  periodical  publication. 

*  Cake  *  is  specialized  to  pastry.  A  *  story '  is  used  to  desig- 
nate a  lie — a  curious  illustration  of  the  frequent  inaccuracy  of 
current  narratives.  *  Pleasure  *  has  oftener  the  signification 
of  a  very  narrow  class  of  enjoyments ;  to  which  corresponds  a 
special  meaning  of  *  virtue'  and  virtuous.  *  Wit '  formerly 
meant  intellectual  power  of  any  kind ;  Bacon,  Milton,  and 
Newton  were  great  wits.  The  modern  tendency  is  to  restrict 
it  to  the  production  of  ludicrous  effects,  and  even  still  farther 
to  the  ingenious  play  upon  words. 

6.  The  precautions  to  be  observed  in  re-adjusting  the 
Bignification  of  terms,  are  these  : — First,  important  mean- 
ings in  current  use,  or  meanings  at  the  base  of  important 
predications,  should  not  be  disturbed  ^  secondly,  the  as- 
sociations of  powerful  sentiment  should  not  be  reversed. 


*0 


406 


GENERAL   NAMES. 


DESCRIPTIVE  TERMINOLOGY. 


407 


In  restricting  the  word  '  beauty '  to  the  refined  pleasures 
of  Art,  and  of  the  artistic  element  of  Nature,  we  do  not  inter- 
fere with  any  received  propositions,  nor  with  the  approving 
sentiment,  connected  with  the  term.  Tiie  word  '  wit,'  in  its 
modern  restriction,  has  undergone  a  much  greater  revolution, 
and  certainly  does  not  support  the  same  propositions,  nor  the 
same  associations  of  dignity  as  in  Queen  Anne's  time.  *  Jus- 
tice '  cannot  be  accurately  defined  without  a  reterence,  in  the 
last  resort,  to  law,  authority,  or  command  ;  or  at  least  to 
men's  opinions  as#o  what  should  bo  authoritatively  enjoined 
or  commanded  ;  a  mode  of  defining  that  has  always  been  un- 
palatable, as  making  the  illustrious  quality  of  Justice,  the 
creature  of  law  and  opinion. 

*  Civilization '  should,  if  possible,  be  so  defined  that  the 
European  nations  should  be  included,  and  the  American 
Indians,  Bosjesmans,  and  aboriginal  Australians  excluded  ; 
while  no  unfavourable  sentiment  should  be  introduced,  by 
giving  preponderance  (as  Rousseau  did)  to  the  supposed  evils, 
or  disadvantages,  attending  on  the  arts  and  discoveries  of 
civilized  nations. 

The  difficulties  attending  the  re-definition  of  a  word  are 
illustrated  by  the  repugnance  felt  by  many  to  Mr.  Grote's 
view  of  the  sophists  ;  a  view  that  conflicted  both  with  prevail- 
ing propositions  and  with  feelings  of  dislike.  A  regard  to 
truth  or  to  justice  may  necessitate  our  violently  interfering 
with  a  received  usage. 

From  the  strong  tendency  to  associate  the  word  *  pleasure ' 
with  the  gratifications  that  border  on  vice,  ethical  theorists 
are  hampered  in  using  it  to  express  the  natural  and  legitimate 
end  of  human  pursuit.  They  have  to  substitute  for  it,  happi- 
ness, well-being,  or  other  words  of  more  feeble  import  as 
regards  the  zest  and  enjoyment  of  life. 

Mr.  Mill  adverts  to  cases  where  he  thinks  it  might  be  a 
great  misfortune  to  banish  entirely  the  former  meanings  of 
words;  inasmuch  as  the  operation  may  involve  the  unfair 
predominance  of  a  one-sided  theory  on  some  important  ques- 
tions. He  supposes  the  temporary  prevalence  of  a  selfish 
theory  of  virtue,  the  consequence  of  which  might  be  that  the 
word  *  virtue  '  would  cease  to  connote  disinterested  conduct, 
and  the  very  idea  of  such  being  dropt,  the  practice  might 
degenerate  accordingly.  The  remark,  however,  has  no  appli- 
cation to  the  words  of  obsolete  physical  theories,  as  *  epicycle,' 
'  phlogiston,'  *  vis  viva^ '  or  to  names  that  distort  and  confuse  the 
phenomena  expressed  by  them,  as  free-will  and  necessity,  or 


to  the  names  of  infelicitous  classifications,  superseded  by 
better.  And  in  those  changes  of  meaning  adapted  to  the  pro- 
gress of  science,  as  with  the  words  salt,  acid,  it  is  expedient 
to  drop  entirely  the  earlier  significations. 

7.  The  second  Eequisite  of  language  is,  that  there  should 
be  no  important  meaning  without  its  word. 
This  involves  (I.)  a  Descriptive  Terminolojy, 

It  is  essential  that  we  should  be  able  to  describe  with  accur- 
acy all  individual  facts  and  observations ;  consequently  names 
must  be  devised  for  all  the  known  qualities  of  things  whether 
physical  or  mental,  and  also  modes  of  signifying  ditferences  of 
degree  whenever  degree  is  taken  into  account.  To  describe 
the  diamond,  we  need  such  names  as  crystal,  refracting  power, 
specific  gravity,  hardness ;  and  a  numerical  scale  for  stating 
the  amount  or  degree  of  each  property.  Separate  names  are 
required  for  all  our  ultimate  feelings  and  sensations. 

As  regards  the  Object  World,  the  fundamental  experiences 
are  the  muscular  states  called  Resistance  and  Motion,  and  the 
Sensations — which,  in  the  order  of  their  objectivity,  are  Sight, 
Touch,  Hearing,  Taste,  Smell,  Organic  Sensations. 

The  property  called  Resistance  has  other  names  ;  as  Force, 
Inertia,  Momentum.  Gravity  is  a  mode  of  the  same  property. 
The  only  farther  requisite  is  a  scale  of  Degree,  which,  in  this 
instance,  is  given  by  the  one  perfect  method — Arithmetical 
numbers. 

On  the  experience  of  movement,  aided  by  sense,  is  grounded 
the  object  property  called  Motion,  in  all  its  varieties  ;  also 
Space,  Extension  or  Magnitude,  and  Form.  The  varieties  of 
motion  are  quick  and  slow,  regular  and  irregular,  of  this  or  that 
form,  and  so  on.  Names  are  given  ko  all  the  modes,  and  for 
most,  there  are  numerical  estimates  of  degree.  The  same  re- 
marks apply  to  Space  or  Magnitude,  which  is  pre-eminently 
open  to  arithmetical  statement. 

Form,  is  a  property  subject  to  great  variations,  and  names 
have  to  be  found  accordingly.  The  simple  forms  of  Geometry 
— as  line,  straight,  angular,  curved,  circle,  triangle,  sphere, 
cone,  &c.,  are  one  department.  The  objects  of  nature  and  art 
have  many  others  besides — heart-shaped,  egg-shaped,  pear- 
shaped. 

The  language  of  Botany  is  most  exigent  of  designations  of 
form. 

Colour  has  been  expressed  by  assuming  a  certain  number 
of  primary  colours,  and  treating  the  rest  as  shades  of  these. 


I  \\ 


408 


GENEBAL  NAMES. 


CLASS   NAMES. 


409 


Thus,  we  have  many  different  greens,  blues,  reds,  yellows, 
greys  ;  often  charactei*ized  in  the  manner  above  described  by 
quoting  objects  that  exemplify  them,  sky  blue,  ultra-marine 
blue,  apple  green,  blood  red,  French-grey.  These  names, 
however,  do  not  define  the  colours;  they  do  not  from  two 
simple  ideas  enable  us  to  conceive  a  compound  without  refer- 
ence to  the  actual  thing,  they  merely  mark  a  species  as  distinct 
from  other  species. 

To  make  colour  as  far  as  possible  a  precise  character  in 
Mineralogy,  there  is  a  classified  list,  introduced  by  Werner, 
giving  a  name  to  every  important  variety  of  mineral  colour. 
Eight  colours  are  chosen  as  fundamental,  white,  grey,  black, 
blue,  green,  yellow,  red,  and  brown,  and  under  each  of  these 
is  arrayed  a  list  of  shades.  Thus,  under  *  blue  '  are  enumer- 
ated,— blackish-blue,  azure-blue,  violet-blue,  lavender-blue, 
plum-blue,  berlin-blue,  malt-blue,  duck-blue,  indigo-blue, 
sky-blue ;  ten  varieties.  Similarly  for  the  others  ;  the  number 
of  shades  being  in  some  cases  greater,  in  others  less. 

For  the  scientific  description  of  the  outer  or  object  world, 
the  most  essential  properties  are  Magnitude,  Form,  Move- 
ment, Kesistance  (including  all  the  modes  of  Force),  and 
Colour.  Next  to  these  in  importance  are  Sounds,  which  also 
ppsess  a  terminology.  The  musical  notes  can  be  given 
numerically  and  symbolically  ;  all  other  varieties  of  sounds 
must  be  designated  by  distinct  names,  as  melodious,  har- 
monious, silvery,  sweet,  soft,  harsh,  grating,  voluminous, 
siivery,  wooden — names  requisite  alike  in  practical  life,  in 
science  and  in  poetry.  In  the  diagnosis  of  the  chest,  there 
are  characteristic  sounds,  which  receive  appropriate  names. 

Touch  proper  is  cognizant  of  roughness  and  smoothness  ; 
in  combination  with  muscular  feeling,  it  gives  hardness,  soft- 
ness, and  elasticity  (within  limits).  The  hardness  of  minerals 
transcends  touch  ;  the  harder  body  scratches  the  softer  ;  and 
a  scale  of  hardness  is  formed  upon  this  test.  The  pulse  is 
estimated  by  touch  proper,  and  besides  the  number  of  beats, 
names  are  applied  to  signify  its  tactile  modes — as  feeble,  firm, 
wiry,  steady. 

Tastes  and  Odours  are  provided  with  names.  After  indicat- 
ing the  more  general  modes — sweet,  bitter,  pungent,  we 
descend  to  the  marked  individualities,  which  are  named  chiefly 
(according  to  the  most  usual  device  for  supplying  terminology) 
from  the  substances  where  they  are  most  marked  —  acid» 
alkaline,  booty,  game,  spirituous,  oily  tastes,  garlic,  spice, 
earthy. 


The  Organic  Sensations — Acute  pains.  Respiratory  feelings, 
Heat  and  Cold,  Digestive  feelings,  &c.,  have  a  nomenclature, 
partly  useful  in  every  day  life,  and  still  more  extensively  in- 
volved in  the  medical  art. 

Although  the  Sensations  have  all  an  object  reference,  they 
yet  each  contain  subjective  elements,  becoming  more  and  more 
prominent  as  we  recede  from  sight  aud  touch  ;  and  being 
almost  the  whole  in  the  organic  sensibilities.  Hence  their 
designations  are  part  of  the  subjective  vocabulary,  or  the 
vocabulary  of  Mitid  proper.  This  is  completed  by  a  series  of 
designations  for  the  Special  Emotions;  for  the  Will  in  its 
various  aspects — including  desires,  appetites,  deliberation, 
resolution,  belief;  and  for  the  Intellectual  processes — idea, 
memory,  reason,  imagination,  association,  agreement. 

8.  11.  There  is  demanded  next  a  name  for  every  general 
notion,  or  distinct  product  of  generalization. 

The  previous  demand  is  limited  to  the  means  of  describing 
every  fact  belonging  to  either  the  object  or  the  subject  world. 
The  present  relates  more  particularly  to  general  notions  or 
generalities.  But  though  the  two  ends  are  different,  the 
means  are  in  great  part  the  same.  All  the  names  of  the 
Terminology  are  general  names  ;  they  mean  qualities  in 
general,  although  by  their  combination  they  can  specify  and 
individualize.  Resistance,  Form,  Colour,  Sound,  Taste, 
are  general ;  and  their  more  specific  modes  heavy,  round,  blue, 
melodious,  sweet,  are  also  general.  So  that  the  Terminology 
already  contains  a  provision  for  expressing  numerous  results 
of  the  generalizing  operation. 

Still,  the  aim  now  propounded  is  so  far  distinct  from  the 
other,  and  may  require  to  be  separately  considered  and  pro- 
vided. The  results  of  generalization  are  of  two  kinds — classes 
in  the  concrete,  the  subject-matter  of  the  concrete  sciences,  and 
qualities  in  the  abstract,  which  are  the  characteristic  subject- 
matter  of  the  fundamental  sciences — Mathematics,  Physics,  &c. 
The  names  for  the  first  department  are  not  provided  for  under 
Terminology ;  thus,  quartz,,  gold,  oak,  rose,  fish,  mammal,  are 
radically  distinct  from  hard,  yellow,  fragrant,  warm — the  one 
group  comprises  class  names,  the  other  the  qualifying  and 
descriptive  adjectives. 

The  Terminology  coincides  much  more  nearly  with  the 
names  used  in  the  general  sciences  ;  the  notions  of  Mathema- 
tics, and  of  Chemistry  (apart  from  the  names  of  the  concrete 
substances,  gold,  &c.),  are  all  more  or  less  a  part  of  the 
descriptive  vocabulary. 


410 


GENERAL   NAMES. 


NEW  TEEMS. 


411 


9.  It  is  important  that  the  names  of  generalities  should 

be  short. 

The  discovery  of  the  relations  of  general  reasoning  is  facili- 
tated by  the  brevity  of  the  designations.  If  we  had  to  employ 
a  lonjr  periphrasis  tor  distance,  square,  gravity,  body  it  would 
be  impossible  to  shape  an  intelligible  notion  of  the  law  ot 
gravitation,  still  less  to  combine  it  with  equally  lumbering 
expressions  for  tangential  force,  and  for  the  resistance  ot  the 
air,  in  considering  projectiles.  The  advantages  of  methods  ot 
abbreviation  are  illustrated  by  the  mathematical  device  ot 
temporarily  substituting,  for  a  long  formula  that  has  to  be 
treated  as  a  whole,  a  single  letter,  a ,;  which  relieves  the  mind 
of  what  would  be  a  cumbrous  impediment. 

De  Moro'an,  with  reference  to  the  Differential  Calculus,  to  avoid 
the  tedious  repetition  of  '  a  quantity  which  diminishes  without 
limit  when  A  x  diminishes  without  limit,'  coined  the  word  coni- 

An  important  enquiry  is  started  by  Mr.   Mill  (Book  IV., 
Chap.  VI.)m  namely,  on  what  occasions  we  may  safely  use 
language   as   mere   symbols,    like   the    symbols   of  Algebra. 
Now,  the  answer  to  this  question  is  obtained  from  the  nature 
of  such  symbols ;    they  are  signs  of  operation,  adjusted  by 
careful  verification,  so  that  no  error  can  creep  in  if  the  rules 
are  adhered  to ;  while  the  operations  are  all  the  more  easily 
and  rapidly  performed  that  the  things  themselves  are  entirely 
kept  out  of  view.     On  the  other  hand,  in  dealing  with  general 
names,  class  names,  and  terminology,  we  have  to  keep  up  a 
constant  reference  to  the  concrete  things,  as  the  only  way  of 
preventing  us  from  incorrect  assertions.     After  a  proposition 
has  once  been  carefully  verified,  as  *  Knowledge  is  fouuded  on 
Agreement  and  Difl'erence,'  we  seem  to  be  under  no  farther 
necessity  of  referring  to  the  concrete  particulnrs  ;    which  is 
true  only  until   we  begin  to  apply  it.     The   Formal  Logic 
shows  us  exactly  how  far,  in  matters  of  general  reasoning,  we 
may  use  language  as  mere  symbols ;  being  to  a  certain  extent 
analogous  to  Mathematics,  although  arriving  far  short  of  that 
science  in  the  possibility  of  working  aloof  from  all  concrete 
meanings  (See  Appendix  B.) 

10.  In  devising  new  general  names,  recourse  may  be 
had  either  to  our  language,  or  to  foreign  languages.  Each 
alternative  has  its  advantages  and  disadvantages. 

The  advantage  of  deriving  from  our  own  language  is  being 
easily  understood  ;   the  disadvantage  is  the  presence  of  mis- 


leading associations.  *  Damp  '  would  not  be  a  good  word  to 
apply  to  the  gaseous  form  of  water  ;  *  vapour  '  is  preferable  as 
being  devoid  of  inappropriate  connexions.  When  Reichen- 
bach  conceived  that  he  had  discovered  an  entirely  new  force 
in  nature,  he  coined  a  word  not  belonging  to  any  language 

*  odyl.'  The  generalization  of  Graham,  comprehending  sub- 
stances of  a  gluey,  or  viscid  nature,  with  flint,  and  minerals 
of  the  glassy  type  (showing  the  conchoidel  fracture)  is  ex- 
pressed by  the  term  *  colloid '  {koWtj  glue) ;  the  English  term 
being    too    exclusively    confined   to    the    viscid    character. 

*  Inertia  '  is  a  useful  word,  although  it  demands  to  be  guarded 
against  the  too  exclusive  suggestion  of  passive  resistance. 

11.  The  mere  improvements  of  classification  may  re- 
quire new  terms. 

This  is  the  case  with  Graham's  Colloids  and  Crystalloids, 
which  arranged  previously  known  substances  into  a  new 
dichotomy,  or  contrast,  founded  on  an  extensive  and  important 
community  of  attributes.  The  improved  classifications  of 
minerals,  plants,  and  animals,  required  new  terms,  monocotvle- 
don,  perianth,  inflorescence,  mammalia,  infusoria,  &c.  Owing 
to  the  imperfection  of  the  contrast  *  mind  and  matter,* 
psychologists  have  introduced  the  terms  *  subject '  and  *  object' 
as  exhibiting  the  antithesis  in  greater  purity. 

12.  By  adapting  old  names,  we  may  be  often  saved  from 
a  new  coinage. 

The  creation  of  new  terms  is  sometimes  wanton  and  need- 
less. When  there  is  no  new  meaning,  no  fresh  product  of 
generalization,  the  adding  of  new  terms  is  not  justified  upon 
slight  pretexts.  Apart  from  increasing  the  already  large 
burden  of  language,  there  is  the  more  serious  evil  of  leading 
people  to  suppose  that  there  is  a  new  meaning.  Some  of 
Kant's  innovations  in  language  are  obnoxious  to  this  criticism. 
His  *  analytic  'and  *  synthetic  *  judgments  '  a  priori '  and  *  a 
posteriori '  have  some  advantages  as  synonyms,  but  the  mean- 
ings had  been  already  expressed. 

A  little  management  may  often  get  over  the  insufi&ciency  of 
the  existing  names.  The  evil  to  be  complained  of  is,  that  a 
popular  name  does  not  exactly  square  with  a  scientific  mean- 
ing ;  thus  the  words,  force,  resistance,  motion,  affinity,  associ- 
ation, are  adopted  into  science ;  while  the  popular  significations, 
so  far  from  suggesting,  are  at  various  points  in  conflict  with 
the  scientific  meanings.     Even  in  such   circumstances,  the 


■I 


412 


GENERAL  NAMEa 


NOMENCLATUEB. 


413 


adherence  to  the  popular  words  may  be  a  less  evil  than  new 
coinages.  The  precautions  accompanying  the  nse  of  old 
names  are  these  : — 

(1)  The  words  may,  at  the  outset,  be  defined  according  to 
their  sense  in  the  particular  science.  Thus,  the  mathematician 
defines  a  point,  a  line,  a  square,  a  cone,  a  spiral ;  the  physicist 
defines  inertia,  force,  velocity,  attraction,  liquid,  lever,  air, 
heat,  &c. 

The  chemist  defines  element,  compound,  affinity,  solution, 
decomposition.  The  botanist  gives  the  name  *'  fruit '  to  all 
seed-vessels.  The  biologist  defines  life,  respiration,  digestion. 
The  psychologist  defines  sensation,  idea,  memory,  association, 
reason,  emotion,  sentiment,  passion,  conscience ;  all  which 
terms  are  liable  to  the  loose  and  uncertain  meanings  of  com- 
mon speech.  The  political  philosopher  defines  government, 
nation,  law,  order,  progress.  These  various  terms  being 
consistently  used,  in  accordance  with  the  several  definitions, 
they  are  known  to  possess  the  significations  indicated,  and  no 
others,  within  the  sphere  of  their  respective  sciences. 

This  plan  was  followed  in  framing  the  language  of  Geometry. 
Names  were  usurped  from  common  speech,  and  used  in 
peculiar  senses  defined  at  the  beginning  of  Geometrical  trea- 
tises. Thus  a  *  sphere  '  {a(j)u7pa),  was  originally  a  playing 
ball,  a  *  trapezium  '  {rpuvi^iov),  a  table ;  but,  the  scientific 
sense  being  defined  at  the  outset,  and  rigidly  adhered  to 
throughout  the  demonstrations,  there  was  no  danger  of  con- 
fusion between  the  popular  meaning  of  the  words  and  the 
mathematical. 

(2)  We  may  employ,  in  science,  the  precaution  required  in 
composition,  with  reference  to  names  having  plural  meanings, 
which  are  abundant  in  all  languages  ;  namely,  so  to  place  and 
fence  each  word  as  to  keep  back  all  the  meanings  not  in- 
tended. The  word  *  moral'  has  various  distinct  significations ; 
yet  the  use  of  it  in  any  one  place  may  be  such  as  to  admit 
only  one.  When  we  speak  of  *  moral  suasion,'  we  exclude  the 
meaning  of  right  and  wrong,  and  indicate  only  '  mental  *  as 
opposed  to  physical.  *  The  morality  of  the  act  was  question- 
able,* shows  that  moral  rightness  is  intended. 

(3)  The  device  of  stating  the  contrary  of  a  term  has  been 
seen  to  be  highly  effectual  in  saving  ambiguity.  '  Reason  and 
not  passion  prevailed '  indicates  that  *  reason  is  intended  in 
the  peculiar  sense  of  *  motives  resulting  from  rational  calcula- 
tion of  the  future.* 

13.  III.  In  addition  to  a  Terminology,  and  names  for 


all  important  Generalities,  there  are  names  adapted  for  the 
purposes  of  Classification. 

This  is  Mr.  Mill's  third  class  under  the  Second  Requisite  of 
a  Philosophical  Language.  It  refers  more  especially  to  the 
device  of  double  naming  (the  invention  of  Linnaeus)  employed 
with  the  lowest  kinds,  or  Species  in  Botany  and  in  Zoology — 
*  Ranunculus  arvensis,*  *  Hirudo  medicinalis.'  In  all  the  higher 
grades — the  Classes,  Orders,  and  Genera — single  names  are 
used  ;  but  since  the  number  of  the  objects  increases  as  we 
descend,  while  in  Botany  and  in  Zoology,  the  lowest  kinds  or 
species  amount  to  many  thousands,  an  abbreviating  device  is 
employed,  namely,  to  retain  the  name  of  the  genus,  and  desig- 
nate the  species  by  a  qualifying  adjective — *  Orchis  maculata.' 
The  saving  of  language  is  not  the  only  advantage  of  the 
double-name  ;  there  is  the  additional  effect  of  imparting  the 
knowledge  of  the  genus  that  the  species  belongs  to,  and  also 
the  mark  or  character  dividing  it  from  the  other  species  of 
the  same  genus.  Thus,  a  name  so  made  up  gives  the  place  of 
the  species  in  the  classification,  so  far  as  effected  by  stating 
the  genus.  The  operation  could  have  been  carried  farther,  so 
as  to  include  the  Family  or  the  Natural  Order ;  thus  the  com- 
mon daisy  would  be  *  Compositae  bellis  perennis.*  But  this 
would  be  held  too  burdensome. 

Under  the  same  head  is  included  the  double  naming  in 
Chemistry — sulphate  of  potash,  or  potassic  sulphate.  These 
designations,  however,  although  serving  to  impart  information 
respecting  the  substances  named,  are  formed  upon  a  principle 
quite  different  from  that  above  explained  with  reference  to  the 
Natural  History  sciences.  They  belong  to  the  special  peculi- 
arity of  the  science  of  Chemistry — the  distinction  of  substances 
into  Simple  and  Compound,  and  of  Compounds  into  different 
modes  and  degrees  of  union  ;  and  in  the  case  of  compounds, 
they  indicate  the  supposed  elements  and  manner  of  composi- 
tion ;  *  protoxide  of  iron,*  states  that  the  substance  named  is 
compounded  of  oxygen  (in  a  certain  measure)  and  iron.  There 
is  scarcely  more  than  an  analogy  between  this  class  of  highly 
significant  names  and  the  double  names  of  Botanical  species. 

Double  naming  has  not  been  admitted  into  Mineralogy.- 
Professor  Nicol  remarks  that  the  science  is  not  yet  ripe  for 
the  change.  In  point  of  fact,  however.  Mineralogy  is  in  its 
nature  more  nearly  allied  to  Chemistry  than  to  Botany  or 
Zoology  ;  and  the  double  naming  if  used  would  not  be  for 
species,  but  for  varieties ;  thus  *  magnetic  iron  *  would  not  be 


414 


GENERAL  NAMES. 


SEQUENCE  OF  CHARACTERS. 


415 


a  proper  specific  designation  ;  the  substance  named  has  a 
chemical  expression,  which  will  always  be  preferred. 

Expressive  names  may  be  employed,  apart  from  any  system 
OP  rule,  in  all  subjects.  Thus,  in  the  Natural  Orders  of 
Botany,  we  have  such  names  as  *  Compositae,'  *  Umbelliferae,* 
which  incidentally  inform  us  of  some  of  the  characters  of  the 
families  named.  So,  the  names  of  the  orders  of  Birds  are  all 
expressive  of  some  leading  feature. 

Whewell  proposed  to  reserve  the  title  *  Nomenclature  *  for 
the  designations  that  we  have  now  been  considering.  Linear, 
lanceolate,  oval,  or  oblong,  serrated,  dentate,  or  crenate  leaves, 
are  expressions  forming  part  of  the  terminology  of  botany, 
while  the  names  *  viola  odorata,'  and  *  ulex  Earopseus '  belong 
to  its  Qomenclature. 


CHAPTER  IIL 


CLASSIFICATJON. 


1.  Tlie  Methods  of  Classification  grow  out  of  its  ends. 

I.  The  sequence  of  the  Descriptive  characters  should 
follow  the  order  of  the  properties  as  expounded  in  the 
department. 

Considering  that  a  natural  kind  or  species — mineral,  plant, 
or  animal — may  have  ten,  twenty,  or  fifty  characters,  great  im- 
portance attaches  to  the  method  of  stating  them.  When  we 
seek  for  a  principle  to  govern  this  arrangement,  we  find  it  in 
the  order  of  the  properties  in  the  general  exposition  of  the 
science  or  sciences  where  they  are  discussed.  Mathematical 
properties  would  naturally  precede  physical,  physical  would 
precede  chemical,  and  so  on.  In  an  organized  being,  the 
tissues  precede  the  organs ;  and  some  organs  precede  others 
upon  the  reasons  assigned  as  governing  the  scientific  arrange- 
ment or  classification  of  knowledge. 

Every  classifying  science  has  two  divisions — one  General, 
the  other  Special.  The  first  or  General  division  explains  the 
characters  to  be  used  in  describing  the  species,  and  expounds 
them  more  or  less  minutely.  The  second  or  Special  division 
tsomprises  the  detail  of  the  objects,  and  assigns  to  each  its 


fihare  or  participation  in  these  characters;  that  is,  describes 
the  objects. 

Thus,  in  a  work  on  Mineralogy,  the  General  Division  com- 
prises Crystallography^  or  the  Forms  of  Minerals ;  the  Physical 
Froperties^  as  Cleavage,  Fracture,  Hardness,  Tenacity,  Specific 
Gravity,  Optical  Properties,  Heat,  Electricity,  Magnetism; 
Chemical  Properties,  as  Chemical  composition  and  re-actions. 
This  division  is  an  abstract  of  Molecalar  Physics  and  Chemis- 
try. The  Special  Division,  named  Description  of  Species,  is 
the  detailed  account  of  all  known  minerals,  according  to  these 
properties.  For  example.  Quartz  is  described  as  possessing  a 
certain  Crystalline  form,  a  peculiar  Cleavage,  Fracture,  &c. 

So  in  Botany.  The  First  Division  comprises  Structural 
and  Morphological  Botany,  or  the  parts  of  the  plant  generally 
— Tissues  and  Organs — stated  on  the  methodical  plan  of  pro- 
ceeding from  the  general  to  the  special,  the  less  dependent  to 
the  more  dependent.  The  Nutritive  Organs  have  precedence 
of  the  Reproductive  ;  their  sub-divisions  are  taken  in  the  order 
— Root,  Stem,  Leaves.  The  Division  is  completed  by  the 
functions  or  Physiology  of  the  different  tissues  and  organs. 

The  Second  Division  is  the  Classification  and  Description  of 
PlantSc  The  complete  account  of  each  species  then  properly 
accords  with  the  order  of  the  exposition  of  the  constituent 
tissues,  organs,  and  functions,  in  the  First  Division. 

In  Zoology,  the  method  is  still  the  same,  although  not  so 
thoroughly  carried  out  as  in  Botany,  on  account  of  the  greater 
complications. 

Care  should  be  taken  to  distinguish  ultimate  from  derivative 
characters.  The  Description  is  fully  exhausted  by  a  complete 
enumeration  of  what  are  supposed  to  be  ultimate  characters. 
The  derivations  or  deductions  from  these,  if  given,  should  be 
given  as  such.  A  character  is  to  be  provisionally  received  as 
ultimate,  if  it  cannot  ba  reduced  under  any  more  general 
character. 

For  example,  the  support  of  combustion  is  a  derivative 
character  of  oxygen,  and  does  not  rank  with  the  properties  at 
present  held  to  be  ultimate,  namely,  the  specific  gravity, 
the  specific  heat,  electro-negative  position,  the  combining 
power  generally. 

2.  II.  Observing  the  golden  rule,  we  must  place  to- 
gether, in  classes,  the  things  that  possess  in  common  the 
greatest  number  of  important  attributes. 

At  the  outset  of  the  present  department  of  Logic— Defini- 


416 


CLASSIFICATION. 


TION,  it  was  necessary  to  state  with  regard  to  the  formation  of 
classes  of  things,  that  preference  is  to  be  given  to  such  groups 
as  contain  in  common  the  greatest  number  of  important  attri- 
butes. This  applies  to  all  the  modes  of  dealing  with  the  Con- 
cept or  Notion.  The  mind  sees  objects  to  most  advantage 
when  it  views  together  those  that  have  the  greatest  number  of 
afiGlnities. 

It  is  on  this  principle  that  the  vertebrate  animals  have  been 
classed  according  to  the  leading  points  of  their  Anatomy  and 
Physiology,  such  as  the  manner  of  bringing  forth  their  young, 
rather  than  according  to  the  element  tliat  they  live  in  (earth, 
water,  air).  The  bat  flies  in  the  air,  but  has  more  real  affinities 
with  quadrupeds  than  with  birds ;  the  whale,  seal,  and  por- 
poise, have  warm  blood  and  suckle  their  young  like  land 
quadrupeds,  although  living  in  the  sea  as  fishes. 

The  importance  of  the  attributes  is  to  a  certain  extent 
governed  by  the  end  in  view.  For  practical  purposes,  whales 
are  classed  with  fishes  (as  in  speaking  of  the  whale  fishery)^ 
because  their  living  in  the  sea  determines  the  manner  of  their 
being  caught.  So,  food  plants,  esculent  roots,  fruit  trees,  are 
groups  practically  important,  but  do  not  coincide  with  the 
classifications  of  botany. 

With  a  view  to  theoretical  science,  whose  purpose  is  to 
assemble  in  the  smallest  bulk,  and  in  the  most  intelligible  and 
suggestive  arrangement,  the  greatest  amount  of  knowledge, 
the  golden  rule  must  be  strictly  carried  out.  Even  for  practi- 
cal ends  taken  collectively,  this  is  the  most  useful  plan,  from 
the  very  reason  that  it  does  not  defer  to  any  one  end  in  parti- 
cular. The  classifications  for  practice  do  not  supersede  the 
classifications  for  knowledge,  but  are  additions  to  these  ;  they 
occur  in  the  practical  or  applied  departments  of  information, 
as  Medicine,  Commerce,  Law,  &c. 

Not  only  in  forming  groups,  but  in  their  juxtaposition  in  the 
consecutive  arrangement,  regard  is  paid  to  the  amount  of  affinity. 
The  Natural  Orders  of  Plants  and  of  Animals  are  so  placed, 
that  any  two  lying  side  by  side  are  more  nearly  allied  than 
any  other  two  that  could  be  fixed  upon ;  and  alterations  are 
constantly  suggested  to  give  proximity  to  the  closest  alliances. 
Thus,  Mr.  Huxley  argues  in  favour  of  an  arrangement  uniting 
the  Proboscidia  with  the  Rodentia^  rather  than  with  the  Artio- 
dactyla  and  FerissodactyJa ;  the  singular  ties  that  ally  the 
Elephants  with  the  Rodents  having  been  a  matter  of  common 
remark  since  the  days  of  Cuvier. 

3.  In  aiming  at  a  Natural  Classification,  that  is,  one 


MAXBIUM   OF  AFFINITY. 


417 


based  on  the  maximum  of  important  agreements,  we  may 
meet  with  alliances  on  different  sides,  of  nearly  equal 
value. 

Different  groups  may  touch  each  other  at  different  points, 
and  may  have  equally  strong  alliances.  Thus,  in  Botany,  the 
natural  order  S'oZa?iaceoB,  if  viewed  with  reference  to  i^io  pistils, 
(the  female  side),  allies  itself  with  Scropliulariacecs  ;  if  viewed 
with  reference  to  the  stamens  and  corolla  (the  male  side),  it 
allies  directly  with  Orohanchacece. 

Various  considerations  may  be  brought  forward  to  deter- 
mine the  choice  under  such  circumstances.  One  mode  is  to 
cast  groups  into  a  circular  classification,  wherein  the  succes- 
sion may  return  to  itself.  Another  mode  is  an  arrangement 
in  two  directions,  as  in  a  square  ;  an  idea  carried  still  farther, 
although  in  practice  scarcely  workable,  by  a  cubical  arrange- 
ment. 

It  may,  moreover,  be  considered  which  method  would  bring 
about  the  maximum  of  alliance  on  the  whole,  or  with  refer- 
ence to  the  entire  classification  from  first  to  last.  In  the 
search  after  this  maximum,  we  may  have  to  be  content  with 
occasional  juxta-positions  of  inferior  degrees  of  resemblance. 

Yet  farther,  we  may  make  provision  for  double  placings  of 
the  same  group,  with  a  view  to  comparing  it  on  all  sides  with 
its  congeners. 

4  In  Zoology,  the  most  natural  classification,  on  the 
whole,  corresponds  very  nearly  with  a  serial  order  accord- 
ing to  the  degree  of  development  of  Animal  Life,  and  thus 
facilitates  the  discovery  of  laws  by  the  Method  of  Con- 
comitant Variations. 

The  great  divisions  of  Invertebrate  and  Vertebrate,  and  the 
sub-divisions  of  each,  represent  a  gradual  rise  in  the  scale  of 
being.  The  Radiata,  as  a  whole,  are  lower  than  the  Articu- 
lata ;  the  Fishes  are  the  lowest,  and  the  Mammalia  the  highest 
class  of  the  vertebrate  type.  There  are  deviations  from  this 
gradual  rise  in  organization.  The  fish  named  amphioxus 
lancenlatus  is  surpassed  in  complexity  of  structure  by  many 
insects  and  molluscs. 

For  plants,  the  method  is  much  more  qualified.  There  is  a 
wide  interval  between  the  lowest  Fungi  or  Sea-weeds,  and  the 
Dicotyledonous  Natural  Orders,  but  there  is  no  line  of  steady 
progression.  The  Monocotyledons  are  not  throughout  of  an 
inferior  grade  to  the  Dicotyledons,  nor  is  there  a  gradatioa 


418 


CLASSIFICATION. 


fl^ 


amonjj  the  Natural  Orders  of  either  division.  The  application 
of  the  method  of  concomitant  variations  is  still  possible,  al- 
though greatly  limited.  It  can  be  seen  that  the  absence  of 
the  inflorescence  in  the  inferior  plants  is  conjoined  with  the 
cellular  structure,  which  is  the  lowest  organization  of  the 
tissue  of  the  plant. 

The  serial  order  would  apply  to  all  kinds  of  objects  where 
there  is  a  progress  or  development,  and  where  the  property 
developed  has  a  commanding  importance.  Thus,  Social  in- 
stitutions, as  Governments,  may  be  classed  according  as  they 
approach  to  the  most  perfect  type. 

The  Races  of  Men,  viewed  with  reference  to  mental  endow- 
ment, lie  in  an  ascending  scale,  with  such  occasional  exceptions 
as  the  possessing  of  some  one  faculty  in  a  higher  grade  by  a 
race  inferior  on  the  whole.  We  can  thus  study  the  concomi- 
tant circumstances  of  superiority  and  inferiority  in  mental 
development. 

Civilization  in  its  larger  leaps  is  linear,  but  in  the  minuter 
differences,  not  so.  Communities  advance  in  special  direc- 
tions, the  progress  in  one  line  being  often  accompanied  by 
backwardness  in  others,  from  the  limitation  of  the  human 
energies  as  a  whole.  It  is  true  of  modern  as  of  ancient  civi- 
lized peoples,  that  each  has  its  own  peculiar  excellencies  and 
defects. 

Excudent  alii  spirantia  mollius  sera, 
Credo  equidem,  vivos  ducent  de  marmore  vultus ; 
Orabunt  causas  melius,  coelique  meatus 
Describent  radio,  et  surgentia  sidera  dicent : 
Tu  regere  imperio  populos,  Romane,  memento  ; 
Hae  tibi  erunt  artes  ;  pacisque  imponere  morem, 
Parcere  subjectis,  et  debellare  superbos. 

5.  III.  It  is  an  end  of  classification  to  save  repetition 
in  the  description  of  objects ;  for  which  end  the  generaliza- 
tion is  made  by  successive  steps,  halting-places,  or  grades. 

Instead  of  describing  the  species  *  elephant  *  by  all  its 
characters,  beginning  with  extension  and  materiality,  the 
naturalist  mentions  as  specific  marks  only  a  small  number,  and 
refers  to  the  rest  by  a  series  of  names  expressing  what  is  com- 
mon to  it  with  other  groups. 

Whenever  two  or  more  individuals  agree,  the  agreement 
may  be  stated  once  for  all,  and  only  the  difference  given  under 
each.  In  characterizing  the  races  of  men,  we  state  first  what 
is  common  to  the  whole,  and  next  what  is  special  to  each 


GRADES. 


419 


taken  apart.  We  might  apply  the  method  to  any  two  classes 
that  contain  agreements  peculiar  to  themselves.  There  is  no 
natural  limit  to  the  process  but  the  existence  of  agreements. 
The  number  of  grades  may  be  carried  to  any  length,  so  long 
as  there  is  a  basis  of  community.  The  more  complicated  the 
objects,  that  is,  the  more  extensive  the  compass  of  their  attri- 
butes, the  farther  may  the  gradation  be  carried.  The  insigni- 
ficance of  the  points  in  common  might  be  a  reason  for  not 
treating  them  as  resting-points  of  the  gradation. 

In  Botany  there  are  four  principal  stages,  marking  Classes, 
Families,  or  Natural  Orders,  Genera,  and  Species.  These  are 
maintained  throughout ;  while,  as  occasion  arises,  intermediate 
grades  are  constituted.     (See  Part  First,  p.  65). 

In  Zoology  there  is  first  the  grand  division  of  Invertebrata 
and  Vertebrata.  The  Invertebrata  were  divided  by  Cuvier  into 
Radiata,  Articulata,  Mollusca,  whose  farther  subdivisions  are 
termed  Glasses  (Infusoria,  &c).  The  Classes  contain  Families 
or  Natural  Orders,  under  which  are  Genera,  and  under  these 
Species.  There  are  thus  six  regular  halting  places  between 
the  individuals  and  the  summum  genus— Animal.  The  verte- 
brate Animals  descend  at  one  leap  to  Glasses  (Fishes,  Reptiles, 
Birds,  Mammalia).  The  class  Fishes  undergoes  a  division 
into  Cartilaginous  and  Osseous ;  under  which  are  the  Natural 
Orders.  The  Reptiles,  Birds,  and  Mammalia  are  occasionally 
broken  up  at  once  into  Natural  Orders. 

The  carrying  out  of  ihe  classificatory  arrangement  demands 
that  by  the  methods  of  Definition,  the  agreements  at  each 
stage  should  be  thoroughly  ascertained,  and  fully  and  precisely 
stated.  The  classification  by  grades  is  a  useless  formality  if 
the  corresponding  characters  are  not  given.  The  chemical 
division  of  simple  bodies  into  Metals  and  Non-metals  is  (or 
should  be)  accompanied  with  the  characteristic  marks  or 
common  properties  of  each  class.  The  farther  sub-division  of 
the  metals  into  Noble  Metals,  &c.,  is  seldom  followed  up  by  a 
rigorous  enumeration  of  all  the  points  of  community  ;  and  the 
only  advantage  gained  is  the  mere  proximity  of  the  resenibling 
bodies.  The  same  incomplete  adoption  of  the  formality  of 
grades  is  found  in  the  classification  of  Diseases  ;  epilepsy, 
chorea,  tremor,  hysteria— are  classed  together,  but  without 
the  enumeration  of  common  characters. 

6  The  statement,  by  successive  gradations,  of  the  points 
of  community,  is  suited  to  the  discovery  of  Laws  of  Con- 
comitauca 


!l 


420 


CLASSIFICATION. 


|i 


i- 


In  ascertaining  whether  a  property  a  is  uniformly  conjoined 
•with  a  property  /,  there  is  an  advantage  in  being  able  to 
separate  the  cases  where  a  is  absent  from  those  where  it  is  pre- 
sent. This  is  done  in  the  system  of  grades.  Thus,  by  isolating 
the  order  Ruminantia,  we  readily  discover  the  concurrence 
of  rumination  with  cloven  hoofs. 

If  there  were  any  laws  of  concomitance  among  the  proper- 
ties of  the  metallic  or  the  non-metallic  bodies  of  Chemistry, 
they  would  best  appear  in  the  study  of  the  groups  formed  upon 
special  properties.  Thus,  when  the  metallic  substances  are 
viewed  together,  they  readily  disclose  any  conjunctions  with 
metallic  peculiarities.  So  in  the  non-metallic  division,  the 
halogens — Chlorine,  Iodine,  Bromine,  Fluorine,  present  a  nar- 
rowed field  of  conjoined  properties. 

7.  The  classifications  of  Natural  objects  are  understood 
to  teiminate  with  the  Species,  or  lowest  Kind ;  and  thus  a 
high  importance  attaches  to  the  defining  marks  and 
boundaries  of  Species. 

In  Botany  and  in  Zoology,  the  view  had  long  prevailed  that 
a  species  was  marked  off  by  community  of  descent,  while  any 
differences  that  might  arise  between  the  descendants  of  a 
common  ancestor  were  regarded  as  varieties  and  not  as  specific 
differences. 

The  doctrine  of  the  absolute  fixity  of  species  is  now  called 
in  question,  and  proofs  are  offered  to  show  that,  in  the  course 
of  descent,  differences  called  specific  may  arise  among  the 
descendants  of  a  common  stock.  This  leads  to  a  modified 
statement  of  the  doctrine  of  species.  The  fact  still  remains 
that  some  characters  have  a  high  degree  of  constancy  or  per- 
sistence through  successive  generations  ;  while  others  are 
liable  to  change. 

"Wherever  a  line  can  be  drawn  between  highly  persistent 
and  highly  fluctuating  characters,  we  may  call  the  first  specific 
characters  and  the  others  mere  varieties.  Thus,  in  numerous 
species,  both  of  plants  and  animals,  colour  is  liable  to  consider- 
able variation  within  limits.  So  the  absolute  size  of  living 
objects  may  alter  greatly.  Also  the  degree  of  any  quality  or 
endowment,  as  the  strength,  or  sagacity  of  an  animal,  may 
change.  But  the  tissues,  organs,  and  structural  arrangements 
persist  through  many  successive  generations. 

Importance  may,  nevertheless,  be  still  attached  to  the  fact 
of  the  fertility  or  infertility  of  the  unions  of  individuals.     The 


SPECIES. 


421 


horse  and  the  ass  are  fertile  for  one  generation,  but  the  progeny 
is  incapable  of  farther  procreation. 

In  Minerals,  the  boundaries  of  species  are  fixed  so  far  as 
regards  crystallization  and  chemical  composition,  and  all  the 
consequences  of  these  properties.  As  regards  compounds,  not 
chemical,  which  may  take  place  in  all  proportions,  there  can 
be  no  fixed  lines,  although  a  few  grades  may  be  assigned  with 
doubtful  margins. 

In  Diseases,  the  presence  of  certain  fixed  characters,  such  as 
the  leading  symptoms  of  Inflammation,  of  Small-pox,  of  Gout, 
offers  distinctions  that  may  be  called  specific. 

8.  In  fixing  the  boundaries  of  Species,  respect  may  be 
had  to  the  number  as  well  as  to  the  persistence  of  the 
characters. 

The  Infima  Species  or  lowest  kind,  in  any  of  the  Natural 
Kingdoms,  is  in  certain  instances  divided  from  all  other  species 
by  a  large  number  of  properties,  known  and  unknown.  The 
characters  of  the  species  *  horse  '  are  very  numerous  :  of  man 
still  more  so.  There  cannot  be  the  same  extent  of  specific 
distinctions  in  the  inferior  animals  ;  nor  in  more  than  a  small 
number  of  plants.  Still,  the  existence  of  as  many  as  three, 
four,  or  six  distinguishing  marks,  all  of  some  importance  and 
constancy,  would  suffice  for  making  a  species :  while  the 
limitation  to  one  or  two  might  leave  a  doubtful  choice  between 
Species  and  Variety. 

Mr.  Mill  puts  the  question,  are  all  the  classes,  in  a  Natural 
Classification,  Kinds  ?  He  answers,  certainly  not.  '  Very  few  of 
the  genera  of  plants,  or  even  of  the  families,  can  be  pronounced 
with  certainty  to  be  Kinds.'  In  point  of  fact,  the  difficulty  would 
be  to  fix  on  any  class  of  the  higher  grades,  whose  properties  are  so 
numerous  as  to  rank  them  with  differences  of  Kind  (understood  in 
Mr.  Mill's  perhaps  over- strained  language  respecting  the  Infima 
Species). 

Another  question  raised  by  Mr,  Mill  is  the  propriety  of  Whewell's 
allegation  that  *  Natural  groups  are  given  by  Type^  and  not  by 
Definition.'  By  a  Type,  Whewell  meant  a  weU-selected  average 
member  of  a  class,  removed  alike  from  all  extremes ;  a  concrete 
embodiment  of  the  class,  to  be  used  for  purposes  of  identification, 
in  preference  to  any  verbal  definition.  The  motive  was  the  exist- 
ence of  anomalous  members  of  many  groups  in  Natural  History, 
which  neither  conform  to  the  verbal  definition  nor  yet  differ  suffi- 
ciently from  the  other  members  to  be  excluded  from  the  group. 
We  may  imagine  a  group  formed  upon  ten  characters,  but  con- 
sisting of  individuals  that  vacillate,  some  upon  one  character  and 
Bome  upon  another,  while  yet  agreeing  in  by  far  the  greater  number. 


11 


422 


CLASSIFICATION. 


We  may  even  make  the  extreme  supposition  that  the  vacillation  u 
such  that  no  single  character  of  the  ton  persists  in  every  indi- 
vidual ;  hence,  in  strictness,  there  would  be  no  common  feature, 
and  yet  there  would  be  a  very  large  amount  of  resemblance. 

In  commenting  on  WheweU's  mode  of  getting  over  the  difficulty, 
Mr  Mill  re-iterates  his  view  of  distinctions  of  Kmd,  which,  when 
fuUV  complied  with,  can  leave  no  such  uncertainty  as  is  supposed. 
Moreover,  he  remarks  that  a  class  must  possess  charadera  tha,t 
these  characters  cannot  be  arbitrary,  and  must  admit  of  bemg 
stated,  which  is  tantamount  to  Definition.         ,      ,       „  - 

Probably  WheweU's  difficulty  might  be  met  by  the  aUowance  of 
a  doubtful  margin,  which  has  been  seen  to  be  essential  in  cases  of 
continuity  far  less  complicated  than  the  demarcations  of  groups  in 
Natural  History. 

9.  The  arrangement  of  descriptive  characters  by  grades 
gives  the  greatest  amount  of  knowledge  in  the  least  com- 
pass. Yet,  for  practical  objects,  it  may  be  desirable  to 
bring  together,  in  consecutive  detail,  all  the  characters  of 
a  given  species. 

The  genus  and  species,  *  Man  *  in  the  class  mammalia^  is 
described  by  the  Zoologist,  like  all  the  other  animals,  by  giving 
a  certain  number  of  characters  at  each  stage— those  common 
to  Vertebrate  Animals,  to  Mammalia,  to  Bimana  (of  which 
man  is  the  sole  representative),  and  finally  the  marks  pecuhar 
to  the  species.  But  the  human  anatomist  treats  Man  m  the 
pure  isolation,  disregarding,  except  incidentally,  his  place  in 
the  animated  series.  So,  from  the  importance  of  the  species 
*  Horse,'  there  is  afforded  a  similar  exhaustive  Anatomy. 

Complete  Monographs  of  important  species  are  not  only 
useful  for  practical  ends  ;  they  are  also  the  constituent 
materiala  of  Zoology. 

10.  IV.  The  statement  of  characters  proceeds,  in  the 
last  resort,  upon  a  close  comparison  of  Agreements  and 
Differences. 

From  the  nature  of  knowledge,  the  highest  degree  of  intelligi- 
bility depends  upon  the  most  complete  exhibition  of  agreement 
and  of  difference. 

The  classification  by  grades  provides  for  stating  Agreement. 
A  grade,  whether  Class,  Order,  or  Genus,  is  defined  by  the 
points  of  agreement  discovered  among  its  members.  The 
Botanical  class  *  Dicotyledon,*  has  a  certain  structure  of  Stem 
and  of  Seeds.  The  Animal  genus  *  Ovis,*  has,  as  common 
characters.  Horns  of  a  peculiar   kind  ;    Hoofs  compressed ; 


STATEMENT   OF  CHARACTERS. 


423 


Mammce  two ;  Chin  beardless ;  region  between  the  eyes  and 
nostrils  convex. 

When  characters  are  stated  shortly,  as  by  a  mere  word 
or  phrase,  the  tabular  method  is  the  most  effective  ;  as  in 
minerals.  In  larger  descriptions,  the  headings  at  least  should 
stand  out  distinct.  Thus,  the  genus  *  Poppy  '  is  discriminated 
(from  the  other  genera  of  the  Poppy  Family)  on  two  points ; 
one  referriug  to  the  capsule,  the  other  to  the  flowers.  The 
generic  agreements  may  be  presented  to  the  eye  thus  : — 

*  Capsule^  Globular,  ovoid  or  slightly  oblong,  crowned  by  a 
circular  disk,  &c.' 

*  Flowers.  In  Size,  rather  large  ;  in  Colour,  red,  white,  (in 
the  British  species)  purplish,  or  (in  some  exotic  ones}  pale 
yellow.'* 

The  greatest  difficulty  and  nicety  belongs  to  the  statement 
of  Differences.  Only  in  dichotomies  can  this  be  accomplished 
to  perfection.  When  a  genus  has  two  species,  we  can  put 
them  against  each  other,  according  to  the  plan  observed  in 
defining  by  antithesis  or  contrast  (see  p.  1 64).  Thus,  in  the 
genus  *Corydalis'  (of  the  Fumitory  Family),  there  are  two 
species  (Yellow  and  Climbing).  Their  differences  admit  of 
pointed  contrast  as  follows  : — 

Yellow  Climbing. 

Stem. 
Short,  erect,  branched  Long,  climbing,  slender. 

Flowers. 
Yellow  Whitish. 

If  on  any  one  part,  there  are  plural  contrasts,  the  presenta- 
tion might  be  varied  thus  : — 

o.  j  Short,  erect,  branched  —  Yellow 
(  Long,  climbing,  slender  —  Climbing. 
When  there  are  several  species,  the  presentation  cannot 
always  be  effectively  given  in  this  manner ;  some  may  contain 
agreements  among  themselves,  as  well  as  differences,  which 
would  perplex  the  contrast.  We  may,  however,  occasionally 
mark  off  any  one  from  all  the  rest,  thus  : — 

*  Modified  from  the  following  description  in  Bentham's  British 
Flora : — 

*  Capsule  globular,  ovoid  or  slightly  oblong,  crowned  by  a  circular  disk, 
upon  which  the  stigmas  radiate  from  the  centre,  internally  divided  nearly 
to  the  centre,  into  as  many  incomplete  cells  as  there  are  stigmas,  and  open- 
ing in  as  many  pores,  immediately  under  the  disk.  Flowers  rather  large, 
red,  white,  or  purpUsh  in  the  British  species,  or  pale  yellow  in  some 
exotic  ones ' 

10 


-  ■s.^iiifc^;.  .J 


11 « 


\ 


424  CLASSIFICATION. 

Opium  Poppy. 

Plant 

Glabrous 

Colour, 

GlancouB 

Leaves, 

Toothed  or  slightly  lobed 


Other  Species. 
Stiff  hairs 
Green 


Once  or  twice 
pinnately  divided. 
We  may  always  select  for  pointed  contrast  the  two  classefl 
that  are  most  like,  and  therefore  most  liable  to  be  confounded. 
Thisisdone  incidentally  (although  not  with  systematic  thorough- 
ness)  in  all   the   classificatory   subjects  —  Minerals    Plants, 
Animals,  Diseases.      Thus  the  Silk-cotton  order  of    Plants 
rsterculiacecej  resemble  Malvacece  in  their  general  characters, 
particularly  then-  columnar  stamens,  but  differ  m  their  two- 
celled    extrorse   anthers.      '  In   their   properties,    Cappands 
resemble    Crucifers'    (difference    not    stated).       The    genus 
Banunculus  is  distinguished  from  Anemone  by  the  want  ot  the 
involucre.     In  the  Field  Poppy,  caj^sule  globular ;  in  the  iiong- 
headed  Poppy,  copswZe  oblong. 

11  V  It  being  requisite  to  a  Natural  Classification  that 
bodies  be  arrange'd  under  deep  and  inaccessible  affinities, 
a  separate  scheme,  of  an  artificial  nature,  must  be  provided 
as  an  Index, 

A  classification  may  accord  with  the  primary  rule,  and  may 
be  defective  in  the  means  of  discovering  the  place  of  a  given 
obiect.  The  determination  of  a  plant  is  puzzling  to  the  beginner 
in  Botany.  Now,  it  was  a  merit  of  the  Linnsean  system 
to  make  this  comparatively  easy ;  and  the  advantage  was 
sacrificed  in  the  adoption  of  a  Natural  system. 

The  ideally  best  classification  is  one  where  the  properties 
common  to  the  members  of  the  several  groups  are  both  im- 
portant and  obvious.      Such  a  combination  is  at  best  but 
partially  realized.     Thus,  in  animals,  the  importxint  affinities 
are  so  far  internal,  being  disclosed  only  on  dissection,  as  those 
refeiTing  to  the  minute  points  of  the  skeleton,  the  nervous 
system,  the  structure  of  the  viscera,  &o. ;  and  so  far  external, 
ai   the   form,   the   external   divisions,   the    integument,  and 
(partly)  the  reproductive  organs.     It  is  fortunate  for  Zoology 
that  these  external  peculiarities  either  constitute  of  themselves, 
or  are  marks  of,  the  important  affinities.     Stil ,  they  are  not 
the  v«rhole,  and  even  if  they  were,  a  scheme  must  be  formed  to 
guide  the  student  in  following  them  out  to  the  determination 


INDBX  CLASSIFICATIONS. 


425 


of  the  name  and  place  of  the  individual.  Such  aid  has  not 
yet  been  afforded  in  Zoology.  Yet,  without  it  the  most  con- 
summate natural  arrangement  must  be  a  sealed  book  to  all 
but  proficients  in  the  detailed  knowledge  of  animal  species. 

Chemistry  (with  Mineralogy)  is  in  a  still  worse  case.  The 
governing  principle  in  arranging  chemical  compounds  being 
their  chemical  composition,  which  is  indiscoverable  by  the 
naked  eye,  the  determination  of  a  specimen  is  impracticable 
without  an  artificial  Index;  Owing  to  the  great  importance 
of  discriminating  substances  chemically,  in  the  arts,  a  method 
is  provided,  known  as  Chemical  Testing  or  analysis,  whereby 
the  student,  with  a  limited  knowledge  of  the  entire  field  of 
Chemistry,  can  yet  determine  a  large  number  of  bodies. 

In  Botany,  the  Index  Scheme,  or  Analytic  Key,  is  highly 
elaborated.  It  consists  of  tables  based  upon  a  succession  of 
properties,  there  being  under  each  a  bracket  containing  two 
(rarely  three  or  more)  alternatives.     (See  Book  V.,  Botany). 

In  a  case  of  equal  importance  to  Chemistry,  the  Diagnosis 
of  Disease,  an  Index  classification  is  still  a  desideratum.  The 
medical  student  has  no  aids  to  the  discrimination  of  disease 
short  of  an  aquaintance  with  diseases  generally,  after  a  full 
study  of  Pathology.  The  mode  of  preparing  an  Index  scheme 
could  be  readily  gathered  from  the  plans  pursued  in  Botany 
and  in  Chemistry. 

LOGICAL  DIVISION. 

12.  The  rules  laid  down  for  Division,  as  a  Logical  Pro- 
cess, are  rules  of  Classification,  of  which  Division,  in  the 
Logical  sense,  is  merely  one  aspect.  , 

There  are  many  ways  of  dividing  a  whole  or  aggregate  into 
component  parts.  A  concrete  or  individual  object,  as  York 
Minster,  may  be  divided  into  choir,  nave,  and  transepts ;  into 
main  building  and  spire  ;  into  walls  and  roof;  into  the  part 
for  public  worship  and  the  private  apartments.  This  is  con- 
crete partition,  or  dismemberment.  In  much  the  same  way, 
an  ox  is  divided  for  consumption.  Again,  a  concrete  object 
is  mentally  divided,  or  analyzed,  into  its  abstract  elements ;  wo 
may  separately  attend  to  the  form,  the  size,  the  brilliancy,  the 
weight,  of  the  diamond.  This  is  Abstraction.  When  a  plurality 
of  forces  concur  to  a  certain  result,  they  often  require  to  be 
studied  in  separation  ;  thus,  in  mechanics,  we  have  to  compute 
moving  power  and  friction  apart ;  in  astronomy,  the  disturb- 
ing forces  are  computed   separately,  and  then  compounded. 


426 


CLASSIFICATION. 


LOGICAL  DIVISION. 


427 


This  is  Analysis  and  also  Dednction,  or  Deductive  Combination 
(See  Induction,  Deductive  Method)^  and  is  one  of  the  most 
familiar  of  scientific  operations. 

Logical  Division  is  different  from  any  of  these  modes  of 
separating  wholes  or  combinations  into  parts.  The  received 
rules  enable  us  to  judge  of  its  precise  meaning  and  compass. 
They  are  the  following  : — 

(1)  'Each  of  the  parts  must  contain  less  than  the  thing 
divided.* 

(2)  *  All  the  parts  together  must  be  exactly  equal  to  the 
thing  divided.' 

(3)  *The  parts  must  be  opposed/  that  is,  *  mutually  exclusive.' 
Hamilton  adds  (4)   *  The  principle  of  Division  should  be  an 

actual  and  essential  character  of  the  divided  notion  ;  and  the 
division,  therefore,  neither  complex  nor  without  purpose.* 

These  rules  point  to  an  actual,  exhaustive,  single-pur- 
posed, and  important  division.  The  first  rule  points  to  an 
actual  division,  for  unless  the  parts  be  less  than  the  whole, 
the  whole  is  not  divided.  The  second  rule  supposes  that  the 
parts  are  to  be  exhausted,  so  that  we  may  declare  everything 
contained  in  the  whole  to  be  found  in  one  or  more  of  the 
parts.  There  may  be  divisions  where  this  is  not  insisted  on. 
The  third  rule  requires  that  the  division  shall  be  upon  one 
purpose  or  plan,  so  that  the  parts  may  be  mutually  exclusive  : 
we  divide  an  army  into  infantry,  cavalry,  and  artillery ;  or 
into  officers,  non-commissioned  officers,  and  rank  and  file ; 
but  not  into  infantry  and  commissioned  officers.  The  fourth 
rule  indicates  that  divisions  should  not  be  on  trivial  or  insig- 
nificant characters,  as  if  we  were  to  divide  an  array  or  a  popu- 
lation into  persons  with  names  of  one  syllable,  and  persons 
with  names  of  more  than  one  syllable. 

The  real  importance  of  these  rules  is  with  reference  to 
Classification  ;  for  other  purposes  they  are  idle,  and  even 
erroneous.  When  a  comprehensive  class,  as  Vertebrata,  has 
to  be  sub- classed,  wo  must  comply  with  the  conditions  of 
classification  generally,  or  such  as  we  observe  in  the  march 
upward,  from  the  lower  to  the  higher  grades.  The  Vertebrata 
are  divided  or  sub-classed  into  Fishes,  Reptiles,  Birds,  and 
Mammals ;  it  being  obvious  that  each  sub-class  is  less  than 
the  whole,  that  all  the  four  sub-classes  amount  to  the  whole  ; 
and  that  each  sub-class  excludes  all  the  rest.  If  there  were  a 
failure  on  any  of  these  points,  the  classification  would  be  bad  ; 
the  field  of  the  sub-divisions  is  supposed  to  be  exactly  the 
field  of  the  entire  group ;  nothing  is  to  be  left  out,  and  nothing 


oonnted  twice.  So  in  every  case  of  genus  and  species.  If 
we  mean  to  give  all  the  species,  we  should  give  them  all. 
Moreover,  a  division  into  species,  where  the  same  individ^ls 
appeared  in  two  species,  would  confound  the  very  idea  of 
specific  distinctions.  If  the  bat  were  placed  among  birds,  and 
also  among  mammals,  there  would  be  two  conflicting  principles 
of  classification. 

Division,  in  the  logical  sense,  is  thus  merely  a  way  of  look- 
ing at  classification  by  grades.  Hamilton's  additional  rule — 
that  the  principle  of  Division  should  be  essential  and  important 
— is  the  golden  rule  alike  of  defining  and  of  classifying. 

A  division,  or  sub-classification,  is  complete  when  we  may 
disjunctively  affirm  a  member  of  the  class  as  in  one  or  other  of 
the  parts  *  Actions  are  either  good,  bad,  or  indifferent,'  sup- 
poses that  Actions  may  be  exhaustively  and  correctly  divided 
or  sub-classed  into  good,  bad,  and  indifferent ;  it  being  under- 
stood farther  that  the  same  action  is  not  both  good  and  bad, 
good  and  indifferent,  or  bad  and  indifferent. 

A  classification  may  be  conveniently  tested  by  the  rules  of 
division,  especially  the  third,  the  violation  of  which  makes  the 
Fallacy  of  Cross-division.  Thus,  the  old  classification  or 
division  of  the  Virtues,  called  the  Cardinal  Virtues — Justice, 
Prudence,  Courage,  Temperance — is  vicious  ;  and  the  vicious- 
ness  may  be  expressed  as  either  a  bad  classification  or  as  an 
illogical  division  ;  for  Prudence  includes  the  whole  of  Temper- 
ance, as  well  as  all  that  part  of  Courage  that  conduces  to 
self-interest. 

The  Analysis  of  a  Compound  is  necessarily  exhaustive; 
it  is  the  purpose  of  analysis  to  ascertain  everything  that 
enters  into  the  given  combination.  A  chemist  examines  a 
meteoric  stone,  with  a  view  to  determine  all  the  chemical 
elements  present.  The  physiological  chemist  desires  to  find 
out  all  the  constituents  of  blood,  of  bile,  of  gastric  juice,  ot 
flesh,  and  so  on.  To  such  cases,  the  rules  of  Division  might 
apply,  if  anything  ever  turned  upon  them. 

The  ultimate  analysis  of  the  Mind,  whether  in  whole  or  m 
part,  might  be  tested  by  logical  division.  Thus,  Mind  as  a 
whole  is  divided  into  Feeling,  Volition,  and  Intellect ;  and  to 
this  division  the  logical  tests  should  apply.  The  three  depart- 
ments should  exhaust  the  mind  without  going  beyond  it ;  and 
they  should  be  mutually  exclusive.  So  in  the  Intellect,  the 
analysis  into  Discrimination  or  Difference,  Agreement  or  Simi- 
larity, and  Retentiveness,  professes  to  be  an  ultimate  analysis ; 
the  three  functions  ought  to  contain  all  that  is  intellectual  and 


428 


CLASSIFICATION. 


nothing  more  ;  while  each  should  contain  nothing  in  common 
with  the  other  two.  The  old  enumeration  of  the  Intellectual 
powers— Memory,  Conception,  Abstraction,  Reason,  Judgment, 
Imagination— is  "not  a  logical  division  ;  it  could  not  be  shown 
to  be  intellect,  all  intellect,  and  nothing  but  intellect ;  while 
the  members  are  not  mutually  exclusive ;  memory  has  some- 
thing in  common  with  all  the  rest. 

13.  Logical  Division  fails  in  classifications  with  undefined 
boundaries. 

The  rules  of  Logical  Division  are  inapplicable  to  classifica- 
tions growing  out  of  combination,  growth,  or  development 
Such/ire  the  compounds  of  chemistry,  the  ofispring  of  living 
bodies,  the  developments  of  human  knowledge,  the  associative 
growths  of  the  mind.  All  these  products  are  naturally  un- 
limited and  inexhaustible.  Oxides,  carbonates,  silicates, 
alkalies,  ethers,  are  interminable ;  their  particulars  cannot  be 
enumerated  ;  no  enumeration  necessarily  takes  in  the  whole. 

In  the  Human  Mind,  the  Senses,  or  primary  elements  of 
tensibility,  comply  with  the  rules  of  Division.  The  Emotions, 
most  of  which  are  growths  or  developments,  do  not  comply 
with  it.  If  any  of  the  emotional  states  were  strictly  ultimate, 
they  would  be  mutually  exclusive ;  but  there  are  very  few 
Buch  ;  Wonder,  Fear,  and  Love,  are  nearly  ultimate,  but  may 
not  be  wholly  so.  The  great  bulk  of  the  Emotions  being 
growths  out  of  common  elements,  they  cannot  have  a  strict 
mutual  exclusion  ;  yet  they  may  have  distinctive  characters, 
and  may  be  properly  viewed  as  emotional  species.  Love,  Self, 
Power,  Irascibility,  Pleasures  of  Knowledge,  Beauty,  Moral 
Feeling — are  all  well-marked  groups  of  emotions,  but  they  are 
formed  out  of  common  elements,  which  are  perceptible  to  our 
self-consciousness.  As  products  of  growth  or  association,  they 
have  no  fixed  number ;  new  occasions  would  give  rise  to  new 
varieties  or  species  ;  and  there  cannot  be  a  mutual  exclusion. 
They  are  subject  to  the  golden  rule  of  classification,  but  they 
do  not  present  a  case  for  logical  division. 

There  is  a  similar  inapplicability  to  the  classification  of  the 
Sciences  ;  these  also  succeed  one  another  by  growth  or  develop- 
ment. Chemistry  involves  Physics,  and  Biology,  Chemistry. 
The  Natural  History  sciences— Mineralogy,  Botany,  Zoology, 
Geology — are  full  of  unavoidable  cross-divisions  and  double 
entries.  In  such  a  science  as  Materia  Medica,  there  are  many 
double  entries ;  the  same  substance  is  at  once  stimulant  and 
narcotic.  The  Social  Sciences — Politics,  Political  Economy, 
Jurisprudence— cannot  be  made  mutually  exclusive. 


BOOK  V. 

LOGIC  OF  THE  SCIENCES. 

To  exhibit  the  principles  and  rules  of  Logic  in  a  new 
aspect ;  to  indicate  the  fields  where  these  are  most  needed, 
and  where  examples  are  provided  with  inexhaustible  ful- 
ness,— we  shall  review  in  order  the  Theoretical  Sciences, 
and  some  of  the  leading  Practical  Sciences. 


CHAPTER  L 
LOGIC  OF  MATHEMATICS. 

1.  In  Mathematics,  logically  viewed,  there  is  afforded 
the  most  consummate  exemplification  of  a  Formal  Deduc- 
tive Science. 

The  processes  of  Deduction  are  seen  to  advantage  in  Mathe- 
matics. The  Definitions,  Axioms,  Demonstrations,  Symbolical 
language,  and  various  devices  for  multiplying  the  relations  of 
quantity,  the  subject-matter  of  the  science,  exhibit  all  the 
machinery  for  performing  Deductive  operations  of  a  Formal 
nature. 

2.  Mathematics  treats  of  Quantity  in  the  Abstract,  so 
far  as  susceptible  of  definite  expression. 

The  first,  the  deepest,  the  most  fundamental  experience  of 
the  human  mind  is  Relation,  or  Relativity  ;  this  is  implicated 
in  the  very  natui^e  of  consciousness.  The  doublenesp,  the 
essential  two-sidedness  of  every  conscious  experience  is  a  fact 
that  has  no  forerunner.  Of  the  differences,  contrasts,  or  cor- 
relative couples,  starting  immediately  from  this  primary 
condition,  the  first  is  difference  in  Quantity  or  Degree — the 
distinction  of  more  and  less. 


430 


LOGIC   OF  MATHEMATICS. 


NOTIONS  OF  MATHEMATICS. 


431 


Quantity  adheres  both  to  subject  and  to  object,  but  it  is  not 
always  detinite  ;  and  none  but  definite  expressions  enter  into 
Mathematics.  The  most  detinite  form  of  quantity  is  Number, 
or  discrete  quantity — one,  two,  three,  &c.  Continuous  or 
nnbroken  quantity  is  made  definite  chiefly  by  its  being  broken 
artificially  and  made  numerical.  In  a  few  instances,  as  in  the 
geometry  of  Incomraensurables,  definite  relations  can  be  ex- 
pressed by  lines  in  figures  ;  such  is  the  relation  of  the  side  to 
the  diagonal  of  a  square.  A  difficulty  of  a  metaphysical  nature 
has  long  attended  the  mathematical  expression  of  continuous 
quantity  in  these  incommensurable  relations. 

Notions  of  Maihematics. 

3.  An  enumeration  of  the  principal  Notions  occurring 
in  Mathematics,  prepares  us  for  ascertaining  the  character 
of  the  propositions. 

The  chief  notion  is  Equalify^  with  its  opposite  Inequality. 
This  is  the  prevailing  predicate  in  Mathematics.  Likeness 
(implicating  unlikeness)  applied  to  amount  or  degree  gives 
Equality.  There  may  be  likeness  in  other  properties,  as  sound, 
colour,  pleasure  ;  but,  except  in  quantity,  there  cannot  be 
Equality.  We  can  both  discriminate  and  classify,  apart  from 
Mathematics,  but  when  we  declare  things  equal  or  unequal, 
we  are  announcing  propositions  purely  mathematical. 

In  detecting  equality,  the  final  appeal  is  to  sense  or  con- 
sciousness. For  Number,  we  identify  a  succession  of  beats, 
or  remitted  impressions,  as  two,  or  three ;  this  is  the  surest 
judgment  that  the  human  mind  can  form.  For  Continuous 
Quantity,  we  discriminate  grades  of  continuance  by  the  sense 
proper  to  the  peculiar  effect —the  eye,  the  ear,  the  touch,  <fec. : 
the  most  delicate  discrimination,  and  the  one  that,  if  possible, 
all  others  are  reduced  to,  is  visible  extension ;  next  in  rank 
is  the  continuance  of  sound.  Euclid's  definition  of  Equality  is 
the  visible  coincidence  of  extended  magnitudes. 

Number  is  thus  seen  to  be  a  fundamental  notion  of  Mathe- 
matics, as  the  science  of  Quantity.  Interrupted  sensations, 
or  transitions,  of  consciousness,  are  vividly  discriminated  ;  and 
by  memory  we  can  easily  retain  a  small  succession  of  these, 
and  identiy  it  with  another  small  succession.  Thus,  three 
coins  seen  by  the  eye,  are  identified  to  a  certainty,  with  the 
three  fingers,  in  respect  of  the  number  of  interruptions  or 
transitions  ;  they  are  felt  to  be  different  from  two  or  from  four 
visible  transitions.      This  is  numeiical  equality  or  inequality. 


For  the  higher  numbers,  artificial  aids  are  requisite  to  ensure 
certainty  of  comparison  ;  but  with  such  aids  (namely,  orderly 
groupings)  we  can  compare  numbers  of  any  amount ;  we 
can  identify  one  hundred  in  two  different  aggregates  of  that 
number,  and  discriminate  one  hundred  from  ninety-nine. 

Names  are  given  to  the  successive  numbers,  one,  two,  three, 
four,  five,  &c. ;  at  the  number  ten.  a  group  is  formed,  and  we 
start  afresh.  This  is  our  decimal  system^  to  which  correspond 
the  designations  units,  tens,  hundreds,  &g. 

Addition  is  the  next  fundamental  notion ;  also  obtained, 
in  the  last  resort,  from  the  senses.  When  we  bring  two 
detached  groups  or  successions  from  different  places  to  the 
same  place,  or  into  one  continuous  group  or  succession,  we 
are  said  to  add ;  the  implicated  contrary  is  to  Subtract.  The 
names  whole  and  part  refer  to  the  same  operation,  and  are  ex- 
plained by  the  same  experience.  Multiplication  is  merely  a 
continued  addition,  and  its  obverse  is  Division.  These  notions 
are  the  names  of  the  four  cardinal  processes  of  the  manipula- 
tion of  numbers.  Related  to  them  are  th^  meanings  of  sum, 
difference,  remainder,  factor,  product,  dividend,  divisor,  quo- 
tient, prime  number. 

Fraction  (versus  Integer)  grows  out  of  division  ;  also  the 
designations  numerator  and  denominator,  common  uneasure. 
To  fractions  are  applied  the  cardinal  operations — addition,  &c. 

Decimal  is  a  fractional  mode,  related  to  our  decimal  enu- 
meration. 

Square,  cube,  square  root,  cube  root,  &c.,  are  special  growtlis 
or  extensions  of  multiplication  and  division  respectively. 

Ratio  is  the  statement  or  implication  of  how  many  times  one 
number  is  contained  in  another  ;  the  ratio  of  three  to  twelve 
is  four,  or  one  to  four.  We  do  not  always  reduce  the  ratio  to 
the  lowest  terms ;  we  may  speak  of  the  ratio  of  three  to  six, 
but  the  comparison  of  the  numbers  is  by  multiplication  or  divi- 
sion.  The  expression  of  ratios  takes  the  form  oi fractions. 

Proportion  is  equality  of  ratios  ;  three  is  to  eight  in  the  pro- 
portion of  nine  to  twenty- four. 

Ratio,  Proportion,  and  Fraction,  conduct  us  to  the  idea  of 
Incommensurable. 

Progression,  or  series,  is  a  succession  of  numbers  according 
to  a  fixed  law ;  the  Arithmetical  progression  being  governed 
by  addition,  the  Geometrical,  by  multiplication.  A  progression 
contains  Extremes  and  Means, 

Permutations  and  Combinations  are  modes  of  operating  upon 
numbers  that  need  not  here  be  explained. 


432 


LOGIC   OF   MATHEMATICS. 


DEFINITIONS   OF  ARITHMETIC. 


433 


h 


Logarithm  signifies  a  still  more  advanced  notion  ;  being  the 
name  for  an  entirely  novel  mode  of  expressing  the  relations  of 
numbers,  which,  when  unfolded  in  tables,  greatly  reduces 
the  labour  of  the  higher  operations,  namely,  multiplication, 
division,  raising  to  powers  and  extraction  of  roots. 

The  foregoing  comprise  the  leading  notions  of  mathematics 
for  the  initial  branch,  called  pure  Arithmetic.  For  Concrete 
or  commercial  Arithmetic,  there  are  involved  farther  the  money 
standards,  the  weights  and  measures,  together  with  the  adapta- 
tion of  the  cardinal  processes  of  proportion  and  of  fractions,  to 
compute  these  several  varieties  of  concrete  quantity. 

Algebra  carries  forward  all  the  arithmetical  notions  to  a 
new  order  of  expressions  of  quantity.  The  detaching  of  the 
operations  from  the  actual  numbers,  by  the  use  of  symbols, 
gives  new  designations,  Negative  Quantity^  Index,  Exponent, 
Surd,  Impossible  Quantities.  The  general  theorem  for  expand- 
ing by  powers  or  roots  is  the  Binomial  Theorem.  Then  follows 
the  Equation — Simple,  Quadratic,  &c. 

The  Notions  of  Geometry  are  comprised  in  the  Definitions 
of  Euclid :— Point,  line,  straight  line,  curve  line,  angle,  paral- 
lels, surface,  solid,  triangle,  quadrangle,  polygon,  circle,  cube, 
sphere,  cylinder,  cone,  &c. 

In  Trigonometry  there  are  new  designations — sine,  co-sine, 

tangent,  secant. 

In  Conic  Sections  are  comprised  the  figures  so  named  with 
the  further  designations — eccentricity,  focus,  directrix,  latus 
rectum,  parameter,  abscissa,  normal,  asymptote. 

Analytical  Geometry  involves  co-ordinates  and  loci  ;  and  ds- 
signates  a  number  of  curves  reserved  for  analytical  handling — 
cissoid,  conchoid,  witch,  lemniscata,  catenary,  cycloid,  invo- 
lutes, spirals,  &c. 

The  higher  Calculus  introduces  us  to  the  notions — Infinite- 
simal, Differential,  Integral,  Limit,  Dependent  and  Independent, 
Variable. 

Fro2)ositions  of  Mathematics, 

4  In  the  logical  aspect,  these  propositions  are  leading 
examples  of  the  predicable,  called  proprium.  The  predi- 
cate is  deducible  and  demonstrable  from  the  subject. 

The  Axioms  are  inductions  of  concomitant  properties.  In 
all  other  propositions  (excepting  those  that  are  in  reality  defini- 
tions), the  predicate  is  deducible  from  the  subject  through  the 
axioms.      Thus,  in  the  simple  Arithmetical  proposition,  six 


times  four  is  twenty  four,  the  predicate  (24)  follows  from  the 
subject  (6  times  4)  by  the  medium  of  the  two  great  axioms  of 
equality.  The  predicates  are  not  contained  in  the  subjects  by 
necessary  or  immediate  implication  ;  they  are  mediate  infer- 
ences drawn  by  the  help  of  the  highest  generalities  ;  exempli- 
fying the  true  nature  of  the  proprium, 

♦  Definition  in  Mathematics, 

6.  Certain  of  the  Notions  of  Mathematics  are  funda- 
mental and  indefinable ;  the  rest  are  defined  by  derivation 
or  Analysis. 

It  will  be  sufficient  to  advert  to  the  specialities  connected 
with  (1)  Arithmetic,  and  (2)  Geometry. 

Definitions  of  Arithmetic. — We  have  seen  that  Number  or 
discrete  quantity,  is  a  series  of  intermitted  impressions  on  the 
mind — patches  of  colour,  sounds,  &c.  This  is  an  ultimate  fact ; 
language  can  give  no^ccount  of  it  in  any  other  way  than  by 
calling  each  one's  attention  to  their  own  experience.  As 
regards  the  numbers  themselves,  experience  must  give  us  a 
few  to  begin  with  ;  the  rest  may  be  derived  and  defined  from 
these.  Unity  is  an  ultimate  reference,  the  abstraction  from 
numerous  concrete  objects,  that  is,  from  many  single  impres- 
sions ;  it  is  contrasted  with  two,  and  with  the  higher  succes- 
sions. We  learn  one,  two,  three,  four,  five,  &c.,  by  repeated 
experiences  of  the  successions  so  named;  the  hand  is  a 
familiar  example  of  five.  We  might  go  a  good  way  in  dis- 
tinguishing the  successive  numbers ;  but,  in  point  of  fact, 
when  a  dozen  or  thereby  is  reached,  we  resort  to  modes  of 
comparison  that  imply  grouped  arrangements. 

So  much  for  our  actual  experience  of  numbers,  which  is 
presupposed  in  the  attempt  to  define  them.  For  the  actual 
purposes  of  a  strict  definition,  we  must  assume  one  as  indefin- 
able, that  is,  as  already  known.  Even  this  supposes  that  we 
know  two  at  least,  for,  without  a  contrast  with  plurality,  we 
cannot  possess  the  meaning  of  unity. 

Before  going  farther,  it  is  necessary  to  suppose  that  we 
understand  addition.  This  is  an  abstract  notion  gained  from 
many  concrete  experiences  of  accumulating  objects  in  mass. 
We  cannot  define  it;  we  must  point  to  the  operation:  an 
operation,  as  already  remarked,  that  makes  known  subtraction 
likewise  ;  and  also  whole  and  part.  To  attempt  to  define  any 
of  these  notions  is  to  encroach  upon  the  ultimate  experiences 
of  the  mind  j  and  the  futility  is  shown  by  the  words  employed. 


434 


LOGIC  OF  MATHEMATICS. 


*  aggregation,*  &c.,  which  are  not  more  elementary,  or  more 
Bimple,  than  the  notions  that  they  are  used  to  define. 

With  a  knowledge  of  one,'  and  of  addition,  we  may  begin  to 
define.  The  lowest  definable  number  is  then  two ;  we  may 
define  it  by  the  addition  of  one  and  one.  The  rest  follow : 
three  is  two  added  to  one  ;  four  is  three  and  one  ;  five  is  four 
and  one,  and  so  on.  Each  number  is  definable  as  one  added 
to  the  previous  number.  Arriving  at  ten,  we  bring  into  play 
the  decimal  notation,  or  the  grouping  by  tens,  which  gives  us 
double  expressions  :  eleven  is  ten  and  one  ;  twelve  is  eleven 
and  one,  and  also  ten  and  two ;  fifteen  is  fourteen  and  one,  and 
ftlso  ten  and  five.  We  may  be  supposed  at  this  stage  to  make 
use  chiefly  of  the  second  form,  although  always  aware  of  its 
equivalence  to  the  first ;  sixteen  is  ten  and  six ;  twenty-seven 
is  twenty  (two  tens)  and  seven. 

All  the  other  notions  of  Arithmetic  are  susceptible  of  defini- 
tion properly  so  called  ;  they  may  be  derived  from  the  notions 
now  given.  In  logical  strictness,  there  is  no  need  for  a  farther 
appeal  to  experience ;  although  the  actual  understanding  of 
the  processes  is  aided  by  using  concrete  examples  of  numbers 
and  their  formations. 

Definitions  of  Geomeiri/. — The  difficulties  here  are  far  more 
serious  ;  yet  the  proceeding  is  the  same.  We  must  recognize 
a  certain  basis  of  the  indefinable,  a  resort  to  experience  for 
what  can  be  given  only  by  experience. 

By  experience,  we  become  familiar  with  all  the  modes  of 
extension,  and  learn  the  names  for  them.  We  know  solid 
bulk,  surface  or  area,  length,  angle,  direction,  straight,  bent, 
curved,  parallel,  and  so  on.  We  also  know  what  a  Point  is, 
in  the  peculiar  acceptation  of  a  landmark,  or  a  place  to  measure 
from,  to  begin,  to  terminate,  or  to  divide  a  length.  While 
Solid  Bulk  is  the  one  concrete  fact,  all  the  rest  are  abstractions, 
and  we  learn  to  understand  them  in  that  character.  We  can 
consider  a  line,  or  length,  without  affirming  anything  of  the 
breadth  of  the  thing  discussed  ;  we  can  restrict  our  affirma- 
tions to  what  would  be  true  under  any  width,  as  when  we 
say  a  piece  of  string  and  a  plank  are  of  equal  lengths.  By  a 
large  concrete  experience  of  this  nature,  we  are  prepared  for 
the  more  rigorous  methods  of  arranging  and  stating  thsse 
notions  in  Geometry. 

To  advert  more  particularly  to  our  experience  of  Lines  or 
lengths,  abstraction  being  made  of  the  accompanying  breadth 
and  thickness.  In  this  one  experience  is  wrapt  up  inextricably 
a  whole  group  of  the  notions  given  by  the  geometer  in  separH' 


DEFINITIONS  OF   GEOMETRY. 


435 


. 


tion.  In  working  with  rods,  with  strings,  with  wires,  and 
other  things,  we  learn,  not  only  length  (as  greater  or  less),  but 
also  the  difference  between  straight  and  bent,  crooked  or 
curved ;  together  with  direction,  angles,  and  parallelism. 
Straightness,  direction,  angle,  convergence,  divergence,  and 
parallelism,  however  separated  in  Geometry,  are  all  inter- 
mingled in  our  primitive  concrete  experience ;  and,  indeed, 
any  one  would  be  incompletely  understood  if  it  did  not  involve 
all  the  rest.  We  cannot  understand  the  full  force  of  '  straight- 
ness '  without  understanding  what  is  meant  by  direction : 
*  direction  *  would  be  very  incomplete  without  involving  the 
meaning  of  an  angle ;  and  the  concrete  experience  of  an  angle 
gives  all  that  is  meant  by  convergence  and  divergence,  and 
also  by  the  opposite  of  these — parallelism. 

All  these  notions,  therefore,  have  to  be  assumed  as  being 
perfectly  intelligible  and  as  wholly  indefinable.  We  can 
assign  nothing  more  simple  or  more  elementary  to  define 
them  by.  The  attempt  to  define  an  *  angle  *  only  returns 
upon  itself ;  thus,  an  angle  is  said  to  be  the  inclination  of  two 
lines,  but  *  inclination '  is  merely  another  name  for  angle ;  as 
well  say,  *an  angle  is  an  angle.'* 

Geometry,  as  well  as  Arithmetic,  is  a  Deductive  Science. 
Now  it  is  the  idea  of  a  deductive  science  to  assume  the  fewest 
notions  possible,  and  to  begin  to  define,  or  derive,  as  soon  as 
there  has  been  laid  an  adequate  foundation  in  the  indefinable. 

To  make  the  application  to  the  case  in  hand.  The  fewest 
elementary  notions  that  we  can  proceed  with  may  be  differ- 
ently stated  by  different  persons  ;  but  one  cannot  be  far  wrong 
in  the  following  : — point  or  landmark,  line  or  length,  straight, 
as  contrasted  with  bent,  angle,  surface,  solid.  The  three — 
line,  straightness,  angle — are  really  phases  of  one  experience  ; 
and,  by  a  great  stretch  of  ingenuity,  we  might  find  it  possible 
to  condense  the  three  expressions  into  two,  or  even  into  one ; 
for  undoubtedly  the  line  (as  carrying  with  it  length)  implicates 

♦  *  Geometrical  definitions  are  of  three  kinds  :  (1)  Those  which  express 
our  primary  ideas  of  space,  such  as  the  definitions  of  a  straight  line,  an 
angle,  a  plane,  &c.  (2)  Those  which  by  means  of  the  first  class  define 
certain  simple  forms^  the  triangle^  the  square,  and  the  circle,  from  the 
properties  of  which  all  calculation  of  relative  positions  and  superficial 
magnitudes  is  derived.  (3)  Definitions  of  other  forms,  as  the  rhombus, 
trapezium,  hexagon,  ellipse,  &c.,  the  properties  of  which  are  found  by  the 
application  of  theorems  obtained  from  the  definitions  ot  the  simple  forms,' 
(Challis  on  Calcula-tion,  p.  61). 

The  last  named  class  exemplify  what  are  called  Deductive  Definitions 
(p.  165). 


^VV.:  /*;;.   - '*!• 


436 


LOGIC  OF  MATHEMATICS. 


FUNDAMENTAL  NOTIONS  OF  GEOMETRY. 


437 


*  straightness,*  which  itself  involves  its  opposite  *  bending,* 
and  also  *  direction ;'  and  from  direction  we  cannot  separate 
change  or  variety  of  direction,  as  exhibited  in  an  *  angle.'  Not- 
withstanding this  inevitable  mutual  implication,  we  may 
retain  the  above  enumeration  of  primary  or  indefinable  notions 
'—^oint,  line  or  length,  straight  (with  hent)^  angle,  surface,  solid 
(it  would  be  a  vain  refinement  to  treat  *  surface  '  and  *  solid  * 
as  derived  from  length,  or  vice  versa).  Prom  these  we  are 
able,  by  proper  analytic  definition,  to  give  an  account  of  all 
the  other  geometrical  notions.  It  is  requisite,  however,  to 
unfold  the  immediate  implications  of  each,  and  to  state  which 
phase,  aspect,  or  property  shall  be  put  forward,  in  the  subse- 
quent demonstrations,  as  the  testing  propert}-. 

Point. — As  stated,  this  is  the  same  meaning  as  landmark  ; 
for  geometric  purposes,  we  hold  it  as  the  beginning,  division, 
or  end,  of  length  or  a  line  ;  all  which  must  be  understood  by 
actual  experience. 

Lirte  or  length. — It  is  impossible  to  give  a  definite  meaning 
to  *  line  '  without  at  once  distinguishing  the  straight  from  the 
bent  line  ;  it  is  only  the  straight  line  that  is  synonymous  with 

*  length.*  The  mutually  implicated  notions — length  and 
straightness — are  absolutely  incommunicable  by  any  device  of 
language ;  they  cannot  even  be  made  clearer  by  discussion. 
We  may,  however,  select  one  feature  or  aspect  as  the  test  to  be 
referred  to  in  the  course  of  the  demonstrations,  namely,  that 

*  two  straight  lines,  if  made  to  coincide  in  two  points,  will 
coincide  wholly,'  will  have  no  interval ;  all  which  ideas  the 
learner  has  to  bring  with  him  from  his  own  independent 
experience.  Another  aspect  of  the  straight  line,  sometimes 
given  as  its  definition,  is  *  the  shortest  distance  between  two 
points ;'  this,  however,  may  be  proved  by  proper  demonstra- 
tion ;  being  a  corollary  to  the  proposition  that  two  sides  of  a 
triangle  are  greater  than  the  third.  At  the  same  time,  it  is 
sufficiently  implicated  with  our  experience  of  lines  to  be 
received  without  proof. 

Angle. — This  also  must  be  known  from  experience.  We 
must  see  with  our  eyes  two  straight  objects  meeting  with  a 
greater  or  less  opening.  That  experience  supplements  our 
education  in    *  direction,'    and  gives  us  what  is  meant  by 

*  divergence  '  and  *  convergence,'  greater  or  less.  There  is  a 
farther  implication  of  two  lines  running  side  by  side,  and 
neither  diverging  nor  converging ;  to  this  fact  we  give  the 
designations  *  sameness  of  direction  and  parallelism ;  '  all 
incommunicable  notions. 


It  may  then  be  formally  proper  to  describe  an  angle  as  two 
Btraigkt  lines  meeting  in  a  point,  with  greater  or  less  diver- 
gence. This  is  merely  one  way  of  referring  us  to  our  experi- 
ence of  the  fact ;  and  it  is  thought  the  best  workable  test  of 
an  angle  in  the  subsequent  references. 

With  the  angle,  we  can  conveniently  connect  the  notion  of 

*  Direction.'  Inasmuch  as  all  direction  is  relative,  there  must 
be  two  lines  given,  and  the  angle  they  enclose  gives  the  com- 
parison of  the  two  directions.  Direction  being  understood, 
we  can  define  a  curve  line,  as  a  perpetually  changing  direc- 
tion ;  which  is  an  obverse  equivalent  of  Euclid's  phi-ase  *  a  line 
of  which  no  part  is  straight ;  '  both  expressions  being  proper 
to  be  retained. 

Parallels. — These  are  inevitably  understood  along  with  the 
notions  already  given.  As  to  their  formal,  or  test  definition, 
Euclid's  original  expression,  *  two  lines  in  the  same  plane,  pro- 
duced ever  so  far  both  ways,  and  yet  not  meeting,'  is  properly 
A  negation  of  both  convergence  and  divergence,  and  is  suffi- 
ciently workable,  which  is  all  that  need  be  said  for  any  defi- 
nition. 

Plane  Surface. — This  is  clearly  an  incommunicable  notion. 
It  would  be  superfluous  to  construct  it  by  the  help  of  lines,  for, 
while  we  are  learning  lines,  we  are  also  learning  surfaces. 
All  that  is  needed  is  a  convenient  testing  peculiarity,  such  as 
that  given  by  Euclid, — *  any  two  points  being  taken  in  a 
plane,  the  straight  line  joining  them  lies  wholly  within  the 
plane.'  The  notions  *  within  '  and  *  without  *  must  be  got 
from  our  manifold  experience  of  extended  bodies. 

Solid  Bulk. — Also  incommunicable  by  any  simpler  notions. 
If  we  seem  to  define  it  by  combining  the  notions  of  *  planes  * 

*  directions,'  &c.,  we  in  reality  repeat  ourselves ;  for  these  very 
notions  were  attained  by  a  mass  of  experiences  including 
solid  bulk  or  volume. 

The  elementary  notions  now  enumerated  being  once  obtained 
from  experience,  the  remaining  notions  of  geometry  are  defin- 
able by  referring  to  these.  No  new  appeal  to  the  senses  is 
absolutely  required  in  defining  a  right  angle,  a  circle,  a  triangle, 
a  square ;  although  we  are  constantly  aided  by  concrete  re- 
presentations in  understanding  these  notions. 

Axioms  of  Mathematics, 

6.  The  Axioms  of  Mathematics  should  conform  to  the 
conditions  of  an  axiom,  namely,  (1)  they  should  be  real 


438 


LOGIC   OF  MATHEMATICS. 


AXIOMS   OF  EUCLID. 


439 


D 


I 
I 


propositions,  and  (2)  they  should  be  underivable  from  any 
other  principles  within  the  science. 

An  axiom  is,  in  the  first  place,  a  real  proposition,  and  not  a 
verbal  or  essential  proposition.  The  axioms  are  the  ground- 
work of  all  the  reasonings  in  the  science,  but  no  reasoning 
can  be  based  on  merely  verbal  propositions. 

In  the  next  place,  the  axiom  should  be  abaolutely  funda- 
mental and  underivable  within  its  own  science.  All  that  is 
characteristic  of  the  axiom  is  surrendered,  it*  we  admit  deduced 
principles.  The  axioms  are  the  uudeducible  grounds  of  all 
the  deductions. 

It  is  not  a  proper  account  of  an  axiom  to  say  that  it  is  a 
self' evident  proposition,  or  a  proposition  assented  to  as  soon  as 
pronounced.  This  may  or  may  not  be  the  case.  Some  axioms 
are  self  evident,  others  not ;  and  many  principles  that  are 
self-evident  are  not  to  be  received  as  axioms. 

Axioms  of  Mathematics  as  a  whole. — The  axioms  of  Mathe- 
matics as  a  whole,  requisite  to  be  given  at  the  threshold  of 
Arithmetic,  are  at  least  these  two — '  Things  equal  to  the  same 
thing  are  equal  to  one  another,'  and  '  The  sums  of  equals  are 
equals.'  These  are  real  propositions,  inductions  from  experi- 
ence, and  undeducible  from  one  another.  Whether  they  are 
sufficient  for  all  purposes,  will  appear  afterwards.  Both  are 
demanded  by  the  processes  of  Arithmetic. 

Axioms  of  Geomttiiij. — As  it  has  been  the  practice  to  teach 
Arithmetic  to  beginners,  not  as  a  reasoned  or  deductive 
science,  but  as  a  series  of  rul^s  given  upon  authority,  and 
merely  confirmed  by  their  actual  results,  the  mathematical 
axioms  usually  confront  the  learner  for  the  first  time  at  the 
beginning  of  Geometry,  which  from  early  ages  has  aspired 
to  be,  not  merely  a  body  of  correct  rules  for  measuring  mag- 
nitude, but  a  perfect  type  of  deductive  reasoning.  As  thus 
presented,  the  axioms  of  all  Mathematics  are  so  mixed  tip 
with  matters  belonging  to  geometry  in  particular,  as  to  seem 
exclusively  geometrical  in  their  bearing,  These  axioms,  made 
familiar  to  us  by  Euclid,  have  to  be  tried  by  the  two  tests 
already  laid  down. 

In  Euclid's  original  text,  there  occur  twelve  axioms  (or 
common  notions  Koiuai  e^f^ouu).  Others  have  been  added  by 
modern  editors ;  it  is  not  unusual  to  give  fifteen.  The  two 
first  in  the  enumeration  are  the  two  already  mentioned  as 
unquestionable  axioms,  conforming  to  both  the  criteria.  The 
five  succeeding  are — 


(3)  If  equals  be  taken  from  equals,  the  remainders   are 

equal. 

(4)  If  equals  be  added  to  unequals,  the  wholes  are  un- 

equal. 

(5)  If  from  unequals,  equals  be  taken,  the  remainders  are 

unequal. 

(6)  Doubles  of  the  same  are  equal. 

(7)  Halves  of  tho  same  are  equal. 

Now,  these  are  all  real  propositions,  and  therefore  not  dis- 
qualified by  the  first  condition  ;  but  as  they  are  all  very  easily 
deducible  from  the  two  first,  they  fail  to  comply  with  the 
second  condition.  They  are  not  axioms  proper,  but  deduc- 
tions or  corollaries  from  axioms,  and  should  be  demonstrated. 
If  we  are  to  call  them  axioms,  there  is  nothing  to  prevent  us 
from  calling  any  real  proposition  whatever  an  axiom.  It 
violates  the  very  essence,  the  first  demand,  of  a  deductive 
science  to  take  for  granted  without  proof  whatever  can  be 
proved  from  another  principle  within  the  science. 

The  eighth  axiom,  *  Things  that  coincide,  or  have  the  same 
boundary,  are  equal,'  violates  the  first  test  of  an  axiom  ;  it  is 
not  a  real  proposition,  but  a  definition  of  equality.  *  Coincid- 
ing '  and  *  being  equal '  are  not  two  facts  but  the  same  fact  in 
two  statements  of  language,  the  one  being  given  as  the  expla- 
nation of  the  other.  Equality  as  applied  to  extended  magni- 
tude is  coincidence  to  the  senses  ;  to  prove  equality  we  prove 
coincidence.  Of  Equality  no  definition  can  be  givdn  in  the 
last  resort ;  it  is  the  feeling  of  similarity  or  identity  as  applied 
to  quantity.  But  in  dealing  with  the  special  kind  of  quantity 
considered  in  geometry,  there  is  a  convenience  in  specifying 
the  test  of  equality  belonging  to  the  case — namely,  the  visible 
coincidence  of  the  boundaries  of  the  two  things  compared — 
lines  or  plane  figures.  The  supposed  axiom  is  theretbre  the 
geometrical  statement  and  adaptation  of  the  fundamental  and 
indefinable  notion  of  equality. 

The  ninth  axiom  is  *  The  whole  is  greater  than  its  part.' 
This  also  violates  the  first  test ;  it  is  not  a  real  proposition  ; 
the  predicate  is  not  difierent  from  the  subject.  It  is  a  pro- 
perty implicated  in  the  common  fundamental  notion  that 
gives  a  meaning  to  addition,  subtraction,  whole,  part.  The 
concrete  experience  implied  by  all  these  words  is  one  and  the 
same  experience,  and  in  it  is  implicated  the  fact  that  what  we 
call  a  sum  is  greater  than  any  one  of  the  amounts  summed 
up  ;  or  what  we  call  a  whole  is  greater  than  any  of  the  parts. 
We  could  not  possess  the  notion  of  whole  and  part  without 


440 


LOGIC  OF  MATHEMATICa 


POSTULATES. 


441 


11 1 


possessing  the  fact  that  the  whole  is  a  larger  magnitude  than 
the  part.  If,  therefore,  there  be  any  necessity  for  distinctly 
announcing  this  peculiar  aspect  of  the  great  fundamental 
notion  of  addition,  it  should  be  given  as  one  of  the  forms  of 
expressing  the  notion  of  Addition,  when  that  notion  is  first 
introduced  at  the  threshold  of  Arithmetic. 

The  tenth  axiom,  '  All  right  angles  are  equal  *  is  implicated 
in  the  definition  of  a  right  angle  ;  and  should  be  stated  as  an 
appendage  to  that  definition. 

The  eleventh  axiom,  in  Euclid's  text,  is  a  difHcult  theorem 
preparatory  to  the  propositions  respecting  parallel  lines.  It 
is  usually  given  in  a  modified  and  simpler  form.  Thus  (by 
De  Morgan)—*  If  a  straight  line  be  taken,  and  a  point 
exterior  to  it ;  of  all  the  straight  lines  that  can  be  drawn 
through  the  point,  one  ordy  will  be  parallel  to  the  first-men- 
tioned straight  line.'  In  whatever  form  given,  it  is  not  an 
axiom,  but  a  proposition  deducible  from  the  definition  of  paral- 
lel lines ;  in  fact,  it  ought  to  appear  among  the  Theorems  of 
the  first  book,  unless,  indeed,  it  be  so  nearly  identified  with 
the  definition  of  parallels  that  it  can  be  given  as  a  mere  various 
wording  or  obvious  implication  of  that  definition;  which, 
however,  is  hardly  the  case. 

Eudid's  twelfth  (and  last)  axiom  is  famous  in  the  History 
of  Philosophy :  *  Two  straight  lines  cannot  enclose  a  space.' 
It  is  not  a  real  proposition,  but  merely  an  iteration  of  the 
very  fac*  of  straiglitness.  The  pro  forma  definition  of  this 
indefinable  notion  is  *  When  two  lines  cannot  coincide  in  two 
points  without  coinciding  altogether,  they  are  called  straight 
lines.'  Now  it  is  a  synonymous  variety  of  the  expression 
•  coinciding  altogether,'  that  there  should  be  no  intervening 
space.  That  the  lines  should  be  *  straight '  and  that  they 
should  *  enclose  a  space '  would  be  a  contradiction  in  terms. 
This  axiom  must,  accordingly,  be  rejected ;  the  phrase  '  not 
enclosing  a  space'  being  transferred  to  the  definition  of 
straightness,  as  an  emphatic  obverse  iteration  of  *  coinciding 
altogether.'  We  might  express  it  thus — *  When  two  lines 
cannot  coincide  in  two  points  without  coinciding  altogether, 
that  is,  without  excluding  an  intervening  space,  they  are 
called  straight  lines.' 

In  the  modern  texts  of  Euclid,  there  are  added  to  the  list  of 
axioms  such  propositions  as  the  following  . — *  If  two  things  be 
equal,  and  a  third  be  greater  than  one  of  them,  it  is  also 
greater  than  the  other.'  This  is  clearly  demonstrable  from 
the  proper  axioms,  coupled  with  the  notions  of  greater  and  less. 


More  notable  is  the  argumentum  a  fortiori,  occasionally  im- 
ported into  Logic,  although  in  its  nature  strictly  mathematical. 
If  A  be  greater  than  B,  and  B  greater  than  C,  much  more  is 
A  greater  than  C.  Every  one  readily  assents  to  this  principle 
as  an  induction  from  facts  of  their  own  observing.  If  it  can- 
not be  deductively  inferred  from  the  two  proper  axioms,  it 
will  have  to  be  received  as  a  third  axiom.  Probably,  however, 
mathematicians  would  be  able  to  demonstrate  it,  if  not  directly, 
at  least  by  reductio  ad  absurdum,  from  those  axioms. 

Another  example  of  a  proposed  axiom  is  the  following : — 
*  Of  all  lines  that  conjoin  two  points,  there  must  be  one  with 
none  less ;  if  only  one,  that  is  the  least.'  If  there  is  any 
necessity  for  enunciating  this  circumstance,  it  should  be 
given  as  implicated  in  our  experience  of  lines  ;  its  opposite  is 
a  contradiction  in  terms  ;  the  very  meaning  of  '  least '  is  that 
there  can  be  nothing  less. 

The  bringing  forward  of  axioms  at  every  new  stage  of 
Geometry  is  wholly  at  variance  with  the  deductive  character 
of  the  science.  There  may  be  required  a  class  of  principles, 
intermediate  between  the  axioms  proper  and  the  demonstrated 
theorems ;  but  they  should  not  be  confounded  with  the  primary 
foundations  of  the  science  ;  they  should  have  a  name  distinct 
from  *  axiom.'  If  inconvenience  were  now  to  arise  from  drop- 
ping the  name  in  connexion  with  these  preliminary  principles, 
some  emphatic  designation  should  be  adopted  for  the  really 
fundamental  truths — *  Axiom s-in- chief,'  *  Axioms  proper,'  *  In- 
demonstrable assumptions,'  *  Final  Inductions.' 
^  The  Postulates.  —These  are  the  groundwork  of  the  construc- 
tive part  of  Greometry — the  problems,  as  distinguished  from 
the  theorems.  It  is  Euclid's  plan  to  carry  on,  side  by  side,  a 
series  of  problems  of  construction  and  a  series  of  theorems ;  the 
constructions  being  required  for  demonstrating  the  theorems. 
These  constructions,  however,  have  an  independent  value  for 
practical  applications ;  the  land  measurer  follows  Euclid's 
method  in  throwing  out  a  perpendicular  from  the  side  of  a 
field.  Now,  in  constructing,  as  in  demonstrating,  something 
must  be  assumed  at  the  outset ;  and  these  assumptions  are 
to  be  the  fewest  possible.  Accordingly,  Euclid  starts  with 
demanding  three  operations — drawing  a  straight  line  from 
one  point  to  another,  prolonging  a  given  straight  line,  and 
describing  a  circle  ;  in  concrete,  he  requires  the  student  to 
have  a  ruler  and  a  pair  of  compasses.* 

•  'The  Postulates  which  are  prefixed  to  Book  I.  require  us  to  admit  thai 
certain  geometrical  operations  may  be  performed,  without  respect  to  the 


U2 


LOGIC   OF  MATHEMATICS. 


* 


J 


It  IS  averred  that,  in  the  course  of  Euclid's  demonstrations, 
tacit  assumptions  are  occasionally  made,  such  as  should  have 
been  placed  among  his  axioms.  Thus,  in  the  fourth  proposi- 
tion, there  is  an  a>sumption  that  a  tiorure  may  be  lifted  and 
turned  upon  itself  without  change  of  form.  This,  however,  is 
part  and  parcel  of  that  great  step,  the  very  earliest  to  be  made 
m  geonaetrical  proof,  whereby  the  comparison  of  two  plane 
figures  is  achieved.  As  regards  the  first  proposition,  Mr.  Ue 
Morgan  points  out  two  postulates  that  should  have  been 
explicitly  given  with  the  others ;  and,  for  the  twelfth,  two 
more  postulates  are  necessary  (Companion  to  the  British 
Almanack,  for  1849). 

The  leading  h ranches  of  Mathematics :— Arithmetic. 
8.  The  foundations  of  Arithmetic  are  the  two  proper 
Axioms  of  all  Mathematics,  the  Definitions  of  the  funda- 
mental operations— Addition,  &c.,  and  the  Definitions  of 
the  Numbers.  The  Propositions  flow  deductively  from 
these  Axioms  and  Definitions  combined. 

I'he  Axioms  being  premised,  the  Operations  understood 
and  the  Numbers  defined,  the  deduction  or  demonstration  of 
the  Propositions  easily  follows. 

The  Propositions  of  Arithmetic  affirm  or  deny  the  equivaU 

ence  in  amount  of  7iumhers  differently  aggregated.     The  follow- 

ing  are  examples.     Six  and  seven  is  equal  to  nine  and  four, 

to  ten  and  three,  &c. ;  that  is,  a  row  of  six  and  a  row  of  seven 

would  be  the  same  total  aggregate  as  a  row  of  nine  and  a  row 

of  four.     These  are  propositions  of  addition.     As  there  is  one 

standard  mode  of  expressing  aggregates— the  decimal  system, 

the  arithmetical  propositions  usually  take  the  form  of  stating 

other  modes  of  aggregation  as  equivalent,  or  not,  to  a  given 

decimal  aggregation  ;  nine  and  five  is  fourteen  (the  decimal 

aggregate— ten  and  four).     There  are  corresponding  proposi- 

tions  of  subtraction  ;  nine  taken  from  fourteen  leaves  five. 

manner  of  performing  them.  In  fact,  they  appeal  to  our  concepiiona,  and 
for  all  the  purposes  of  reasoning  might  be  expressed  thus  : 

Any  two  points  may  be  conceived  to  be  joined  by  a  straight  line. 

Any  terminated  straight  line  may  be  conceived  to  admit  of  unlimited 
extension. 

A  circle  may  be  supposed  to  have  any  position  for  its  centre,  and  a 
radius  of  any  magnitude. 

The  following  is  another  postulate  of  the  same  kind,  which  we  shall 
have  occasion  to  refer  to  hereafter  : — 

A  straight  line  passing  through  any  point  may  be  conceived  to  be  paral- 
lel to  another  straight  line.*    (Challis  on  Calculation,  pp.  63-4.) 


PEOOF  OF  THE  PROPOSITIONS  OF  NUMBIilR. 


US 


The  proof  of  such  propositions  is  the  application  of  the 
axioms  to  the  definitions  of  the  numbers  as  already  given  : 
the  axioms  are  the  major  premises,  the  definitions  the  minors. 
Thus,  to  prove  that  three  and  four  is  seven,  in  other  words, 
that  a  row  of  three  together  with  a  row  of  four  is  the  same 
as  a  row  of  seven.     We  may  proceed  as  follows  : — 

By  the  definition,  3  is  2  -f  1  (or  again  1  -f-  1  +  !■)• 

Hence,  4  -|-  3  is  the  same  as  4  -|-  1  -h  1  -f-  !• 

Now  4  +  1,  =  5  ;  5  +  1  =  6 ;  and  6  4-  1  =.  7. 

The  warrant  for  these  substitutions  is  the  law  '  the  sums  of 
equals  are  equal,'  applied  thus  : — 

1  -f  1  +  1  =  3. 

Hence  4  -f  1  -f  1  +  1  (7)  =  4  +  3. 

Arithmetical  probation  thus,  at  the  outset,  creeps  along  by 
a  unit  at  a  time ;  when,  in  that  way,  larger  leaps  are  estab- 
lished, the  deductions  are  much  shorter.  For  example,  we 
can  construct  and  commit  to  memorv  a  table  for  the  addition 
of  every  two  numbers  up  to  ten  (2  and  3,  2  and  4,  &c). 

Propositions  of  multiplication — six  times  eight  is  forty- 
eight— are  a  mere  extension  of  the  process  of  addition.  The 
celebrated  multiplication  table  embodies  144  of  these  proposi- 
tions, and,  by  implication  an  equal  number  of  propositions  of 
division. 

Thus,  while  the  affirmation  *  3  and  1  is  4,'  is  a  verbal  pro- 
position (being  declaratory  of  the  meaning  of  4),  *  2  and  2 
is  four  *  is  a  real  proposition  deduced  from  the  induction  *  the 
sums  of  equals  are  equal.'  This  last  is  sometimes  called  a 
necessary  truth,  but  it  is  not  necessary  in  the  sense  of  an 
identical  or  implicated  truth  ;  it  is  true  only  if  the  above 
axiom  be  true.  It  is  sometimes  called  self-evident,  but  that 
merely  means  that  it  is  very  rapidly  appreciated  ;  it  is  essen- 
tially of  the  same  scientific  character  as  16  times  16  is  256, 
which  would  not  be  called  self-evident. 

As  there  is  no  limit  to  Numbers,  so  there  is  no  limit  to  the 
propositions  asserting  (or  denying)  the  equivalence  of  numbers 
difiierently  stated. 

Algebra. 

9.  The  vast  mechanism  of  Algebra  rests  upon  the  funda- 
mental axioms  of  all  Mathematics.  It  is  a  great  extension 
of  the  compass  of  Arithmetic  depending  upon  using  sym- 
hols  of  numbers,  and  signs  of  operation,  for  actual  numbere 
and  actual  operations. 


4M 


LOGIC   OF  MATHEMATICS. 


OPERATIONS  OF  ALGEBRA. 


M5 


No  new  principles  of  reasoning  or  computation  are  intra- 
daced  into  Algebra ;  its  foundations  are  solely  the  axioms 
common  to  all  mathematics.  Its  characteristic  feature  is,  in 
the  place  of  actual  numbers,  to  employ  symbols  representing 
numbers  generally  ;  and,  for  the  actual  operations  of  addition, 
subtraction,  multiplication,  division,  to  use  signs  of  opera- 
tion, -}"»  — »   X,  -H,  &c. 

Numbers  are  no  longer  compared  by  their  actual  amount, 
but  by  their  modes  of  formation.  One  number  is  regarded  as 
made  up  of  others  formed  in  a  particular  way,  shown  by  the 
signs  of  operation.  A  number  a  is  given  as  made  up  of  the 
8ui|^  of  h  and  c,  as  &  -f-  ^  >  °^  ^^  ^^®  product  of  h  and  c,  as  6  c  ; 
or  of  the  square  of  h,  h^.  On  this  scheme  the  one  number  is 
said  to  be  a  function  of  the  others ;  and  the  science  of  Algebra 
is  said  to  be  the  calculus  of  Functions. 

The  simple  functions  of  numbers  are  few,  being  the  ex- 
pression of  the  elementary  relationships — addition,  subtraction, 
multiplication,  division,  powers,  roots,  logarithms,  sines. 

Mr.  Challis  distinguishes  between  Algebra  and  the  Calculus  of 
Functions.  He  restricts  Algebra  to  the  instrumentality  and  mani- 
pulating of  Equations.  Algebra  is  a  more  highly  generalized 
scheme  of  symbolical  expression  than  Arithmetic;  it  represents 
quantities  by  letters,  a,  h,  a,  y,  which  may  have  any  numerical 
value,  the  only  thing  considered  being  their  relationships  to  one 
another,  as  sums,  differences,  products,  roots,  &c.  The  Calculus  of 
Functions  is  a  still  farther  step  in  the  same  direction.  It  uses 
symbols  to  show  that  one  quantity  has  relationships  to  others, 
without  condescending  on  any  one  form  of  the  relationship  ;  /  (x) 
expresses  that  a  certain  quantity  is  made  up  of  some  modifications 
of  £c,  without  saying  what  they  are.  It  operates  generally  upon 
the  form  2/  =  /  (^J).  One  leading  and  important  enquiry  is  to  find 
the  symbolical  expression,  when  the  variable  x  receives  a  certain 
increment  h,  and  becomes  /  (a;  +  h).  This  gives  birth  to  distinct 
theorems,called  Taylor's  Theorem,  Maclaurin's  Theorem, Lagrange's 
and  Laplace's  Theorems,  and  conducts  to  the  Differential  Calculus. 

10.  Algebra  shows  the  equivalence  of  different  opera- 
tions ;  and  thereby  gives  the  means  of  resolving  the  one 
into  the  other. 

This  is  to  extend  the  propositions  of  Arithmetic.  By  study- 
ing the  Algebraic  forms,  we  find  that  the  square  of  a  sum 
(a  -\-  b)  is  equivalent  to  the  squares  of  the  separate  factors 
abided  to  twice  their  product  (a-  -^  h'  -\-  2  a  b)  -^  no  matter 
what  the  numbers  are. 

1 1.  The  use  of  signs  of  operations  readily  leads  to  ex- 


pressions not  interpretable  into  any  actual  facts  ;  and  the 
distinctive  business  of  Algebra  is  to  define  and  justify  all 
its  combinations. 

Subtraction  in  Arithmetic  cannot  be  performed  without 
something  to  subtract  from ;  the  Algebraic  sign  — ,  may  be 
prefixed  to  a  number  irrespective  of  this  fact.  Not  only  so,  but 
the  number  so  qualified  may  be  formally  subjected  to  all  the 
operations  performable  upon  real  numbers.  We  may  suppose 
two  negative  quantities  multiplied  together,  a  process  not  to 
be  realized  in  fact.  There  is  a  still  greater  departure  from 
possibility  in  placing  a  negative  quantity  under  the  sign  for 
extracting  the  square  root,  V  —  1,  v/  —  a. 

It  is  necessary  to  qualify  the  rules  for  the  cardinal  opera- 
tions of  Arithmetic,  in  their  extension  to  Algebraic  quantities, 
by  explaining  the  conditions  of  the  use  of  the  signs  : — to  lay 
down  and  demonstrate  such  rules  as  *  minus  multiplied  by 
plus  gives  minus ;'  *  minus  multiplied  by  minus  gives  plus.' 
Although  the  demonstration  of  such  rules  is  a  matter  for 
logical  discussion,  we  do  not  enter  upon  it  here  Mathe- 
maticians usually  satisfy  themselves  in  all  such  cases  by  an 
appeal  to  the  verification  of  experience  ;  to  which  they  append 
some  form  of  deductive  proof.  But  deductive  proofs  in  such 
matters  would  never  be  trusted  by  themselves,  or  in  the 
absence  of  verifications.  Thus,  *  minus  multiplied  by  minus 
makes  plus,'  is  shown  by  manipulating  the  product  of  two 
differences  as  a  —  6,  by  c  — ^d ;  where  it  is  seen  that  only  by 
this  rule  can  we  obtain  a  correct  result. 

12.  The  highest  form  of  the  Algebraical  problem  is  the 
Eesolution  of  Equations. 

This  contains  all  the  preceding  processes,  and  applies  them 
in  an  advantageous  manner  to  disentangle  complicated  relation- 
ships of  numbers. 

In  an  Equation,  two  expressions  known  to  be  equal  are 
placed  against  one  another  ;  as — 

13iB  +  2a  —  6  =  6aj  —  c. 
By  applying  the  fundamental  axioms  of  equality,  and  a  few  of 
the  convenient  derivatives  from  them  (the  differences  of  equals 
are  equal,  equal  multiples  and  equal  quotients  of  equals  are 
equal,  the  squares,  square  roots,  &c.,  of  equals  are  equal),  the 
equation  may  be  so  manipulated  that  there  may  stand,  at  last, 
on  one  side,  the  quantity  x  (whose  value  is  desired),  and,  on 
the  other,  a  function  made  up  of  a,  6,  c,  to  the  exclusion  of  «  ; 


1 


446 


LOGIC   OF  MATHEMATICS. 


Strict  equality  being  preserved  at  every  step  of  the  transform- 
inff  operation.  No  logical  difficulties  are  involved  in  this 
refined  and  powerful  machinery  ;  while  it  may  be  quoted  as 
happily  exemplifying  the  intervention  of  the  axioms  and 
derivative  propositions  of  equality. 

Geometry. 

13.  Some  of  the  more  difficult  logical  questions  arising 
out  of  Geometry— those  relating  to  the  Definitions,  Axioms, 
and  Postulates— have  been  already  considered ;  it  remains 
to  advert  to  the  order  of  topics. 

Every  science  reposes  alike  on  Definitions  and  on  Axioms ; 
which  accordingly  are  stated  at  the  outset.  Generally  speak- 
ing, the  Definitions  come  first,  the  Axioms  next.  But  the 
Axioms  of  Geometry  may  be  supposed  already  given,  as  the 
indispensible  basis  of  Arithmetic,  and,  therefore,  need  only  to 
be  recited  along  with  any  corollaries  or  derivatives  especially 
required  in  Geometry.  ^    -,     - 

It  would  be  advisable  to  state  first  of  all  the  concrete  basis 
of  Geometry— to  give  the  notions  attainable  only  from  concrete 
experience.  These  have  been  already  enumerated.  To  niake 
a  broad  separation  between  these  ultimate  indefinable  notions, 
and  the  properly  definable,  the  expositor  might  interpose  the 
review  of  the  Ax'ioms,  especially  dwelling  upon  their  inductive 
character,  and  drawing  the  line  between  the  fundamental  and 
the  derivative.  At  this  stage  the  teacher  should  allow  himself 
the  fullest  latitude  of  concrete  illustration. 

Next  would  follow  the  remaining  Definitions  in  order  of 
derivation  or  dependence.  Frequently,  corollaries  are  given 
also  ;  but  these  are  not  proper,  or  mediate,  inferences ;  they 
are  mere  equivalents  of  the  definition,  not  to  be  denied  with- 
out self-contradiction.  Such  are,  *  only  one  straight  line  can 
be  drawn  between  two  points  ;  *  '  all  right  angles  are  equal. 
No  mediate  inference  can  be  drawn  from  a  Definition  without 
the  introduction  of  an  axiom;  a  truly  deductive  process, 
amounting  to  a  theorem. 

Euclid's  three  first  propositions  are  problems  or  construc- 
tions. The  first  theorem  is  the  real  start  of  the  Geometrical 
concatenation  ;  namely,  the  fourth  proposition— establishing 
the  equality  throughout  of  the  two  triangles  having  two  sides 
and  the  included  angle  equal.  This  is  the  sole  basis  of  geo- 
metrical comparison,  the  commencing  stride  that  renders  pos- 
sible  all   the   subsequent   assertions  as  to  the   equality  and 


EUCLID'S   FOURTH   PROPOSITION. 


447 


inequality  of  triangles,  parallelograms,  &c.  The  proof  of  the 
proposition  is  peculiar;  only  once  again  (I.  8)  is  the  same  opera- 
tion made  use  of;  namely,  the  ideal  placing  of  the  one  triangle 
npon  the  other.  Here,  in  fact,  we  have  an  inevitable  appeal 
to  experiment  or  trial  in  the  concrete  ;  just  as  in  the  defini- 
tions and  the  axioms,  we  must  take  our  first  lessons  from  the 
manipulation  of  actual  objects.  Euclid,  by  his  mode  of  stat- 
ing the  demonstration,  professedly  goes  through  a  process  of 
pure  deduction,  all  the  time  that  he  requires  us  to  conceive  an 
experimental  proof.  He  appears  to  be  using  merely  an  illus- 
tration in  the  concrete  ;  but  if  bis  readers  had  not  made  actual 
experiments  of  the  kind  indicated,  (doubtless  the  same  ex- 
periments as  gave  the  original  notions  of  line,  angle  and  sur- 
face) they  could  not  be  convinced  by  the  reasoning  in  the  de- 
monstration. 

If  apparently  a  proposition  be  proved  without  appealing 
to  an  axiom   (either  directly  or  indirectly),  shows  that  the 
proposition  cannot  be  real ;  the  subject  and  predicate  must 
be  identical.     The  proof  rests  solely  on  definitions  ;    but  a 
definition   by  itself  cannot  advance   us  a  step.     The  propo- 
sition must,  in  fact,  be  a  mere  equivalent  of  the  notions  of 
line,  angle,  surface,  equality — a  fact  apparent  in  the  operation 
of  understanding  these  notions.     It  is  implicated  in  the  experi- 
ence  requisite  for  mastering  the  indefinable  elements  of  Geo- 
metry ;  and  should  be  rested  purely  on  the  basis  of  experience.* 
The  6th  proposition  is  what  really  constitutes  Euclid's  first 
demonstration  by  a  genuine  process  of  reasoning.     In  it,  there 
is  a  legitimate  deduction  from   tho  axioms   common  to  all 
mathematics,  conjoined  with  the  induction^  falsely  called   a 
demonstration,  given  as  the  4th  proposition.      The   axioms 
applied  are,  the  proper  axiom,  *the  sums  of  equals  are  equal,' 
and  the  derivative,  *  the  differences  of  equals  are  equal.' 

14.  It  is  the  characteristic  of  elementary  Geometry  to 
maintain  the  concrete  reference  to  diagrams,  which  gives 
the  subject  to  appearance,  but  only  to  appearance,  an 
inductive  or  experimental  character. 

♦  Mr.  Challis  remarks,  on  tho  Fourth  Proposition,  that  the  proof  rests 
on  no  previous  proposition,  and  appeals  only  to  the  simplest  conceptions 
of  space.  *  This  proposition  is  proved  by  the  principle  of  superposition^ 
neither  requirinji^,  nor  admitting  of,  any  other  direct  proof.'  A  casual 
observation  of  Mr.  De  Morgan's  is  well  exemplified  by  Euclid's  attempt 
to  demonstrate  this  fundamental  assumption — '  the  Conversion  of  identity 
by  help  of  a  syllogism  is  reasoning  in  a  circle.* 

20 


448 


LOGIC  OF  MATHEMATICS. 


INCOMMENSURABLES. 


449 


AH  symboKcal  reasonings  are  liable  to  mistake.  Not  to 
Bpeak  of  the  slips  that  the  reasoner  himself  may  commit 
tmknowincrly,  there  is  often  a  failure  of  adaptation  between 
the  laws  of  the  symbols  and  the  laws  of  the  matter  they  are 
applied  to.  For  this  the  remedy  is  the  constant  verilica- 
tion  of  the  results.  Now,  in  Geometry,  an  actual  figure  is 
always  before  the  eyes,  and  the  effect  of  every  construction 
and  every  step  of  reasoning  is  judged  of  by  axjtual  inspection. 
When  the  direction  is  given  to  join  the  opposite  angles  ot  a 
quadrilateral,  there  is  apparent  to  the  glance  the  division  ot 
the  figure  into  two  triangles.  For  the  most  paH,  Euclid  offers 
no  other  proof  of  this  class  of  consequences.  Sometimes  he 
applies  the  reductio  ad  absurdum  in  such  cases,  as  in  the  proof 
that  the  tangent  to  a  circle  falls  without  the  circle. 

So  long  as  Geometry  is  discussed  in  the  concrete,  or  by 
naming  lines,  angles,  circles,  the  mind  must  conceive  them  in 
the  concrete,  which  would  be  impracticable  without  the  help 
of  diagrams.  In  Algebraic  Geometry,  the  concrete  form  is 
exchanged  for  numerical  equivalents,  to  be  manipulated  accord- 
ing to  the  laws  of  operation  in  Arithmetic  or  Algebra ;  a 
rectangle  is  no  longer  a  fact  of  space  but  a  product  of  numbers 
or  symbols  ;  a  curve  is  an  equation.  The  student  is  cautioned 
by  Mr.  De  Morgan  that,  although  the  names  *  square  ^  and 
♦  cube '  are  transferred  to  Algebraic  quantities,  as  a ,  a ,  the 
naraea  wm  different  things  from  geometrical  squares  and 

cubes. 

Algebraic  Geometry, 

15  The  expression  of  Geometrical  quantities  by  Algebra, 
while  depriving  the  mind  of  the  assistance  of  the  diagrams, 
greatly  enlarges  the  power  of  demonstration  and  mference. 

Compare  Euclid's  2nd  book  with  the  same  propositions 
algebraically  rendered ;  the  one  is  laborious,  the  other  com- 

paratively  easy.  .  , 

The  great  device  of  Descartes,  for  expressing  curves  alge- 
braically by  co-ordinates  whose  relation  in  each  case  could  be 
stated  in  a  formula,  opened  up  a  new  field  of  mathematics. 
The  conic  sections  became  comparatively  easy  ;  and  curves  ot 
a  still  higher  order  that  would  have  bafiQed  common  geometry 
were  brought  under  investigation.  The  method  was  also  an 
essential  prelude  to  the  Difierential  calculus. 

16.  Algebraic  Geometry  furnishes  specific  rules  for  the 
embodiment  ^nd  for  the  interpretation  of  formulaB.  The 
rest  is  pure  algebra. 


It  is  easy  to  embody  a  rectangle,  in  terms  of  the  sides ;  an 
algebraic  product  is  sufficient  for  the  purpose.  Angles  may 
be  expressed  by  their  proportion  to  the  circle,  that  is  by  their 
subtended  arc,  and  also  by  their  sines,  tangents,  &c.  Curves 
are  given  by  co-ordinates  on  the  Cartesian  plan.  The  rules  of 
embodiment  are  also  the  rules  of  interpretation.  But  as  there 
is  frequent  danger  of  overstepping  geometrical  conditions  by 
algebraical  operations,  the  interpretation  must  be  continually 
verified.  Mathematics  is  the  slipperiest  of  sciences  ;  its  ana- 
lytical processes  are  full  of  pitfalls;  but  luckily,  it  is  the  easiest 
to  keep  right  by  verification.  The  arithmetical  symbols  0  and 
1  are  used  with  a  latitude  that  makes  them  ambiguous,  unless, 
for  each  case,  there  is  a  distinct  understanding  made  and  ad- 
hered to. 

The  Higher  Calculus, 

1 7.  The  representation  of  continuous  quantity,  by  means 
of  numbers,  in  certain  cases,  fails  to  give  a  neat  or  definite 
result. 

Continuous  quantity,  as  exemplified  in  lines  and  in  motions, 
must  be  supposed  to  be  broken  up  into  equal  portions  in  order 
to  be  expressed  numerically,  and  thereby  to  be  made  the 
subject  of  arithmetical  computation.  In  certain  instances,  the 
division  cannot  be  made  without  a  remainder.  Hence  arises 
a  peculiar  difficulty. 

In  vulgar  fractions,  first  emerges  the  peculiar  case  of  incom- 
mensurable quantities,  that  is,  quantities  that  have  no  common 
measure.  In  Geometry,  the  side  and  diagonal  of  a  square  are 
incommensurable ;  if  the  side  be  divided  into  equal  divisions, 
no  matter  how  many,  these  divisions  will  not  apply  to  the 
diagonal  without  a  remainder.  So  with  the  diameter  and  the 
circumference  of  a  circle. 

18.  The  solution  of  Incommensurables,  and  the  acom- 
modation  of  numbers  to  continuous  quantities  generally, 
can  only  be  approximate.  A  variety  of  modes  have  been 
devised,  at  bottom  the  same,  for  working  out  the  approxi- 
mation. 

Mathematicians  long  struggled  to  evade  the  difficulty  before 
acknowledging  the  true  character  of  the  solution.  A  great 
number  of  persons  refused  to  believe  that  the  diameter  and 
circumference  of  a  circle  would  for  ever  remain  incommensur- 
able. 


450 


LOGIC  OF  MATHEMATICS. 


TWO   DEPARTMEJn'S    OF  PHYSICS. 


451 


W 


Euclid's  definition  of  proportionals  is  deservedly  admired 
for  its  ingenuity  in  endeavouring  to  comprise  incommensurable 
quantities  ;  but  it  is  not  satisfactory.  A  competent  judge 
(De  Morgan)  remarks,  first,  the  want  of  obvious  connexioa 
between  it  and  the  ordinary  well-established  ideas  of  propor- 
tion ;  secondly,  its  involving  an  idea  of  infinity ;  and  lastly, 
the  apparent  unlikelihood  that  any  quantities  exist  capable  of 
satisfying  the  definition.  The  difficulties  can  be  met  only  by 
the  method  of  approximation,  on  which  is  based  the  whole 
structure  of  the  higher  or  transcendental  analysis. 

The  first  application  of  the  approximate  methods  was  to  the 
quadrature  of  the  circle,  as  given  in  Euclid.  The  process 
there  given  is  commonly  called  the  method  of  Exhaustions. 
The  gist  of  the  matter  lies  in  the  proposition—*  A  circle  bemg 
given,  two  similar  polygons  may  be  found,  the  one  described 
about  the  circle  the  other  inscribed  within  it,  such  as  shall 
differ  by  a  space  less  than  any  given  space."  These  last  words 
give  the  idea  running  through  all  the  processes,  named  the 
Theory  of  Limits,  Prime  and  Ultimate  Ratios,  Infinitesimal 
Quantities.  A  curve  line  can  never  be  a  straight  line,  but  by 
diminishing  the  arc,  the  approximation  of  the  two  increases, 
until  at  last  we  pass  not  only  beyond  any  sensible  error,  but 
beyond  any  error  that  may  be  assigned.  Thus  an  arc  may  be 
said  to  be  the  limit  of  its  chord  ;  the  area  of  a  circle  may  be 
said  to  be  identical  with  an  inscribed,  or  a  described,  polygon 
of  an  infinite  number  of  sides.  Now  as  the  polygon  consists 
of  a  series  of  triangles  with  a  common  apex  in  the  centre,  t ho 
area  of  the  polygon  is  equal  to  half  the  product  of  the  radius 
and  the  sum  of  the  bases,  or  chords  :  and  by  diminishing  these 
chords  without  limit,  they  become  identical  with  the  circum- 
ference of  the  circle. 

The  method  of  Exhaustions  was  applied  by  Archimedes  to 
the  quadrature  of  the  parabola,  and  to  the  solid  measurement 
of  the  cone,  sphere,  and  cylinder  ;  all  which  give  neat  solutions, 
or  expressions  in  finite  terms.  The  subsequent  deve  opments 
were  left  for  modern  times,  after  the  discovery  of  algebra  ;  and 
they  advanced  as  algebra  and  its  applications  to  geometry 
advanced.  The  Fluxions  of  Newton  and  the  Diff'ereutial  Cal- 
culus of  Leibnitz  were  the  great  algebraic  embodiments. 
These  methods  contained  a  new  order  of  quantities,  called 
Fluxions  (by  Newton)  and  Differential  Co-efficients  (by  Leib- 
nitz), formed  from  ordinary  quantities  on  considerations  grow- 
ing out  of  the  method  of  Limits,  and  resolved  back  again  on 
the  same  laws.     The  quantities  once  created,  the  operations 


were  treated  as  pure  algebra,  and  mathematicians  left  them  to 
be  justified  by  their  results,  rarely  attempting  to  render  a  rea- 
son for  the  assumptions  lurking  under  them.  Hence,  such 
attacks  upon  the  system  as  Berkeley's  famous  sarcasm,  that 
the  fiuxioiial  calculus  operated  upon  the  ghosts  of  departed 
quantities.  The  neglect  to  assigu  the  true  basis  of  the  cal- 
culus, and  the  treatiug  it  from  first  to  last  as  a  pure  algebraic 
assumption,  culminated  in  Lagrange ;  against  whom  Whewell 
and  De  Morgan  have  reclaimed,  and  have  provided  the  neces- 
sary reconciliation  of  the  algebra  with  the  conditions  of  the 
various  problems  to  be  solved  ;  showing  that  approximation 
and  compromise  must  be  held  as  essential  to  the  operation. 


CHAPTER  IL 

LOGIC   OF    PHYSIOS. 

1.  It  has  been  seen  (rntrodnction)  that  the  branch  of 
science  termed  Natural  Philosophy  or  Physics  is  divided 
into  two  parts— i/o^ar  Physics  and  Molecular  Physics. 

The  aggregate  called  Natural  Philosophy  scarcely  admits  of 
definition,  until  separated  into  distinct  departments — Molar 
Physics,  or  Motion  in  Mass,  and  Molecular  Physics,  or  Motion 
in  Molecule. 

The  Physics  of  Masses,  Molar  Physics,  includes  the  pheno- 
mena of  Motion  and  Force,  as  belonging  to  bodies  in  the 
aggregate.  Such  are  the  phenomena  of  planetary  motions,  of 
falling  bodies,  rivers,  winds,  &c. 

The  Physics  of  Molecules,  Molecular  Physics,  relates  to  the 
motions  and  forces  operating  between  particles  or  molecules, 
these  being  of  a  degree  of  minuteness  far  beyond  the  reach  of 
the  human  senses.  The  phenomena  representing  such  notions 
and  forces,  are  the  Aggregations  into  masses  ;  Cohesions  and 
Adhesions  generally;  Heat;  Electricity;  Light.  Reserva- 
tion is  made  of  the  peculiar  form  of  molecular  force,  called 
Chemical  force,  as  having  a  character  and  consequences 
peculiar  to  itselH 


452 


LOGIC   OF  PHYSICS. 


MOLAR   PinSICS. 

Divisions  of  the  Subject. 

2.  The  Abstract  Branches,  comprising  Motion  and 
Force  in  general,  and  susceptible  of  Deductive  and  Mathe- 
matical treatment  are  these  : — 

Mathematics  of  Motion     — Kinematics. 
Forces  (1)  in  Equilibrio     — Statics. 
Forces  (2)  causing  Motion — Dynamics. 

The  Concrete  Brancbes  are — 

Mechanic  Powers  and  Solid  Machinery, 
Hydrostatics  and  IlydrO'dynamics. 
Aerostatics  and  Fneumatics, 
Acoustics. 
Astronomy, 

Notions  of  Molar  Fkysics. 

3.  In  Physics,  are  pre-supposed  the  Notions  (as  well  as 
the  Propositions)  of  Mathematias.  Only  those  special  to 
the  science  are  here  reviewed. 

Motion — Rest. — This  antithetic  couple  is  the  fundamental 
conception  of  Physics,  and  is  probably  an  ultimate  experience  of 
the  human  mind.  We  obtain  the  idea  of  Movement  by  a 
peculiar  employment  of  our  active  energies,  assisted  by  sen- 
sation. We  also  obtain  a  knowledge  of  the  varieties  of  move- 
ment— quick,  slow,  uniform,  varying,  straight,  curved,  con- 
tinuous, reciprocating,  pendulous,  wave-like,  &c.  The 
xnodes  that  depend  upon  degree,  or  Velocity,  are  part  of  the 
ultimate  experience  of  motion  as  such  ;  those  characterized  by 
shape  or  Fomi  have  a  property  common  to  mere  extension. 

Force. — This  is  without  doubt  the  most  fundamental  notion 
of  the  human  mind  ;  in  the  order  of  evolution,  it  concurs  with, 
if  it  is  not  prior  to,  both  motion  and  extension.  It  cannot  be 
defined  except  in  the  mode  pecuHar  to  ultimate  notions.  The 
feeling  that  we  have  when  we  expend  muscular  energy,  in 
resisting  or  in  causing  movement,  is  unique  and  irresolvable. 

Inertia,  Resistance^  Momentum. — These  names  designate  our 
experience  of  force  from  the  objective  side,  or  as  embodied  in 
the  things  of  the  object  world.  The  occasion  of  calUng  forth 
our  feeUng  of  energy  when  referred  to  an  external  fact  is  Re- 
sistance, Inertness,  Momentum,  or  External  Force — all  signi* 


NOTIONS  OF  MOLAR  PHYSICS. 


453 


fying  the  same  thing.  This  great  fact  must  be  learnt,  in  the 
first  instance,  by  each  one's  separate  experience  ;  the  best  mode 
of  scientifically  expressing  it  is  a  matter  for  discussion. 

Matter  is  Extension,  coupled  with  Force  or  Inertia.  Any- 
thing extended  and  at  the  same  time  possessing  force,  either 
to  resist  or  to  impart  motion  is  Material. 

Mass,  Density,  Solidity,  are  derived  notions ;  they  are  ob- 
tained by  putting  together  Force  and  Extension  or  Volume. 
The  Mass  is  the  collective  Force  of  a  body,  shown  by  its  degree 
of  Resistance,  and  also  by  the  amount  of  Resistance  it  can 
overcome  when  moving  at  a  given  rate.  The  Density  is  the 
degree  of  space  concentration  ;  a  given  power  of  resistance, 
with  a  smaller  bulk  or  volume,  is  a  greater  Density.  Solidity, 
when  not  signifying  the  solid  state  of  matter  generally,  as 
opposed  to  liquid  or  gas,  is  another  name  for  Density. 

Impact  is  a  phenomenon  expressed  by  means  of  Space  or 
Extension,  Motion,  and  Force.  It  is  one  mode  of  imparting 
visible  or  kinetic  energy,  and  is  a  test  or  measure  of  Force. 

Attraction  is  definable  by  Extension,  Motion,  and  Force. 
It  is  a  mode  of  communicating  Force,  distinct  from  Impact, 
and  in  some  respects  simpler.  Among  its  specific  examples 
are  Gravity,  Cohesion,  Adhesion.  Magnetism,  Electrical  Attrac- 
tion, (Chemical  Attraction). 

Repulsion  is  definable  by  reference  to  the  same  fundamental 
notions.  It  also  is  a  mode  of  imparting  or  redistributing 
force,  and  differs  from  Attraction  only  in  the  way  that  it 
changes  the  relative  situation  of  the  masses  concerned.  It  is 
exemplified  in  the  Expansive  energy  of  Grases  in  their  ordinary 
state,  in  the  Expansion  of  Liquids  and  Solids  from  rise  of 
temperature  and  after  compression  (called  Elasticity).  The 
Polar  Forces — Magnetism,  Electricity,  &c., exercise,  along  with 
Attraction,  a  counterpart  Repulsion. 

By  still  farther  combining  these  primary  notions,  we  obtain 
— Equilibrium,  Composition  and  Resolution,  Resultant,  Virtual 
Velocity,  Centripetal,  Centrifugal,  Tangential  force,  Projectile. 

To  Mechanics  belong  Specific  Gravity,  Centre  of  Gravity, 
Stability,  Oscillation,  Rotation,  Percussion,  Friction,  Mechanic 
Power,  Machine,  Work. 

In  Hydrostatics,  occur  Liquid,  Liquid  Pressure,  Liquid 
Level,  Displacement,  Flotation,  Column  of  liquid. 

In  Hydro-dynamics,  Liquid  Motions,  Efflux,  Discharge, 
Liquid  Waves. 

In  Aerostatics  and  Fneumatics,  Air,  Atmosphere,  Expansion 
of  Gases,  Flow  of  Gases,  Undulations,  Atmospheric  pres- 
sure. 


464 


LOGIC  OP  PHYSICS. 


In  Acoustics^  Sound,  Pitch,  Timber,  Vibrations,  Noise; 
Note,  Echo,  Harmony. 

In  Astronomy,  San,  Planet,  Satellite,  Comet,  Aerolite, 
Bolid,  Star,  Nebula,  Orbit,  Ecliptic,  Year,  Month,  Day,  Eclipse, 
Transit,  Parallax,  Aberration,  flight  Ascension,  Declination, 
Eccentricity,  Node,  Apside,  Perihelion,  Perturbation,  Libration, 
Precession,  Nutation,  Tides. 

Propositions  of  Molar  Physics, 

4.  These  are  of  the  follovviug  classes  :— (1)  The  Induc- 
tions of  Force  and  Motion ;  (2)  The  Deductive  Propria 
asserting  the  quantitative  relationships  of  Motion  and 
Force ;  (3)  Empirical  laws  of  the  concrete  phenomena. 

(1)  The  great  Inductions,  commonly  called  the  Laws  of 
Motion,  are  the  axioms  of  the  science.  These  will  be  con- 
sidered afterwards.  They  are  all  quantitative  in  their  expres- 
sion.    Another  fundamental  Induction  is  the  Law  of  Gravity. 

(2)  The  science  being  pre-eminently  Deductive,  its  proposi- 
tions are  for  the  most  part  deductions  from  the  axioms.  Such 
are — the  propositions  of  the  Composition  and  Resolution  of 
Motions  and  Forces  ;  the  proposition  called  the  *law  of  Areas;* 
the  principle  of  the  Mechanic  Powers ;  the  principles  of  the 
pendulum  ;  the  law  of  liquid  pressure  ;  the  principle  that  con- 
nects fluid  motion  with  fluid  support ;  the  laws  of  the  propa- 
gation and  the  reflection  of  sound. 

All  these  matters  are  stated  in  the  form  of  real  propositions, 
which,  however,  may  be  deduced  from  the  axioms  or  induc- 
tions of  the  science  applied  to  the  particular  cases  as  scientifi- 
cally defined.  For  example,  the  law  of  fluid  pressure  is  a 
proposition  to  this  eflect.  '  At  any  point  in  a  fluid  at  rest,  the 
pressure  is  equal  in  all  directions ;'  the  subject  of  the  proposi- 
tion supposes  a  fluid  at  rest,  a  point  taken  in  it,  and  considera- 
tion given  to  the  pressure  ;  the  predicate  is  *  equality  in  all 
directions.*  The  proof  is  deductive,  and  ultimately  rests  on 
the  axioms  of  motion  and  force,  together  with  the  definition  of 
fluidity,  although  the  proximate  majors  are  the  propositions  of 
the  Composition  of  Forces. 

^  Subsidiary  to  the  working  out  of  the  science  are  the  propo- 
sitions expressing  the  quantities  of  motion,  force,  &c.,  existing 
in  actual  things.  Thus,  besides  the  Law  of  Gravity,  we  have 
a  statement  of  the  numerical  amount  of  gravity  at  the  earth's 
surface  ;  also  the  relative  gravities  of  different  solids  and 
fluids.      These  numerical  propositions   are  called  the   data^ 


DEFINITION   OF   MOTION. 


455 


conslantsy  or  co-efflci&nts  of  the  science,  and  are  ascertained  by 
observation  and  experiment. 

(3)  There  are  certain  empirical  laws  obtained  by  observa- 
tion or  experiment.  Such  are  the  laws  of  the  Strength  of 
Materials  (to  some  extent  Deductive),  the  laws  of  Friction, 
the  Motion  of  Projectiles  (partly  Deductive),  the  Flow  of 
Rivers,  the  Spouting  of  Liquids,  the  Compression  of  Liquids 
and  of  Gases,  the  Difl'usion  of  Sound,  the  action  of  Vibrating 
Strings,  &c.  These  are  all  real  propositions  ;  they  are  in  their 
nature  propria,  or  deducible  from  ultimate  principles  ;  but,  in 
the  present  state  of  knowledge,  they  must  be  gained  by  direct 
experiment. 

Definiiio'iis  of  Molar  Physics, 

5.  As  in  Mathematics,  so  in  Physics,  there  are  certain 
properties  that  are  ultimate,  and  incommunicable  by  lan- 
guage ;  being  known  by  each  one's  independent  experi- 
ence. Nevertheless,  it  is  open  to  us  to  consider  the  best 
mode  of  generalizing  and  stating  this  experience. 

The  facts  named  Motion,  Force,  Matter,  are  understood  only 
by  our  concrete  experience  of  the  things  denoted  by  the  names. 
But  our  crude  observations  may  be  rectified  by  more  careful 
comparisons,  and  may  be  reduced  under  precise  general  state- 
ments. Moreover,  as  in  Mathematics,  we  may  select  the 
aspect  most  suitable  as  a  point  of  departure  for  our  deductive 
reasonings. 

Definition  of  Motion. — Of  the  fact  of  motion  no  knowledge 
can  be  imparted ;  there  is  nothing  simpler  to  express  it  by  : 
*  change  of  place  '  is  not  more  intelligible  than  *  motion.*  We 
must  assume  that  each  one  understands  motion  both  generically, 
and  in  its  degrees  (capable  of  numerical  statement) ;  and  also 
in  such  simpler  modes  as  straight  or  divergent.  The  more 
complex  movements  are  then  definable.  Velocity  means  degree 
of  motion.  The  only  thing  needing  to  be  expressed  formally 
is  the  measure  of  Motion  or  Velocity  with  reference  to  Space 
and  to  Time ;  these  last-named  elements  being  presupposed  as 
themselves  intelligible. 

^  Matter,  Force,  Inertia.  These  are  three  names  for  substan- 
tially the  same  fact.  At  the  bottom,  there  is  but  one  experi- 
ence, although  varied  in  the  circumstances,  namely,  the 
experience  of  putting  forth  muscular  energy  in  causing  or  in 
resisting  movement.  To  this  experience  we  give  the  names 
Force  and  Matter,  which  are  not  two  things  but  one  thing ; 


456 


LOGIC  OF  PHYSICS. 


i 


of  which  Inertia  is  merely  another  expression.     It  is  pnro 
tautology  to  define  one  of  these  terms  by  the  others  ;  matter  is 
nothing  except  as  giving  the  experience  called  also  force ;  force 
is  only  revealed  by  matter  moving,  or  obstructing  movement. 
Matter,  however,  affects  us  in  other  ways  than  by  the  mus- 
cular feeling  of  resistance  or  of  expended  energy.    It  is  always 
extended,  and  in  most  cases  visible,  and  also  tangible.     Are 
we  not,  then,  to  include  these  facts  in  the  definition  ?     No, 
and  for  these  reasons: — (1)    Extension   is  not   confined  to 
matter ;  it  belongs  also  to  empty  space ;  therefore,  though  a 
predicate  of  all  matter,  extension  is  not  the  exclusive  charac- 
teristic of  matter.     (2)   Visibility  and  TangibUity  belong  to 
many  kinds  of  matter,  but  not  to  all  matter ;  hence,  these 
properties  cannot  be   the    defining   characters   of  matter  in 
general,  or  of  all  matter ;  they  are  to  be  reserved  as  properties 
of  the  kinds  of  matter  wherein  they  occur  ;  solids  and  liquids, 
for  example.      Accordingly,  the   only   fact   occurring  in   all 
matter  is  the  fact  expressed  by  resistance,  force,  or  inertia; 
all  which  are  names  for  a  single  phenomenon.     This  phenome- 
non, when  fully  examined,  and  generalized  to  the  utmost,  has 
two  different  aspects,  which  we  may  separate  in  expression,  bat 
cannot  separate  in  nature  ;  the  one  is  the  resistance  to  move- 
ment by  bodies,  whether  at  rest  or  in  motion,  and  the  other, 
the  imparting  of  movement  or  momentum  by  being  in  motion. 
The  first  aspect  of  resistance  is  the  more  popular  meaning  of 
inertia ;  the  second  aspect,  the  imparting  of  movement,  is  the 
popular  view  of  force  ;  but  in  the  scientific  consideration  of 
the  subject,  these  are  but  one  property. 

The  definition  of  Matter  and  of  Inertia,  or  Inert  substance, 
is,  therefore,  but  one.  It  generalizes  our  familiar  experiences 
of  resisting  motion  and  of  communicating  motion,  which 
always  concur  in  the  same  thing.  Fully  expressed,  it  amounts 
to  the  statement  given  in  the  First  Law  of  Motion.  We  are 
entitled  to  lay  down  as  the  fundamental  or  defining  attribute 
of  matter,  in  whose  absence  matter  is  not,  that  if  once  at  rest 
it  remains  at  rest,  and  if  once  in  motion,  it  continues  moving 
in  a  straight  line.  To  put  it  from  rest  to  motion,  moving 
power  must  be  employed ;  to  arrest  its  course,  matter,  either 
in  motion  or  at  rest,  must  be  opposed  to  it.  All  this  is 
involved  in  the  very  meaning  of  matter.  We  cannot  divide 
these  expressions,  and  assign  one  as  the  defining  mark  of 
matter,  and  the  other  as  a  predicate  distinct  from  the  defini- 
tion. No  one  has  ever  succeeded  in  constituting  a  real 
proposition  out  of  these  properties.     The  appearance  of  a  real 


DEFINITION  OF  MATTER. 


457 


proposition  could  be  given  only  by  assuming  as  the  meaning  of 
matter  the  imperfect  view  entertained  by  the  unenlightened 
mind  (which,  owing  to  adverse  appearances  and  imperfect 
knowledge,  does  not  fully  recognize  the  persistence  of  moving 
matter),  and  giving  as  the  predicate  the  scientifically  recti- 
fied generalization  of  matter ;  but  when  this  generalization  is 
attained,  it  is  wholly  embodied  in  the  definition  of  matter ;  it 
cannot  furnish  one  fact  as  a  defining  property  and  reserve 
another  as  a  predicate.  There  is  a  definition  of  Inertia ;  there 
is  no  law. 

Thus,  then,  the  persistence  in  a  state  of  rest  or  in  a  state  of 
uniform  rectilineal  motion,  is  the  meaning  of  Inertia,  and  of 
Matter  in  general ;  in  which  meaning  there  is  an  unavoidable 
implication  of  active  resistance,  and  active  communication  of 
motion.  The  difficulty  is  to  find  an  expression  to  comprehend 
all  these  aspects  of  one  indivisible  property.  Matter  at  rest 
operates  at  one  time  in  dead  resistance,  at  another  time  in 
using  up  force  by  itself  passing  into  motion  ;  matter  in  motion 
may  resist  movement,  or  it  may  generate  movement ;  but, 
these  are  not  a  plurality  of  properties  ;  we  cannot  suppose  one 
of  them  separated  from  the  others.  The  definition  employs 
plurality  of  phrases  in  order  to  encompass  a  unity. 

Matter  and  Inertia  being  thus  defined  by  one  stroke,  Force 
is  merely  another  reference  to  the  same  fact.  Inert  Matter  in 
motion  is  the  most  characteristic  expression  or  aspect  of  Force, 
and  is  adopted  as  its  numerical  measure ;  but  we  cannot  ex- 
clude from  the  idea  the  consideration  of  matter  at  rest.  In 
measuring  force  by  moving  matter,  we  mean  matter  transferred 
from  rest  to  motion,  or  from  one  rate  of  motion  to  a  quicker ; 
this  is  force  as  generated.  Again,  the  force  is  manifested  in 
the  abatement  of  the  motion,  in  reducing  bodies  to  the  state 
of  rest ;  this  is  force  as  expended. 

As  there  is  but  one  fact  underlying  Matter,  Inertia,  Force, 
so  there  is  but  one  measure.  A  larger  quantity  of  matter,  op 
inertia,  is  the  same  as  a  larger  expenditure  of  force  to  change 
the  matter  from  rest  to  a  given  pace  of  motion.  The  ultimate 
measure  is  the  human  consciousness  of  expended  energy. 
There  is  a  palpable  impropriety  in  the  expression,  given  as  a 
law, — *  The  amount  of  inertia  increases  with  the  quantity  of 
matter  ; '  the  two  properties  stated  are  but  one  fact. 

To  sum  up.  Each  person  by  their  own  experience  must 
become  acquainted  with  the  concrete  examples  of  matter  and 
force.  A  comparison  of  all  varieties  of  the  phenomenon  re- 
veals the  presence  of  a  common  feature,  at  bottom  one  and 


458 


LOGIC  OF  PHYSICS. 


indivisible,  but  variously  manifested  as  resistance,  as  a  source 
of  movement — as  persistence  in  rest  or  in  uniform  rectilineal 
movement.  To  this  many-sided  unity,  we  give  the  names 
Matter,  Inertia,  Force,  which  have  a  common  definition  and  a 
common  estimate.  The  word  Matter  is  the  concrete  name, 
while  Inertia  and  Force  are  the  asbtractions  for  what  is  com- 
mon to  all  matter. 

Mass,  Density. — Mass  is  the  quantity  of  matter,  measured  in 
the  mode  already  described,  namely,  by  the  expenditure  re- 
quisite to  change  the  body's  state  by  a  given  amount.  When 
the  Mass  is  given,  and  also  the  volume,  or  bulk,  we  obtain  the 
Density,  Volume  and  Mass  rightly  precede  Density,  in  order 
of  definition.  Messrs  Thomson  and  Tait  make  Density  pre- 
cede Mass. 

Momentum  means  quantity  of  motion ;  its  measure  is  the 
mass  multiplied  by  the  velocity.  The  unit  quantity  of 
motion  is  some  unit  of  mass,  multiplied  by  a  unit  of  velo- 
city. Mass  is  usually  estimated  by  weight,  but  this  is  to 
anticipate  the  consideration  of  gravity,  which  should  be  ex- 
cluded from  the  elementary  definitions  of  motion,  matter,  and 
force. 

The  defining  of  the  notions  following  on  these — Impact, 
Attraction,  Repulsion,  Gravity,  Cohesion,  kc. — pri'sents  no 
logical  difficulties.  They  are  all  derivative  notions,  their 
elements  being  the  above  named  primary  notions  coupled  with 
those  of  mathematics  ;  and  they  are  defined  as  such,  although 
concrete  examples  may  be  given  to  aid  the  understanding  of 
the  more  difficult  abstractions. 

Thus,  Impact  is  the  transfer  of  force  from  one  body  to 
another  by  momentary  concourse ;  the  direction  communicated 
being  the  direction  possessed.  Attraction  is  the  continued  gene- 
ration of  moving  force  shown  in  the  mutual  approach  ot  two 
bodies  ;  liepulsion  is  the  generation  of  force  leading  to  the 
mutual  recess  of  bodies.  Gravity  is  the  attraction  inherent, 
persistent,  and  unchangeable  in  all  matter,  being  proportioned 
to  the  mass,  and  extending  to  all  distances,  at  a  uniform  rate  of 
decrease. 

Axioms  of  Molar  Physics. 

6.  The  chief  axioms  of  the  science  are  usually  stated 
under  the  title — Laws  of  Motion. 

^  In  the  statement  of  these  laws  verbal  and  real  proposi- 
tions are  confounded. 


kewton's  laws  of  motion. 


459 


Kewton's  First  Law — *  Every  body  perseveres  in  its  state 
©f  rest  or  of  uniform  rectilineal  motion,  unless  compelled  to 
change  that  state  by  impressed  forces ' — is  merely  the  full 
expansion  of  the  definition  of  matter,  inertia,  or  body.  It  no 
doubt  expresses  more  than  the  vague  unscientific  notion  of 
matter,  but  no  more  than  is  absolutely  inseparable  from 
matter.  It  is  a  verbal  and  not  a  real  proposition — a  definition 
disguised  as  a  proposition.  'Body  '  means  what  Newton  pre- 
dicates of  it ;  withdraw  from  *  body  '  all  that  the  law  affirms 
and  implies,  and  there  would  be  nothing  left.  If  a  body  did 
not  persevere  in  its  state  of  rest  or  motion,  until  disturbed  by 
another  force,  it  would  not  possess  the  most  elementary  con- 
ception that  we  can  form  of  body,  the  property  of  resistance. 
Of  the  various  modes  of  exhausting  the  aspects  of  body, 
matter,  inertia,  force,  it  may  be  doubted  whether  Newton's  is 
the  most  felicitous.  At  all  events,  the  attempt  would  succeed 
better,  if  the  statement  were  in  the  only  legitimate  guise — a 
Definition. 

Newton's  Second  Law  is — *  Change  of  Motion  is  proportional 
to  the  impressed  force,  and  takes  place  in  the  direction  of  that 
force.*  This  law  assumes  the  fact  of  the  communication  or 
transfer  of  motion,  and  affirms,  althouofh  not  in  the  best 
manner,  the  quantitative  equivalence  of  the  motion  given 
with  that  received. 

The  Third  Law  is — *To  every  action  there  is  always  an 
equal  and  contrary  re-action ;  or  the  mutual  actions  of  any 
two  bodies  are  always  equal  and  oppositely  directed.'  More 
shortly  expressed  thus — '  Action  and  Reaction  are  equal  and 
contrary.'     Objections   have    often  been  taken  to  the   word 

*  Re-action'  in  this  law.  The  meaning  put  upon  it  by  Newton 
is  gathered  from  his  own  illustrations.  His  examples  are  of 
two  classes.  The  first  puts  the  case  of  impact,  as  in  pressing 
a  body,  or  in  drawing  it  by  some  solid  medium  as  a  cord  or  a 
rod.  There  is,  to  say  the  least,  great  awkwardness  in  repre- 
senting the  communication  of  force  by  impact,  in  these  terms  : 
— *  when  we  push  a  stone  with  the  hand,  the  hand  is  pushed 
back  by  the  same  force  as  the  stone  is  moved  forward  ;*  or 

*  a  horse  towing  a  boat  is  dragged  backwards  by  the  same  force 
as  the  boat  is  dragged  forwards.'  The  more  natural  expres- 
sion is  that  when  one  moving  body  gives  motion  to  another, 
it  loses  exactly  the  energy  that  it  communicates ;  or  that  on 
the  re-distribution  of  force  or  moving  power  nothing  is  lost. 
Now,  if  there  be  any  real  affirmation  in  the  Second  Law,  it  ia 
this  and  nothing  else. 


460 


LOGIC   OF  PHYSICS. 


ONLY  ONE  LAW  OF  MOTION. 


461 


The  other  class  of  examples  given  by  Newton  comprises  a 
distinct  case,  and  the  only  case  that  gives  the  appearance  of 
propriety  to  the  word  *  re-action.*  It  is  the  communication  of 
movement  by  distinct  attraction  (or  repnlsion).  When  one 
body  attracts  a  second,  the  second  equally  attracts  the  first ; 
the  attractions  are  mutual  and  eqaal ;  the  momenta  produced 
are  exactly  the  same  in  each.  This  is  a  fact  of  great  import- 
ance in  nature  and  deserves  to  be  singled  out ;  indeed,  it  is 
the  only  case  of  communicated  momentum  where  the  result  is 
unaffected  by  disturbances  that  interfere  with  exact  calcula- 
tions. 

Now  this  is  to  be  regarded  as  a  separate  induction.  It  is 
fully  consistent  with  the  principle  of  the  conservation  of 
energy,  under  re-distribution,  as  represented  by  impact, 
and  has  some  inherent  probability  in  its  favour,  but  still 
requires  the  confirmation  of  experience.  Ingenious  reasons 
might  be  given,  why  no  other  result  should  arise,  but  there  is 
no  infallible  deductive  cogency  in  applying  the  Law  of  Conser- 
vation, founded  on  impact,  to  the  equality  of  mutual  attrac  • 
tions. 

Searching  thus  through  the  three  Laws  of  Motion,  we 
encounter  only  one  principle — the  principle  of  Conservation 
of  Force  under  re-distribution.  The  second  law  has  no  mean- 
ing but  this.  That  *  change  of  motion  is  proportional  to  the 
impressed  force '  with  difficulty  escapes  from  being  a  verbal 
proposition,  for  there  is  no  other  measure  of  force  but  *  change 
of  motion,'  imparted,  or  impartible  movement.  The  assertion 
would  have  no  reality  but  for  the  circumstance  that  a  moving 
body  encounters  another  body  and  changes  the  state  of  that 
other  body — urging  it  to  move  or  arresting  its  movement. 
This  is  a  supposition  not  made  in  the  bare  definition  of  force ; 
and,  therefore,  we  do  something  more  than  repeat  the  defini- 
tion, when  we  affirm  that  the  force  imparted  to  the  second 
body  is  lost  to  the  first.  Now,  this  is  all  thai  the  Third  Law 
contains ;  only  that  law  brings  into  prominence  the  distinct 
case  of  force  arising  by  attraction  or  repulsion  at  a  distance. 
Discarding,  therefore,  the  present  First  Law,  as  being  but  the 
definition  of  Inertia,  we  may  condense  the  second  and  third 
into  a  single  statement  declaring  the  Conservation  motive 
Energy,  under  re-distribution,  whether  by  impact,  or  by 
attraction  or  repulsion.  This  is  the  one  axiom  of  the  Science ; 
its  foundations  are  inductive.  It  is  a  partial  statement, 
applicable  to  molar  forces,  of  the  all-comprehending  law  of  the 
Conservation  of  Force.      Indeed    in  the  limitation  to  molar 


force,  the  principle  is  not  strictly  true ;  it  is  true  with  regard 
to  attractions  and  repulsions,  and  hence  in  Astronomy  no 
error  is  committed  in  applying  it ;  it  is  not  true  of  impacts  ; 
there  is  always  force  lost  in  a  mechanical  collision,  or  in  the 
transfer  by  machinery  ;  the  lost  mechanical  energy  re-appear- 
mg  as  molecular  vibration  or  heat. 

Newton's  second  law  has  been  considered  as  a  way  of  pro- 
viding for  the  case  of  the  communication  of  movement  to  a 
body  already  moving  in  some  other  direction.  A  force  impel- 
ling in  any  direction  will  accomplish  its  full  effi^ct  in  that 
direction,  even  although  the  body  should  be  already  in  motion 
in  some  diffisrent  direction  ;  as  when  a  ship  sailing  in  a 
westeriy  current  is  propelled  by  a  north  wind.  This  is  the 
foundation  of  the  law  of  composition  of  Motion  and  Force,  but 
it  IS  still  only  an  application  of  the  principle  of  Conservation 
of  Energy  under  re- distribution.  Direction  as  well  as  amount 
are  included  in  the  principle  ;  a  body  moving  in  a  certain 
direction  and  imparting  motion,  imparts  it  in  its  own  direc- 
tion, and  in  no  other.  Before  affirming  the  Law  of  Conser- 
vation in  its  full  generality,  we  are  bound  to  verify  it  for  this 
case  as  well  as  for  mutual  attraction;  it  has  been  verified, 
and  is  affirmed  accordingly. 

The  so-called  *  Principle  of  Virtual  Velocities '  is  a  hypo- 
thetical expression  of  the  Law  of  Conservation  suited  to  various 
mechanical  applications,  such  as  the  demonstration  of  the 
mechanic  powers.  We  cannot  prove  the  statical  proposi- 
tion of  the  lever,  without  supposing  it  to  move.  Dynamically 
the  law  of  the  mechanical  powers  is  the  only  one  consistent 
with  the  Conservation  of  Force  ;  and  the  dynamical  proof  is 
given  as  the  statical  by  the  supposition  of  a  very  small  motion. 

7.  The  second  great  Induction  of  Molar  Physics  is  the 
Law  of  Gravity. 

The  Law  of  Gravity  associates  the  two  distinct  properties — 
Inertia  and  Gravity,  and  declares  the  one  to  be  proportioned 
to  the  other,  throughout  all  varieties  of  matter.  The  Law  is 
sufficiently  expressed  thus : — Every  portion  of  matter  attracts 
every  other  portion,  the  attraction  in  each  being  in  proportion 
to  the  mass  (or  inertia),  and  inversely  as  the  square  of  the 
distance. 

This  Law  has  been  frequently  referred  to,  in  previous  parts 
of  this  work,  as  the  one  unequivocal  case  of  two  co-extensive 
properties,  constituting  a  proposition  fully  reciprocating,  and 
convertible  by  simple  conversion. 


462 


LOGIC  OF  PHYSICS. 


Onr  tmifc  of  force  (so  much  inerta  actiug  throtigli  so  mnch 
space)  is  thus  the  unit  of  weight,  say  a  pound,  moved  against 
gravity  through  the  unit  of  space,  say  a  foot. 

Concatenation  and  Method  of  Molar  Physics. 

8.  The  branches  of  Molar  Physics  follow  a  Deductive 
arrangement.  The  Abstract  departments  are  purely  deduc- 
tive ;  the  Concrete  unite  Deduction  with  Experimental 
determinations. 

The  great  division  into  Statics  and  Dynamics — Equilibrium 
and  Movement — exhausts  the  abstract  portion  of  the  subject. 
These  are  thoroughly  mathematical  in  their  structure  ;  the 
propositions  and  demonstrations  are  worked  out  according  to 
Geometry,  Algebra,  or  the  higher  Calculus,  respectively.  A 
preliminary  mathematical  department  is  constituted,  which 
has  been  termed  *  Kinematics,'  containing  propositions  that 
assume  only  the  fact  of  Motion,  together  with  mathematical 
elements.  The  Composition  and  Resolution  of  Motions,  under 
every  possible  variety  of  complication,  are  mathematically  de- 
veloped under  this  branch  ;  it  being  also  applicable  to  Optics. 
The  theorems  are  then  found  to  be  transferable  to  Statical  and 
to  Dynamical  Problems,  which  regard  Motion  as  the  result 
and  the  essential  fact  of  Force,  whose  full  expression  includes 
as  factors  the  Velocity  and  Mass. 

The  Concrete  Branches  are  : — I.  The  Mechanic  Powers,  and 
Machinery  generally  (fluid  action  not  included).  Here  there 
is  an  application  of  the  deductive  laws,  bub  these  have  to  be 
modified  by  the  molecular  structure  of  bodies ;  and  the  modifi- 
cations are  ascertained  experimentally.  The  laws  of  friction, 
of  stress  and  strain,  of  molecular  transfer  in  impacts,  &c.,  are 
the  subject  of  experiment  almost  exclusively.  Where  deduc- 
tion is  applied,  it  must  be  submitted  at  every  step  to  experi- 
mental confirmation. 

II.  Hydrostatics  and  Hydro- Dynamics,  or  abstract  Statics  and 
Dynamics  applied  to  Liquids.  There  is  here  also  the  employ- 
ment of  experiment  to  find  out  the  modifications  of  dynamical 
laws  due  to  the  molecular  structure  of  liquids.  There  is  a 
farther  use  of  experiment,  in  aid  of  the  deductive  process 
itself,  which  is  apt  to  be  foiled  by  the  complications  of  fluid 
mobility. 

III.  Aerostatics  and  Pneumatics  comprise  the  treatment  of 
gaseous  bodies,  to  which  the  foregoing  remarks  also  apply. 

IV.  Acoustics  treats  of  vibrations  of  the  air  and  other  bodies, 


CONCRETE   DEPARTMENTS   OF  MOLAR   PHYSICS.         463 

eonstituting  the  agency  of  Soand.  Here  we  have  the  transition 
from  the  molar  to  the  molecular ;  bat  the  mode  of  dealing 
with  the  phenomenon  (through  the  similitude  of  pendulous 
and  wave  motions)  has  close  alliances  with  the  preceding 
molar  branches.  In  this  department,  however,  experiment 
predominates  over  deduction. 

V.  Astronomy  might  be  taken  either  first  or  last  among 
the  Concrete  branches.  It  departs  the  least  from  abstract 
Statics  and  Dynamics  ;  which  is  owing  to  the  purity  of  the 
gravitating  force ;  there  being  no  friction  and,  in  the  celestial 
region,  no  resistance.  It  is  deductive  throughout ;  yet,  owing 
to  the  great  mathematical  difficulties,  the  deductions  must  be 
checked  by  continual  observation  ;  while  to  observation  alone 
we  owe  the  knowledge  of  the  co-efficients  or  constants. 

In  Astronomy,  there  are  various  problems  that  draw  upon 
the  other  concrete  branches  of  molar  physics,  and  even  upon 
molecular  physics  ;  so  that  the  position  of  priority  among  the 
concrete  branches  has  to  be  qualified.  The  tides,  the  physical 
constitution  of  the  sun  and  the  planets,  the  theory  of  solar  and 
planetary  heat  and  light — are  examples  of  these  far-branching 
portions  of  the  subject. 

MOLECULAR  PHYSICS. 

9.  In  Molecular  Physics,  the  phenomena  have  reference 
to  the  action  of  the  component  molecules  of  matter. 

The  chief  subjects  are  — 

Molecular  Attractions — Cohesion,  ^'c, 

Heat^ 

Light, 

JEleciricity, 
The  primary  assumption,  axiom,  or  induction  of  Molecular 
Physics  is  to  the  effect  that  the  masses  of  matter  are  composed 
of  small  particles,  atoms,  or  molecules,  attracting  or  repelling 
each  other  in  various  modes,  and  possessing  intestine  motions. 
This  is  a  real  proposition  respecting  matter,  and  not  a  mere 
repetition  of  its  defining  property — Inertia.  It  is  pre-emi- 
nently hypothetical  in  its  character  ;  that  is,  the  evidence  for 
it  is  only  the  suitability  to  express  the  phenomena  open  to  the 
eenses ;  as,  for  example,  the  solid,  liquid,  and  gaseous  forms 
of  bodies,  the  heat  or  temperature  of  bodies,  luminous  and 
electrical  effects. 


464 


LOGIC   OF  PHYSICS, 


MOLECULAB  ATTRACTIONS. 


465 


I 


Notions  of  Molecular  Physics. 

Molecule,  Atom.— It  is  known  as  a  fact  that  every  kind  of 
matter  is  made  up  of  very  minute  portions,  called  atoms  or 
molecules;  the  limit   of  minuteness   being  hitherto  unascer- 
tained.    By  supposing  attractions  and  repulsions  between  the 
atoms,  we  can  represent  the  varieties  of  solid,  liquid,  and  gas, 
as  well  as  the  imponderable  forces — heat,  &c.    The  phenomena, 
however,   require    that   there   should   be  different   orders    of 
atoms  or  molecules;    the  ultimate  atoms  being  grouped  into 
complex  atoms,  and  those  again,  perhaps,  into  still  higher  com- 
pounds.   Thus,  the  Cohesion  atom,  the  Heat  atom,  the  Chemical 
atonas,  the  Solution  or  Diffusion  atom,  are  all    hypothetically 
distinct,  the  assumptions  being  varied  to  suit  the  appearances. 
The  definition  of  the  atom  or  molecule,*  therefore,  is  hypo- 
thetical and  fluctuating  ;  the  only  constant  assumption  is  a  very 
minute  element  gifted  with  attractions  and  repulsions,  by  which 
is  brought  about  the  aggregation  into  masses. 

Molecular  Attractions — Properties  op  Matter.  Nume- 
rous important  notions  arise  out  of  this  department  of  Physics, 
which  discusses  the  various  modes  of  aggregation  of  material 
masses,  and  their  causes,  real  or  hypothetical. 

Solid,  Liquid,  Gas. — These  names  for  the  three  states  of 
matter,  have  already  occurred  under  Molar  Physics,  and  must 
there  have  been  defined  up  to  a  certain  point.  The  exhaustive 
definition  of  the  various  forms  of  solidity  falls  under  Molecular 
Physics.  I  shall  indicate,  for  ulterior  ends,  what  seems  the 
best  arrangement  or  succession  of  the  properties  of  Solids. 

Crystal — Antithesis  oi amcyrphous.  The  crystal  is  not  difficult 
to  define.  The  common  fact  is  a  regular  and  constant  geo- 
metric form  as  determined  by  the  angles  of  the  faces  or 
boundary  planes.  A  substance,  for  example,  always  found  in 
cubes,  or  with  right-angled  solid  angles,  is  a  crystal ;  a  sub- 
stance that  has  no  regular  or  constant  form  is  amorphous; 
Buch  is  a  cinder.  Subsidiary  to  the  main  idea,  are  the  notions 
•^face,  axis,  nucleus,  cleavage,  fracture — and  the  several  systems 

•  Although  the  adjective  'molecular'  is  used  in  the  broad  contrast  with 
the  molar,  while  the  substantive  '  molecule*  also  corforms  to  the  usage,  a 
more  specific  meaning  has  lately  been  attached  to  the  molei  ulo,  in  con- 
tradistinction to  the  *  atom.'  An  atom  is  supposed  to  be  chemically  indi- 
visible ;  a  molecule  is  the  smallest  combination  believed  to  exist  separately. 
There  is  a  hydrogen  atom  represented  by  H  ;  but  the  hydrogen  molecule 
is  H  H,  or  Ha.  The  molecule  of  Phosphorus  and  of  Arsenic  is  each 
composed  of  four  atoms.  All  this  belongs  wO  the  hypothetical  part  of 
Chemical  Combination. 


of  crystals— Tesseral,    Tetragonal,    &c. ;    also    Isomorphism, 
Dimorphism,  AUotropy. 

Hard,  Elastic,  Tenacious,  Ductile,  Malleahle.  These  are 
names  for  a  series  oi  important  attributes  of  solid  bodies,  to 
which  there  is  a  corresponding  series  of  contrasting  properties 
-—soft  or  flexible,  inelastic,  brittle,  inflexible,  inductile  or  unmaU 
leable.  They  are  mostly  distinct  properties,  althongh  to  some 
extent  related.  They  are  all  strictly  definable,  and  measurable 
m  amount  or  degree  by  given  tests.  Hardness  is  the  resistance 
to  change  of  form,  as  by  scratching  or  dinting ;  Elasticity  is 
the  rebound  from  compression.  Tenacity  is  opposed  to  being 
pulled  asunder.  Dactility  is  tenacity  under  the  process  of 
being  drawn  out  into  wire ;  if  the  hammer  is  employed,  the 
substance  is  called  Malleable. 

Viscosity  is  a  softness  approaching  to  liquidity.  *  All  bodies 
capable  of  having  their  form  indefinitely  altered,  and  resisting 
the  change  with  a  force  proportioned  to  the  alteration,  are 
called  Viscous  Bodies.'  (J.  Clerk  Maxwell). 

Cohesion  (Homogeneous  attraction).  Definable  as  the  mutual 
attraction  of  particles  of  the  same  substance,  as  iron,  flint,  or 
ice.  The  crystalline  structure,  hardness,  and  other  qualities  in 
the  previous  enumeration,  may  be  expressed  as  different 
degrees  and  modes  of  cohesive  energy.  Cohesion  is  therefore 
the  hypothetical  summary  of  the  properties  just  named ;  and 
its  modes  are  to  be  accommodated  to  represent  these  with 
accuracy.  A  crystal  must  have  one  mode  of  cohesion,  a 
lump  of  clay,  a  different  mode.  The  limits  of  cohesion  are 
small ;  two  pieces  of  plate  glass  will  adhere  strongly  if  in 
close  contact,  but  will  not  attract  one  another  through  a 
sensible  distance. 

Adhesion  (Heterogeneous  attraction).  A  wide-ranging  phe- 
nomenon. It  is  defined  —  the  attraction  of  particles  of  one 
substance  for  particles  of  a  different  substance,  as  when  glue 
sticks  to  wood,  mortar  to  stone,^water  to  wood,  &c.  Cements, 
Capillary  action.  Solution,  Absorption  of  Gases,  Alloys — all 
suppose  this  mode  of  action.  To  express  the  full  details— 
which  substances  attract  which,  and  with  what  degrees  of 
force— requires  a  great  many  prepositional  statements,  most 
conveniently  given  in  the  mineral  or  the  chemical  description 
of  each  substance.  Under  the  present  head,  the  general 
results  should  be  presented. 

Diffusion,  Osmose. — These  are  properties  extending  beyond 
what  is  implied  in  solution,  and  even  anticipating  Chemical 
processes.     Still,  they  are  the  immediate  sequel  to  the  preced- 


^m 


LOGIC   OF  PHYSICS. 


f 


• 

ing  group  of  phenomena.      Their  dpfinifmn  ;a 

t^on^on.e  p,eno.ena  Uroug.el^  ^t;'Z  re^Str 

expressed  by  the  antitbesL-C  .ttat urar  c7"^,  '1''=^' 
definition  is  in  the  highest  degree  irelanf  !l°'^'  ^^."'^ 
attributes.  (1)  The  cdloid  stete  is  IS  of  tZtT^'^^l' 
me  or  amorphous  modification  of  matter  («>  tL  i  J'*^'" 
inert  chemioallv.  thev  aro  .mf  „    ^^^P"^-     (-';  1  he  colloids  are 

In  their  own  form  thev  hav/>      "^  '''=''^'  "■■  ^'''^'-     (3) 

semi-liquid  thevTllow   ottj     T." ''^''  P^"'^*"' '    "*«  ^o^  '^^ 
rA\  aril  <  '"^"^  substances   to  diiiuse  in    tl.»^ 

(4)  btiH  more  important  is  their  ««/«7„7,v,,  ,u  •  ?■     ^'"• 

pass  into  change,  and  eraduall  i^  •  u^:,  "'" '^^'^'"^^^ '° 
deadnessandfifitVofthfcS-  durin  r^  *°""'"''^  *^« 
are  sources  of  molecular  p3  '  TiZ?  l''\  P'""?'  *'"'y 
fit  them  to  play  a  nirt  fn  I •  •'  .  '■"'°  ^"^^  peculiarities 
enter  lar  Jy  as  consSl^,  f."^  structures,  into  which  they 
colloids).^  ^5)  ColL  ds  ilii^'^'""^"'  fr?'  «'='>•<-•''.  Ac,  are 
crystalloid  class  as  salt'anTl,  P^"°"'^^^^  ^y  bodies  of  the 
other  ;  a  most  imoortinMn  ^^'"''  u ''l  "^P^rmeable  to  each 
his  method  of  7^X^f^d:i,°?  "^^'Ji^  ^""^^"^  •'^^  fo'">'J«d 
interesting  phenomena"  "^  ''  '^'  explanation  of  many 

they  have  a  mod^Sefii^tnTcarr '"  ""^^  "  ^"" ' 
the^£ill  Tra^S  ^11?^ Sy^r  ^^1?^°-  "J 

Scat?';i:;-ti?:crf°\°'^^^^^^ 

bescending^Xth Herdent'hs^;  *'r  'f '  '°^""'  °'«*°''. 
avoidablyanticipate  oth?r^!?f  %  T'^?''*'"  ^"°°-  *hey  nn- 
of  Chemfstry  EuUh  s  's  Zt  r  M°M  ""^^  ^^y^^'' «""!  «ven 
The  priorit/of  posit^nTsTi  «/ f  lu*"^  ""^  "^rangement. 
Cohesive  Forceps  the  L-'ru^.*^^  circumstance  that 
matter,  andTthecon„trf^.t""''"'<'°f  «»  ^-nds  of 

expressed  by  thfc^S^^dFo'c'es*!*^^^^    "fKf  ^-^^ 
we  find  it,  on  the  one  h^A    T       u!'^"'    *^a«eriswhat 

internal  cohesions  and  on  the  'of  ^°K^^*il^  °PP°''"S  play   of 
derived  from  the  transferlv.1  1       hand  through  the  repulsion 

-  Hca,  Electrici^lTgbUlTFlJXfr     ''  '^ 
the  great  scale  of  molar  movfmel?     "'""'^"'''^  ^^^^''^  °° 


DEFINITION   AND  PROPOSITIONS   OF  HEAT. 


467 


Heat. — The  next  department  in  order  is  the  primary  and 
the  typical   form   of  molecular  energy,  in  the  great  circle  of 
Oonservred  or  Persistent  Forces.     The   leading  notion— Hea« 
itself  IS  the  only  one  attended  with  logical  difficulties  of  deE- 
nition.     Properly  speaking  it  is  an  ultimate,  indefinable,  in- 
communicable notion,  and  its  essential  character  is  subjective. 
iiach  of  us  must  be  referred  to  our  own  sensations  of  heat  and 
cold  m  their  different  degrees,  which  sensations  are  unique 
and  not  to  be  confounded  with  any  others.     Nor  is  there  any 
perplexity  in  generalizing  the  particulars,  with  a  view  to  a 
comprehensive  definition,  as  there  is  with  matter  and  inertia ; 
he  that  has  one  or  a  few  experiences  of  change  of  temperature 
knows  all. 

The  physical  or  objective  counterparts  of  this  unmistakeable 
subjective  experience  are  numerous  and  various,  and  belong  to 
strictly  physical  investigation.      The  most  obvious  are  the 
increase  of  bulk  by  warmth,  and  the  so  called  destruction, 
(more  properly  re-construction)  of  material  masses.     A  great 
and  protracted  effort  of  generalization  has  been  requisite  to 
encompass  all  the  manifestations  of  this  physical  correlate  of 
a  familiar  feeling,  and  to  embrace  the  whole  in  a  unity  of 
expression.     Even   at  the  present  moment,  the  generalized 
unity  rests  upon  a  hypothetical  assumption,  true  in  the  main 
fact,  but  uncertain  in  the  shaping,  and  as  yet  imperfectly  adap- 
ted to  the  multiplicity  of  the    thermal   phenomena.      Heat, 
physically,  is  a  mode  of  molecular  motion,  exchanging  at  a 
definite  rate  with  mechanical  movement,  as  well  as  with  the 
other  molecular  modes  termed  Electricity  and  Chemical  force. 
If  we  define  Heat  by  its  subjective  phase,  the  great  physical 
generalization  is  a  predicate  of  concomitance,  constituting  a 
real  proposition.     If  we  use  the  subjective  fact  merely  as  a 
clue  to  the  objective,  and  insist  on  making  the  definition  ob- 
jective, this  property  is  then  the  defining  property,  from  which 
would  flow  innumerable  deductive  attributes  (propria) ;  while 
there  would  be  propositions  (either  propria  or  concomitants) 
affirming  the  relationships  of  heat  to  other  forces,  and  also  the 
material   collocations  or  arrangements   connected    with   the 
transmutation. 

The  notions  involved  in  the  various  phenomena  of  Heat,  give 
the  heads  of  the  science  ;  they  are  all  definable  by  generaliza- 
tion, and  their  elucidation  needs  abundant  reference  to  facts  in 
the  concrete  : — Conduction,  Convection,  Radiation,  Reflexion, 
Absorption,  Diathermacy,  Refraction,  Specific  Heat,  Latent 
Heat,  Melting,  Freezing,  Evaporation,  Condensation,  EbuUi- 


!' 


4G8 


LOGIC  OF  PHYSICS. 


CHARACTERS   OF  ELECTRIC   FORCE. 


469 


\\i 


tion,  Boiling  Point,  Distillation,  Tension  of  Vaponr,  Dew 
Point,  Heat  of  Combination,  Calorific  equivalents. 

Light. — The  exact  position  of  this  subject  in  a  strictly 
studied  arrangement  of  topics  is  somewhat  dubious.  In  some 
important  points,  it  has  a  close  alliance  to  Heat ;  its  manifesta- 
tion in  a  body  is  almost  always  dependent  on  a  certain 
temperature.  Moreover,  as  an  influence  radiating  through 
space,  it  has  not  only  great  similarity  to  heat,  but  also  is 
singularly  open  to  mathematical  treatment.  Still,  being  as 
yet  imperfectly  understood  in  its  reciprocation  with  the  cor- 
related forces,  it  does  not  stand  to  heat  on  the  same  footing  as 
electrical  and  chemical  force.  But  for  the  close  and  easy 
transition  from  Electricity  to  Chemistry,  we  might  put  Light 
at  the  end  of  Molecular  Physics.  Or,  as  having  abstruse 
chemical  relationships,  it  might  succeed  to  Chemistry.  Thus, 
the  position  actually  accorded  is  owing  to  a  seeming  prepon- 
derance in  favour  of  one  out  of  several  alternatives. 

Light,  like  heat,  must  have  a  subjective  definition  to  start 
with  ;  and,  in  this  view,  it  has  the  same  freedom  from  ambi- 
guity. Bat  as  Sight  is  a  highly  objective  sense,  we  can  incor- 
porate with  the  subjective  property  the  objective  particulars 
— radiation  and  transmission  in  space — which  are  revealed  at 
once  to  the  luminous  sensibility. 

We  may  give  the  definition  thus  : — Light  expresses  a  dis- 
tinct state  of  mind  known  only  to  individual  self-consciousness, 
to  which  state  is  added  the  objective  experience  of  an  emana- 
tion from  a  material  body  to  the  eye,  whereby  we  become 
cognizant  of  the  characteristic  properties  of  matter  named 
visible. 

The  subsidiary  notions  are  the  main  topics  of  the  science  : — 
Transparent,  opaque,  translucent,  shadow  ;  Incidence,  Refrac- 
tion, Index  of  Refraction,  Lens,  Image,  Reflexion,  Mirror, 
Caustic,  Focus,  Colour,  Spectrum,  Complementary  Colours, 
Dispersion,  Chromatic  Aberration,  Diffraction,  Rainbow, 
Double  Refraction,  Polarization,  Interference,  Undulatory 
Theory. 

So  far  as  these  topics  are  concerned,  the  science  of  optics 
depends  upon  no  extraneous  source  beyond  Mathematics,  and 
might  have  precedence  of  all  the  other  subjects  of  molecular 
physics.  The  connexion  of  Light  with  Heat,  with  Electricity, 
and  with  Chemistry,  would  then  fall  under  these  several 
departments. 

Electricity. — As  the  denotation  of  Electricity  takes  in — 

Magnetism  Voltaic  Electricity    Magneto-Electricity 

Friction  Electricity  Electro-Magnetism  Thermo-Electricity — 


it  is  no  easy  matter  to  find  an  exact  connotation  for  the 
general  name.  Two  properties  may  be  put  forward  :  (1) 
Polarity,  and  (2)  Current  action.  As  regards  the  firsi^ 
Polarity,  there  is  uniform  agreement  in  all  the  modes  ;  and, 
moreover,  the  polar  attribute  is  prominent  and  pervading,  and 
imparts  a  destinctive  character  to  all  the  phenomena.  Still, 
in  carrying  out  the  idea,  we  are  met  by  the  ambiguous  phe- 
nomenon, named  by  Faraday,  Diamagnetism,  a  force  mani- 
fested by  the  magnet  upon  heavy  glass  and  certain  other 
substances,  but  without  polarity,  being  equal  repulsion  by  both 
poles.  This  phenomenon,  however,  must  be  held  in  suspense 
in  the  meantime,  and  not  allowed  to  interfere  with  the  defini- 
tion on  so  vital  a  point. 

The  second  characteristic  of  the  Electric  Forces,  is  their 
being  carried  to  any  distance,  through  solid  conductors,  so  as 
to  discharge  themselves  at  any  point.  In  ordinary  chemical 
action,  as  in  the  double  decomposition  of  two  salts,  the  sub- 
stances must  be  in  contact ;  but  by  an  electrical  arrangement, 
the  oxidation  of  zinc  in  one  vessel,  may  lead  to  the  decompo- 
sition of  water  in  another.  This  important  point  of  commu- 
nity makes  a  strong  alliance,  although  with  difi'erences,  between 
the  electric  forces. 

These  two  leading  features,  coupled  with  subjection  to  the 
great  Law  of  Conservation,  are  all  that  can  be  at  present 
brought  under  the  connotation  of  Electricity  as  a  whole.  The 
difierent  branches  have  each  their  special  definition,  attainable 
by  the  same  generalizing  process.  Definitions  are  also  to  be 
provided  for  the  subsidiary  notions — Magnetic  Poles,  Meri- 
dian, Declination,  Inclination  ;  Electrics,  Non- Electrics,  Con- 
duction, Insulation,  Circuit,  Induction,  Charge,  Discharge, 
Electrical  tension  ;  Electrolysis,  Electrodes. 

Propositions  of  Molecular  Physics, 

Axiom  of  Conservation  of  Force. — At  the  threshold  of  mole- 
cular physics,  there  must  be  provided  a  statement  of  the  Law 
of  Conservation,  in  all  its  compass,  or  as  embracing  alike  the 
molar  and  the  molecular  forces.  Although  the  law  cannot 
be  fully  comprehended  at  this  stage,  yet  some  attempt  should 
be  made  to  exemplify  its  workings  as  Heat,  as  Electricity,  and 
as  Chemical  force,  and  also  to  point  out  the  mutual  conversion 
of  all  the  modes — molecular  and  molar.  The  law  is  the  pre- 
siding axiom  of  molecular  Physics,  and  of  Chemistry,  and 
through  them  reaches  the  domain  of  Physiology.  It  is  every- 
where the  sufficing  explanation  of  the  origin  of  Force  ;  leaving 


470 


LOGIC  OF  PHYSICS. 


to  be  investigated,  the  arrangements,  situations,  or  circnm- 
stances,  attending  on  tbe  manifestation  of  force  in  each  par- 
ticnlar  case. 

Other  propositions  of  Molecular  Fhjsics. — The  various  notions 
or  defining  properties  being   clearly   characterized,  we  may 
readily  ascertain  what   class  of  predicates   usually  go  with 
them  so  as  to  constitute  the  real  propositions  of  the  science. 
Thus,  with  reference  to  the  first  department — Molecular  Attrac- 
tions,  or  the  Properties  of  Matter,  from  which  are  excluded 
whatever  comes  under  Heat,  Electricity,  and  Chemistry — the 
atom  or  molecule  being  defined,  we  have,  as  real  propositions, 
the  following  :  *  Matter  is  composed  of  atoms  ;'  *  the  atoms  of 
matter  attract  each  other.*     This  last  proposition  being  one  of 
wide  generality,  there  fall  under  it  many  special  propositions, 
or  modes  of  attraction,  for  different  kinds  of  matter  ;  but,  in 
this  department,   we   are    perpetually   disposed    to   palm  off" 
verbal  propositions  for  real — as  in  affirming  that  hard  bodies 
have  a  powerful  atomic  cohesion.     Examples  of  strictly  real 
propositions  are  these  : — crystals  are  hard  bodies,  that  is,  the 
cohesion    of  crystallization   is   intense   in   degree  ;    crystals 
are  usually  brittle,  or  the   cohesion  of  cryst:ils  is  of  a  short 
range.     Again,  with  regard  to  Adhesion,  there  is  an  import- 
ant inductive  generalization,  that  bodies  of  a  nearly  similar 
nature  are  those  possessing  mutual   adhesion ;    thus   metals 
adhere  in  solders  and  in  alloys,  earihy  bodies,  in  cements  and 
in   cohesive   mixtures,    and   so   on.      Farther,    the   Diffusive 
volume  of  a  gas  is  inversely  as  the  square  root  of  its  density. 

These  are  propositions  of  co-inhering  attributes,  verified 
only  by  wide  and  exhaustive  agreement  through  the  whole 
sphere  of  the  things  concerned. 

Another  large  class  of  propositions  under  the  same  depart- 
ment includes  the  numerical  expressions  of  the  degrees  of  the 
different  attributes.  These  are  the  constants  of  the  department, 
and  need  no  farther  remark. 

The  propositions  of  Heat  have  the  reality  arising  in  the 
concomitance  of  subject  and  object  facts.  Apart  from  this, 
they  may  be  classified  under  the  following  heads.  The  first 
class  takes  in  the  deductions  from  the  law  of  Conservation, 
confirmed  by  observation  and  induction  : — such  are  the  facts 
of  the  dilatation  of  bodies  by  heat,  of  which  fusion  and  eva- 
poration are  special  manifestations.  There  is  herein  comprised 
a  wide  field  of  natural  phenomena ;  and  many  specific  state- 
ments are  needed  to  cover  the  variety  of  modes  in  different 
substances.      Another  class  of  propositions   affirm,  in  their 


PKOPOSITIONS   OF  HEAT. 


471 


several  modes,  the  great  molecular  property  named  Conduction^ 
a  property  with  numerical  degrees  ;  while  important  laws  of 
dependence  or  concomitance  connect  this  property  with  the 
molecular  properties  of  bodies.  Radiation  next  demands  to 
be  considered,  a  fact  with  geometrical  aspects  and  correspond- 
ing predicates  ;  this  part  of  the  subject  having  a  considerable 
parallelism  to  the  leading  facts  of  Optics.  The  specific  rates 
of  radiation  of  different  bodies  may  be  numerically  ascertained, 
and  laws  enounced,  whose  character  is  jointly  deductive  and 
inductive.  Absorption  is  another  predicate,  and  similar 
remarks  apply  to  it. 

^  The  exhaustion  of  the  consequences  of  the  Law  of  Conserva- 
tion, would  require  a  statement  of  the  mode  of  derivino-  heat 
from  Mechanical  force  (crushing,  collision,  or  friction*),  and 
from  the  other  molecular  forces  ;  and  also  the  situations  or 
arrangements  whereby  it  returns  to  these  again  ;  the  case  of 
producing  mechanical  force  having  been  given  under  the  great 
fact  of  Dilatation. 

On  the  whole,  propositions  of  heat  are  (1)  Derivatives  from 
Conservation  ;  (2)  Constants,  or  numerical  measures  of  the 
various  phenomena  for  different  bodies  ;  (3)  Laws  connecting 
inanifestations  of  heat  with  molecular  structure  ;  (4  j  Laws  of 
situation,  or  conditions  of  the  transmutation  cf  Heat,  to  and 
from,  the  other  energies,  with  the  constants,  expressing  the 
rates  of  equivalence. 

The  foregoing  account  may  suffice  to  exemplify  the  propo- 
sitions  of  molecular  physics.  Were  we  to  proceed  to  Light, 
we  should  find  a  statement  of  definite  phenomena— called 
radiation,  refraction,  reflexion,  dispersion,  colour —all  expressed 
under  numerical  and  geometrical  relations.  We  should  also 
find  some  cases  of  concomitance  of  attributes,  as  Double  Re- 
fraction and  Polarization.  The  connections  of  Light  with 
Heat  and  with  Chemical  Force,  being  underivable  from  the 
great  Law  of  Conservation,  must  be  given  as  empIHcal  induc- 
tions of  co-inhering  attributes,  some  of  them  of  considerable 
generality,  as  the  connexion  of  light  with  temperature;  others 
narrow  and  special,  as  in  the  chemical  relations. 

Electricity  has  the  advantage  of  being  fully  correlated  with 
the  other  forces.  It  involves,  however,  great  complexity  of 
arrangements,  as  conditions  of  its  manifestation  in  the  various 
species  ;  whence  the  propositions  are  greatly  occupied  in  stating 
these  arrangements  or  collocations  ;  many  of  them  being  hidden 
in  the  molecular  depths  of  bodies,  and  rendered  in  hypothetical 
language. 

21 


472 


LOGIC   OF  CHEMISTRY. 


Predominant  Methods  of  Physics, 

10.  Physics  has  been  seen  to  be  partly  Deductive,  and 
partly  Inductive.  The  Inductions  principally  relate  to 
Cause  and  Effect ;  while,  in  Molecular  Physics,  there  are 
inductions  of  Co-inhering  Attributes.  The  principles  of 
Definition  are  appealed  to,  and  more  especially  for  the 
primary  notions  ;  but  there  is  scarcely  any  opening  for 
Classification. 

As  a  Deductive  Science,  Molar  Physics  is  a  branch  of  applied 
Mathematics,  checked  and  controlled  by  the  perpetual  reference 
to  facts. 

As  an  Inductive  Science,  Physics  makes  an  unsurpassed 
display  of  the  machinery  and  resources  of  Observation  and 
Experiment.  It  also  shows  to  advantage  all  the  Methods  of 
Experimental  Elimination.  The  facts  being  subject  to  the 
great  law  of  Conservation,  the  deeper  experimental  problems 
consist  in  ascertaining  the  collocations  or  arrangements  for 
transmuting  or  evolving  the  diflferent  modes  of  force.  The 
researches  arid  discoveries  relating  to  Heat,  Electricity,  and 
Light  have  this  character  to  a  very  large  degree. 

The  Hypotheses  of  Physics  exemplify  all  the  forms  of  Hypo- 
thesis formerly  laid  down.  The  chief  instances — the  Dynamical 
Theory  of  Heat,  the  Undulatory  Theory  of  Light— have  already 
been  adduced  in  expounding  the  general  subject.  Another 
hypothesis  of  inferior  weight  and  character  is  the  two  Elec- 
trical Fluids,  for  representing  the  polar  phenomena  of  Elec- 
tricity. 


CHAPTER  IIL 


LOGIC  OF  CHEMISTEY. 

1.  The  relationships  of  Chemistry  to  all  the  departments 
of  Molecular  Physics  are  intimate  and  sustained.  The 
special  fact  of  the  science  is  given  in  the  name  Chemical 
Attraction. 

Chemistry  deals  with  the  union  and  the  separation  of  ele- 
ments ;  it  regards  all  the  substances  of  nature  as  either  simples 


REAL   PREDICATIONS   OF   CHEMISTRY. 


473 


or  compounds  ;  the  manner  of  union  or  composition  being 
special  to  the  science.  There  are  unions  not  chemical ;  as 
when  bodies  are  pulverized  and  mixed  together  without  farther 
intimacy.  There  is  a  still  more  intimate  union  in  solution, 
which,  however,  also  comes  short  of  chemical  union. 

2.  Chemical  Attraction,  or  Union,  involves  these  facts  : 
(1)  The  Properties  are  definite.  (2)  in  the  act  of  union, 
there  is  Heat  evolved.  (3)  The  chief  properties  of  the 
elements  disappear. 

A  fourth  mark,  which  may  either  enter  into  the  definition, 
or  be  reserved  as  a  predicate,  is  that  chemical  union  takes 
place  between  dissimilar  substances,  while  solution  or  adhesion 
is  between  similars.  If  reserved  as  a  predicate,  this  property 
will  be  one  of  the  properties  forming  real  propositions,  as  ex- 
emplified in  next  section. 

It  is  not  necessary  here  to  exemplify  these  defining  proper- 
ties. In  a  work  on  chemistry,  it  would  be  advisable  to  ofier 
in  advance  a  few  illustrative  cases,  as  a  preparation  for  enter- 
ing on  the  systematic  detail. 

This  disposes  of  the  leading  notion  of  Chemistry,  being  the 
essence  or  connotation  of  the  name,  the  Definition  of  the 
Science.  A  mistake  in  Logic  is  made  when  these  properties 
are  stated  as  real  propositions  ;  they  are  not  predicated  of  a 
subject  called  Chemical  Attraction,  they  constitute  or  make  up 
that  subject. 

3.  The  Propositions,  or  real  predications,  of  Chemistry 
relate  (1)  to  the  circumstances,  or  conditions  of  Chemical 
change,  (2)  to  the  substances  that  undergo  the  chauge. 

(1)  When  we  have  defined  the  fact  of  Chemical  union, 
(with  its  correlative  and  implicated  facts,  Decomposition, 
bimple  Body,  Compound  Body),  we  have  to  state  the  various 
circumstances,  conditions,  or  modifying  influences  of  Chemical 
change.  This  constitutes  numerous  real  predications,  of  great 
theoretical  and  practical  moment. 

(2)  The  wiumeration  of  substances  that  combine  together 
chemically,  or  that  bring  about  chemical  decompositions  yields 
a  large  mass  of  real  propositions,  under  the  general  predicate 
ot  Uo-existence,  or  Co-inhering  attributes.  Oxygen  com- 
bines with  hydrogen,  and  forms  water ;  sulphuric  acid  decom- 
poses chalk,  common  salt,  <fec. 

The  expressions  for  the  definite  combining  numbers  are  real 
propositions,  corresponding  to  the  *  constants'  of  Physics. 


474 


LOGIC   OF   CHEMISTRY. 


METALS  AND   NON-METALS  CLASSIFIED. 


475 


The  relation  of  Chemical  Force  to  the  other  Correlated 
Forces  may  be  re-iterated  at  the  commeocement  of  the  subject ; 
although,  as  with  the  other  preliminary  statements,  the  under- 
standing of  it  will  grow  with  the  unfolding  of  the  future  details. 

Arrangement  and  Methods  of  Cliemistry. 

4.  The  division  of  Chemistry  is  into  Ikokganic   and 

Organic. 

Inorganic  Chemistry  is  laid  out  under  the  succession  of 

the  Simple  Bodies. 

The  distinction  of  Inorganic  and  Organic  would  exemplify 
definition  with  a  broad  doubtful  margin.  The  basis  of  the 
distinction  is  the  circumstance  that  a  large  class  of  highly 
important  substances  can  be  obtained  only  from  living  bodies ; 
such  are  starch,  sugar,  albumen.  This  peculiarity  of  origin  is 
associated  with  two  other  peculiarities,  namely,  the  limited 
number  of  elements  in  organic  bodies,  and  the  great  complexity 
of  the  chemical  constitution.  There  would  be  a  convenience  in 
adopting  all  the  three  facts  as  a  complex  definition  of  Organic 
bodies,  from  which,  by  antithesis  or  negation,  we  have  the 
definition  of  the  Inorganic. 

The  Chemistry  of  the  Inorganic  or  Mineral  world  comes 
first ;  and  its  method  of  arrangement  is  to  adopt  some  succes- 
sion of  the  Simple  Bodies,  and  undtT  them,  to  distribute  the 
various  Compounds, 

Classification  of  the  Simple  Bodies  or  Elements. 

5.  The  Simple  Bodies,  or  Elements,  are  divided,  in  the 
first  instance,  into  Metals  and  Non-Metals.  Although 
there  are  transition  elements,  as  Tellurium  and  Arsenic, 
the  distinction  is  founded  on  important  differences. 

The  Metals  have  certain  prevailing  characteristics,  but  yet 
in  a  varying  degree,  and  with  occasional  exceptions.  (1)  Most 
striking  are  the  visible  properties — Opacity,  Lustre,  and  Colour. 
Metals  are  opaque;  they  have  thepeculiar  lustre  termed  metallic; 
and  their  colour  is  white  or  grey,  with  the  exceptions— Gold, 
Copper,  and  Titanium  ?  which  are  yellow.  (2)  They  are  solid^ 
Mercury  and  Hydrogen  being  notable  exceptions.  The  solidity 
is  usually  joined  with  compactness  of  structure,  as  shown  in 
the  properties — hardness  and  tenacity.  (3)  They  are  com- 
paratively good  conductors  of  Heat.  (4)  They  are  conductors 
oi  Electricity.     (5)  They  are  E  ectro-positive.     (6)  They  com- 


bine chemically  with  the  Non-Metals.     (7)  Their  compounds 
with  Oxygen  are  for  the  most  part  Bases^  and  not  Acids. 

The  question  is  not  here  raised  how  far  some  of  these  pro- 
perties are  implicated  in  others.  Since  the  implication  is  not 
obvious,  the  properties  are  provisionally  given  as  distinct.  A 
more  important  remark,  from  the  logical  point  of  view,  is  the 
occurrence  of  exceptions  to  almost  all  the  properties.  In  the 
complex  defining  of  natural  objects,  we  must  be  prepared  for 
this  circumstance,  which  does  not  render  the  classification  vain 
or  nugatory.  Although  mercury  is  a  liquid  we  neither  sui- 
render  the  property  of  solidity,  nor  exclude  it  from  the  class- 
Solidity  is  wanting  only  in  two ;  and  mercury  has  all  the 
other  six  properties.  This  is  probably  one  of  the  cases  where 
Whewell  would  desiderate  a  tijpe^  or  average  representative 
specimen,  some  metal  possessing  in  fair  measure  all  the 
prevailing  characters. 

The  Non- Metals  are  defined  by  the  antithesis  of  the  above 
group  of  properties.  As  regards  Light  they  are  not  uniformly 
opaque,  and  when  opaque,  they  are,  except  selenium,  wanting 
in  lustre.  There  is  only  one  Gaseous  metal,  there  are  four 
gaseous  non-metals.  They  are  non-conductors  of  Electricity, 
and  Electro-negative.  Their  compounds  with  oxygen  (one  of 
their  number)  tend  to  Acids,  and  not  to  Bases. 

Whenever  a  classification  is  possible,  there  must  be  common 
properties,  and  these  are  possible  to  be  stated.  Still,  in  the 
usage  of  Chemical  writers,  the  statement  of  the  generic  pro- 
perties of  the  classes  *  metal  *  and  *  non-metal,'  does  not  dis- 
pense with  the  repetition  of  these  in  the  detail  of  the  species. 
The  Natural  History  methods,  not  being  susceptible  of  exten- 
sive application  in  Chemistry,  are  hardly  attended  to,  even 
where  admissible.  Nevertheless,  as  the  situations  arising  in 
the  classification  of  the  Simple  Bodies  are  highly  illustrative 
of  situations  in  Botany  and  in  Zoology,  we  may  follow  out 
the  present  case  a  little  farther. 

6.  Both  Metals  and  Non-Metals  are  sub-divisible  into 
smaller  classes  or  groups. 

In  the  Metals,  there  are  certain  groups  that  have  important 
affinities—such  are  the  Alkali-Metals  (Sodium,  &c.),  the 
Alkaline-Earth  Metals  (Barium,  &c.),  the  Earth-Metals 
(Aluminium,  &c.),  the  Noble  Metals  (Mercury,  Silver,  Gold, 
ic. )  remarkable  for  refusing  combination.  A  group  is  also  indi- 
cated by  the  important  fact — exceptional  to  the  tendency  of  the 
metals  as  a  whole — namely,  forming  acids  with  oxygen.   A  few, 


si 

5  1 


476 


LOGIC    OF  CHEMISTRY. 


presenting  analogies  to  iron,  make  an  Iron  group— Manganese, 
Cobalt.  Nickel,  Chromium,  Uranium.  A  certain  amount  of 
resemblance  su^rgests  the  juxta-position  of  Zinc,  Cadmium  and 
Magnesium.     (Miller's  Chemistry,  I.  11). 

The  expositor}'  succession  adopts  the  order  of  greatest 
resemblances.  The  succession  is  necessarily  linear,  and  leads 
inevitably  to  the  wide  removal  of  bodies  that  agree  in  some 
important  particulars.  The  idea  is  sometimes  conceived  of  a 
circular,  or  superiBcial  arrangement  for  bringing  together 
resembling  bodies  on  two  sides ;  while,  by  a  diagram  of  solid 
dimensions,  each  body  may  be  brought  into  relationship  on 
three  sides.  Still,  the  expository  order  can  follow  but  one 
course,  indicated  by  the  maximum  of  resemblance  ;  and  pro- 
vision has  to  be  made  under  each  body  for  indicating  agree- 
ments between  it  and  bodies  in  other  groups. 

There  can  scarcely  be  any  doubt  as  to  the  propriety  of 
placing  the  substances  of  strongest  chemical  affinity  at  one 
end  of  the  line  (Hydrogen,  Potassium,  &c.),  and  of  weakest 
affinity  at  the  other  end  (the  noble  metals). 

The  Non-Meta,ls  (13  in  number)  contain  a  few  groups,  and 
some  isolated  individuals.  The  halogen  group  of  Berzelius — 
Chlorine,  Bromine,  Iodine,  and  Fluorine;  and  the  sulphur  group 
—Sulphur,  Phosphorus,  Selenium,  and  Tellurium— are  classed 
as  having  considerable  and  important  resemblances.  Silicon 
and  Boron  have  points  in  common :  and  their  suffix  on  was 
given  to  show  some  small  analogy  between  them  and  carbon. 
The  substance  of  most  marked  isolation  is  Nitrogen  ;  while 
Oxygen  is   pre-eminent  by   the   catholicity   of  its  chemical 

affinities. 

By  unanimous  consent,  Oxygen  has  precedence.  The  second 
place  is  variously  assigned.  To  take  up  Hydrogen  could 
never  have  been  strongly  justified,  and  is  now  less  so  than  ever. 
For  the  single  advantage  of  having  Water  brought  forward  at 
an  early  stage,  a  leap  is  taken  to  the  extreme  opposition, 
making  the  last  first.  Most  is  to  be  said  in  favour  of  Nitro- 
gen, as  the  second  body.  Remarkable  for  its  chemical  neu- 
trality, it  also  gives  an  opportunity  for  dwelling  on  the 
mechanical  peculiarities  of  gaseous  elements  ;  and  it  may  be 
followed  up  by  the  consideration  of  the  Atmosphere— a  me- 
chanical admixture  of  Oxygen  and  Nitrogen. 

Except  to  hurry  on  to  familiar  and  interesting  combinations 
there  is  no  need  to  bring  forward  carbon  among  the  very 
first ;  the  nearest  kindred  to  oxygen  is  found  in  the  halogens 
—Chlorine,  &c.    To  these  might  follow  Carbon,  and  perhaps 


•JWiHiiiiiii  MfifciMi inir  . 


PLACE   OF   EXPOSITION   OF  COMPOUNDS. 


477 


Boron  and  Silicon,  while  the  Sulphur  group  wonld  close  the 
array.  Leaving  the  question  open,  whether  Carbon,  Silicon, 
and  Boron,  should  one  or  all  precede  or  follow  the  Sulphur 
group,  the  rule  of  arranging  by  the  maximum  of  agreement 
on  the  whole  would  be  best  carried  out  thus  : — 

Oxygen,  Chlorine,  Carbon,  Sulphur, 

Nitrogen,         Bromine,  Boron,  Phosphurus, 

Iodine,  Silicon,  Selenium, 

Fluorine,  Tellurium. 

Since  the  exposition  of  Chemistry  follows  a  certain  order  of 
the  Simple  Bodies — the  Non-Metals  first,  and  the  Metals  next — 
some  consideration  is  necessary  in  order  to  assign  a  place  for 
the  Compounds,  which  far  outnumber  the  Elements.  As  it 
would  be  inconsistent  with  the  very  nature  of  the  subject  to 
separate  the  Compounds  from  the  Simples,  seeing  that  the 
chemical  characters  of  a  simple  body  are  expressed  by  its 
forming  compounds  with  other  bodies,  the  Compounds  must 
be  interpolated  in  the  exposition,  and  appended  to  such  of  the 
Simple  Bodies  as  they  are  most  intimately  allied  with. 

Hence  there  will  always  be  a  choice  of  positions  ;  the  com- 
pound *  water '  may  be  attached  either  to  the  element  oxygen, 
or  to  the  element  hydrogen. 

There  is  one  obvious  consideration  applicable  to  this  peculiar 
emergency.  A  compound  need  not  be  brought  forward  for 
full  description  till  all  its  elements  have  been  stated ;  water 
may  wait  till  hydrogen  is  given  ;  carbonic  acid  may  follow 
carbon,  oxygen  being  previously  given;  the  salts  may  be 
appended  to  the  metals  that  are  their  bases.  Yet  this  arrange- 
ment is  not  without  its  disadvantage.  The  element  given 
last  may  not  be  considered  the  most  important  in  regard  to 
the  characters ;  thus  hydrogen  is  the  completing  element  of 
so  many  important  compounds,  as,  for  example,  the  hydrogen 
acids,  that,  supposing  it  placed  at  the  head  of  the  metals,  it 
would  be  followed  by  an  enormous  crowd  of  compound  sub- 
stances ;  many  of  which  would  seem  more  naturally  related  to 
other  elements,  as  the  acids  to  their  several  radicles — nitrogen, 
chlorine,  sulphur,  &c. 

The  difficulty  in  this  particular  instance  may  be  supposed 
to  be  got  over,  by  the  expedient  of  bringing  on  hydrogen  soon 
after  oxygen.  The  operation,  however,  begins  by  an  act  of 
violent  transposition  that  may  be  expected  to  land  us  in  some 
other  fix.  And  so  it  is.  Enabling  us  without  loss  of  principle 
to  attach  the  acids  to  their  several  radicles — nitric  acid  to 
nitrogen,  &c.,  the  proposed  step  compels  an  abrupt  stoppage 


478 


LOGIC   OF  CHEMISTRY. 


where  tliere  is  a  natural  transition,  namely  from  the  acids  to 
the  salts.  In  point  of  fact,  the  barrier  is  always  forced  at  this 
point ;  the  salts  are  brought  in,  notwithstanding  that  the 
metallic  bases  are  still  far  ahead.  Thus,  after  all,  the  trans- 
planting of  hydrogen  from  its  proper  allies  merely  postpones 
an  inconsistency  for  one  moment. 

On  the  other  hand,  it  may  be  maintained  that  the  proper 
place  of  the  important  hydrogen  compounds  is  after  hydrogen ; 
its  most  characteristic  feature  being  to  constitute  and  com- 
plete these  compounds.  The  class  ^hydrogen  acid'  is  connoted 
by  the  presence  of  hydrogen  ;  sulphuretted  hydrogen  and 
sulphuric  acid  are  more  in  place  among  hydrogen  acids  than 
among  sulphur  compounds.  This  alone  would  be  a  strong 
reason  for  not  bringing  on  hydrogen  till  the  end  of  the  non- 
metals,  in  which  are  contained  the  other  acid  constituents. 
If  these  acids  are  disposed  of  tirst,  the  interest  of  hydrogen  is 
used  up  ;  except  as  composing  water,  everything  about  it  is 
become  stale. 

Descriptive  Characters  of  CJiemical  Substances. 

7.  The  descriptioa  of  bodies  in  Chemistry,  whether  the 
Simple  Bodies  or  Compounds,  should  coincide  with  the 
expository  order  of  the  properties— physical  and  chemical. 

In  Chemistry,  no  less  than  in  the  Natural  History  sciences, 
a  regular  and  uniform  plan,  in  the  descriptive  arrangement,  is 
more  than  an  aid  to  memory  ;  it  is  farther  an  instrument  of 
investigation.  The  plan  adopted  in  Chemistry,  slightly  modi- 
fied, will  serve  also  in  Mineralogy. 

The  Chemist  professedly  exhausts  the  physical  as  well  as 
the  chemical  characters  of  each  substance.  Hence  the  scheme 
should  comprise  both  groups  in  the  best  order  of  succession  ; 
which  order,  as  regards  physical  properties,  is  seen  in  the 
exposition  of  Molecular  Physics.  There  are  some  open  points 
of  arrangement,  chiefly  with  reference  to  the  Crystalline  form 
and  the  Optical  properties.  Apart  from  these,  the  succession 
woQld  be  Molecular  Cohesion,  Heat,  Electricity.  If  the 
Crystalline  form  is  viewed  in  the  first  instance  as  a  purely 
geometrical  fact,  it  might  take  precedence  of  all  Physical 
properties.  The  Optical  properties,  stated  as  such,  without 
enquiring  into  their  connexions  with  molecular  structure  or 
with  chemical  arrangements,  might  be  given  next.  The 
priority  of  these  two  properties  would  have  the  expository 
advantage  of  mentioning  first  what  soonest  strikes  the  senses ; 


OPtDER  OF  DESCRIPTIVE  CHARACTERS. 


479 


the  eye  taking  the  lead  in  the  scrutiny  of  whatever  is  visi- 
ble. 

To  the  Crystalline  and  Optical  properties  might  succeed  the 
Specific  Gravitt, 

Next  in  order  would  be  the  properties  hypothetically  re- 
sumed as  modes  of  Cohesion  : — Hardness,  Tenacity,  Elasticity. 

There  would  then  succeed  the  properties  summed  up  in 
Adhesion  : — Solution,  Difi'usion,  Osmose,  Efi'usion  and  Trans- 
piration (of  gases). 

The  relations  to  Heat,  are  given  in  the  following  proper- 
ties : — Rate  of  Dilatation  ;  Melting  and  Boiling  Tempera- 
tures ;  Conduction  ;  Specific  Heat,  Latent  Heat,  Radiation, 
Absorption,  Refraction,  Polarization. 

Relations  to  Electricity  : — Magnetic  Property ;  Conduction 
or  Insulation  of  Friction  Electricity ;  Conduction  or  Insulation 
of  Voltaic  Electricity ;  place  in  the  Electro-positive  to  Electro- 
negative series  ;    place  in  the  Thermo-electric  series. 

The  Chemical  properties  are — Chemical  Composition  (if  not 
an  Element);  the  bodies  that  the  substance  combine  with ; 
the  circumstances  of  the  combinations  ;  and  the  agency  of 
each  in  decompositions. 

Of  these  characters,  two — Adhesion  and  Chemical  Attrac- 
tion— are  by  their  nature  correlative  characters  ;  they  involve 
the  mutual  action  of  at  least  two  substances.  With  reference 
to  them,  the  property  of  any  one  body  is  relative  to  some 
second  body  ;  a  substance  is  not  universally  adhesive,  nor 
universally  disposed  to  chemical  unions.  Hence  the  account 
of  the  Adhesive  and  the  Chemical  properties  is  complicated 
and  not  easy  to  manage.  There  is  from  this  cause,  an  especial 
difficulty  in  giving  an  adequate  notion  of  the  bodies  that 
happen  to  come  first ;  indeed  it  is  impossible  to  do  justice  to 
Oxygen,  for  example,  nntil  a  great  many  more  bodies  are 
described,  namely,  the  long  list  that  oxygen  combines  with. 

The  proper  course,  in  such  circumstances,  is  to  avow  the 
difficulty,  and  not  to  expect  that  a  learner  can  receive  other 
than  an  inadequate  or  half  notion  of  Oxygen,  nntil  he  has 
come  on  to  the  full  description  of  such  bodies,  as  Carbon,  Sul- 
phur, Hydrogen,  and  a  few  of  the  metals. 

Examples  of  Description. 

(1)  Light. — A  gas.  Transparent  and  colourless.  Index  of 
Refraction  1.00027. 

i2)  Specific  Gravity  1.1056  ;  the  atmosphere  being  1. 
3)  Adhesion  for  ether  substances. — Solubility  in  water,  from 


480 


LOGIC   OF  CHEMISTRY. 


OXYGEN  DESCRIBED. 


^I 


about  one   twentieth  to  one  thirtieth  of  its  bulk  (.04-114  ai 
32°  F. ;  .02989  at  59°  F.). 

(4)  Relations  to  Heat. — Rate  of  Dilatation  not  stated.  As 
regards  the  temperatures  of  Liquefaction  and  Freezing,  has 
never  been  liquified,  although  condensed  to  -^f  of  its  bulk. 
Specific  Heat,  about  one  fourth  of  water  (.2405). 

(5)  ReXsktions  to  Electricity. —  Is  a  magnet  at  common  tem- 
peratures. In  the  Voltaic  series,  it  is  at  the  head  of  electro- 
negative elements. 

(6)  Chemical  relations. — Speaking  generally,  it  is  the  most 
widely-combining  element  in  nature.  With  a  doubtful  excep- 
tion (fluorine),  it  combines  with  every  known  element ;  not 
merely  its  natural  opposites,  the  metals,  but  non-metals  like- 
wise. Classes  of  leading  importance  in  chemistry  are  com- 
pounds of  oxygen  with  the  other  elements  ;  the  oxides  of  the 
metals  are  what  are  termed  bases  ;  the  oxides  of  the  non- 
metallic  elements  are  generally  acids.  With  Hydrogen,  it 
yields  water.  The  act  of  combining  with  Carbon,  either  alone, 
or  along  with  hydrogen,  is  the  most  familiar  example  of 
violent  and  rapid  chemical  union,  with  evolution  of  heat  and 
of  light,  and  is  termed  *  combustion.' 

The  peculiar  circumstances  attending  the  combinations  of 
oxygen  vary  with  the  character  of  the  second  element.  Thus, 
in  the  leading  fact — Heat  of  combination — the  maximum 
evolved  is  with  Hydrogen ;  Carbon  yields  one  fourth  of  that 
amount ;  Phosphorus,  about  a  sixth ;  Sulphur,  about  a 
fifteenth ;  Zinc,  Iron,  Tin,  about  a  twenty-sixth. 

Atomic  number,  16. 

As  regards  the  conditions  of  entering  into  combination, 
there  is  great  variety,  from  the  extreme  of  readiness  at  the 
ordinary  temperature  of  the  atmosphere,  to  the  extreme  of 
indifference,  conquered  only  by  the  aids  to  combination, 
namely,  artificial  condensation,  heat,  the  electric  spark,  the 
contiguity  of  chemical  action  already  begun,  &c.  Part  of  the 
peculiarity  is  due  to  the  state  of  oxygen  itself: — which  may 
be  either  in  the  ordinary  atmospheric  dilution ;  or  prepared 
apart  free  from  any  other  gas  (whereby  all  combinations  are 
acclerated)  ;  or,  lastly,  in  combination  with  other  bodies  as 
in  water  (a  powerful  oxidizer) ;  in  the  nitrates,  in  chlorate  of 
potash — which  salts  permit  of  the  liberation  of  their  contained 
oxygen  in  a  highly  concentrated  form. 

Local  spread  of  Oxygen. — Need  not  be  here  detailed. 

Modes  of  obtaining  Oxygen. 

I  doubt  the  propriety  of  including,  under  Oxygen,  any  more 


detailed  account  of  the  oxygen  compounds.  There  are  better 
opportunities  afterwards,  under  the  several  elements  that  form 
the  other  members  of  the  compounds, — carbon,  hydrogen,  the 
metals,  &c.  Nor  is  it  necessary  to  bring  forward  Combustion, 
of  which  a  sensational  use  is  commonly  made,  in  the  descrip- 
tion of  oxygen.  A  disproportionate  prominence  is  thereby 
given  to  what  is,  strictly  speaking,  incidental  only  to  some  of 
the  modes  of  oxidation,  and  is  found  in  other  chemical  com- 
binations if  they  happen  to  be  rapid  and  energetic.  Combustion 
is  a  special  thesis  under  the  general  head —  Chemical  Union,  its 
conditions,  and  circumstances — and  is  of  great  importance 
both  theoretically  and  practically,  but  it  need  not  be  appended 
to  Oxygen.  If  involving  too  much  anticipation  of  details  to 
be  given  in  the  preparatory  view  of  Chemical  Combination 
(where,  however,  it  might  be  briefly  indicated),  it  might  be 
brought  in  at  some  convenient  point,  by  way  of  digression, 
as  for  example,  at  the  end  of  Carbon,  the  chief  element  in 
ordinary  combustion. 

Ozone. — A  supposed  allotropic  form  of  Oxygen,  under 
which  the  oxygen  is  rendered  more  active  in  entering  into  its 
various  combinations. 

The  specific  gravity  of  ozone  is  greater  than  of  oxygen. 
Adhesion. — It  is  not  soluble  in  water,  nor   in  acids  or  in 
alkalies ;  but  it  is  soluble  in  iodide  of  potassium. 

Relations  to  Heat. — Its  active  character  is  destroyed  by  a 
temperature  not  much  above  boiling  water. 

Relations  to  Electricity. — The  transmission  of  a  series  of 
electric  sparks  through  dry  oxygen  is  one  of  the  modes  of 
producing  it. 

Odour. — It  has  a  characteristic  odour,  whence  its  name.* 
Chemical  properties. — While  it  does  not  combine  with  any 
substance  but  those  that  oxygen  combines  with,  it  combines 
at  temperatures,  and  under  circumstances  where  oxygen  does 
not  combine.  Hence  it  is  a  powerful  oxidizing  agent — in  oxi- 
dizing metals,  in  destroying  vegetable  and  animal  compounds, 
in  bleaching,  in  purifying  the  air  from  miasmata,  in  stimulating 
the  respiratory  organs. 
Modes  of  preparing  Ozone. 

Remarks  on  Ozo7ie.f — It  is  interesting  to  note  the  power  of 
electricity  to  give  a  new  combining  aptitude  to  oxygen. 

*  Taste  and  Odour  may  provisionally  be  given  after  Electricity,  and 
before  Chemical  properties.  They  are  doubtless  a  consequence  of  Chemi- 
cal reactions. 

4  The  heading  *  Bemsurks*  is  intended,  among  other  uses^  to  avoid  the 


482 


LOGIC  OF  CHEMISTRY. 


Nitrogen. — A  gas. 

As  regarda  Lights  transparent,  colourless ;  Refracting  In- 
dex, 1.0093. 

Specific  gravity. — .9713.     Atmosphere  1. 

Adhesion. — Water  dissolves  about  a  thirtieth  of  its  bulk  at 
ordinary  temperatures. 

Relations  to  Heat.  —Dilatation  not  stated.  Never  been 
liquefied.     Specific  Heat,  slightly  less  than  Oxygen,  .2368. 

Relations  to  Electricity. — Next  to  oxygen  in  the  Electro- 
negative series. 

Chemical  relations. — Nitrogen  enters  into  a  very  limited 
number  of  compounds.  Where  it  does  combine,  it  is  sin- 
gularly inert,  or  indisposed  to  enter  into  combination  ;  de- 
manding to  be  placed  in  the  most  stimulating  conditions. 
Many  interesting  consequences  in  vegetable  and  in  animal  life 
are  traceable  to  this  peculiarity. 

Compounds  with  Oxygen. — Recited  in  go  far  as  illustrating 
Nitrogen. 

Compounds  with  Hydrogen. — Ammonia,  &c 

Compounds  with  Carbon. — Cyanides. 

Spread  of  Nitrogen. — Modes  of  obtaining  it.  Remarks  : — 
bearings  upon  Chemical  theory. 

The  next  example  is  a  solid  element. 

Carbon. — A  solid,  in  two  states — crystallized  Diamond,  and 
amorphous  Graphite.  These  occur  in  such  a  degree  of  purity 
that  they  may  be  taken  as  typical  of  the  element. 

(Diamond). — The  Crystallization,  Optical  Properties,  Speci- 
fic Gravity,  need  not  be  here  recited. 

Cohesion. — The  hardest  body  known ;  hence  at  the  top  of 
the  scale  of  mineral  hardness. 

Adhesion. — A  very  important  circumstance  as  regards  other 
forms  of  carbon,  but  not  ascertainable  in  the  diamond  itself. 

Relations  to  Heat. — Is  not  fused  or  volatilized  by  the  highest 
known  heat ;  is  not  known  to  exist  either  as  liquid  or  as  vapour. 
An  intense  heat  merely  reduces  it  to  a  black  opaque  mass. 

Relations  to  Electricity. — A  non-couductor.  Carbon  has  a 
high  relative  place  in  the  Electro-negative  series  (place  given). 

Before  stating  the  chemical  relations,  a  similar  recital  should 
be  given  for  the  other  form,  Graphite^ 

Chemical  relations.  The  range  of  elements  combining  with 
carbon  comprises — Oxygen,  Nitrogen,  Hydrogen,  Phosphorus, 
Sulphur,  and  many  Metals,  especially  Iron.     It  does  not  enter 

confusion  and  perplexity  of  introducing  speculative  consideratioos  into 
the  methodical  deiicription. 


DESCRIPTITE  METHOD. 


483 


into  combination  unless  at  high  temperatures,  and  then  com- 
bines with  rapidity  and  copious  evolution  of  heat. 

Compounds  with  Oxygen. — Carbonic  Acid,  Carbonic  Oxide 
(described  at  full  length). 

With  Nitrogen. — Cyanogen  ;  alluded  to. 

The  other  compounds  may  be  postponed. 

Spread  and  Sources  of  Carbon. — Impure  Forms. 

BemarJcs  on  Carbon.— ^Combustion. 

These  examples  are  sufficient  for  the  purpose  of  indicating 
a  systematic  mode  of  describing  the  elementary  bodies.  They 
would  apply  equally  to  compounds.  In  them,  however,  the 
chemical  relations  involve  another  circumstance,  namely,  the 
modes  of  decomposition. 

In  certain  of  the  elements,  the  chief  practical  i^^'"\.«L  lo 
found  in  impure  forms — alloys,  or  mixtures  with  other  in- 
gredients ;  for  example,  Iron.  Still,  it  is  desirable,  for  theo- 
retical completeness  and  consistency,  to  advert,  in  the  first 
instance,  to  a  pure  or  typical  form,  in  order  to  know  what  the 
substance  is  in  itself,  both  physically  and  chemically.  The 
alloys  or  mixtures  may  then  be  given  ;  but  before  their 
practical  bearings  are  touched  upon,  their  properties  are 
to  be  recited  as  illustrating  the  changes  brought  about  by 
mixture,  thereby  contributing  facts  to  the  inductive  lavvs 
of  Adhesion. 

8.  In  Descriptive  Method,  it  is  of  importance  not  to 
mix  explanations  and  theorizings  with  the  description. 

In  describing  a  quality,  the  first  thing  is  to  state  precisely 
what  it  consists  in,  or  how  it  is  discriminated.  Moreover,  the 
whole  series  of  qualities  should  be  gone  through,  in  the  first 
instance,  and  no  attempt  made  to  connect  them  with  one 
another,  or  with  other  properties,  in  general  laws.  This 
last  operation  should  always  be  kept  distinct.  The  remark 
applies  to  every  science  where  description  enters. 

9.  When  bodies  are  closely  allied  in  their  nature,  and 
are  in  conseqaence  grouped  as  genera,  their  differences 
should  be  exhibited  in  marked  contrast. 

The  Halogens  among  the  non-metals,  the  Metals  of  the 
Alkalies,  &c.,  make  groups  or  genera,  with  agreeing  peculiari- 
ties. These  points  of  agreement  are  stated  at  the  outset,  so 
as  to  abbreviate  the  details  of  the  species.  Attention  should 
next  bo  given  to  contrasting  pointedly  the  agreeing  members 
among  themselves.      Thus  Sodium  and  Potassium  agree  to  a 


484 


LOGIC  OF  CHEMISTRY. 


very  large  extent ;    and  after  the  agreements,  the  differences 
fihould  be  given  in  a  tabular  antithesis. 

10.  The  generalities  of  Chemistry  are  Eminrical  Laws, 

The  Atomic  Theory  is  commonly  said  to  be  the  highest 
generalization  of  Chemistry.  This,  however,  must  be 
guardedly  stated  so  as  not  to  confound  definition  with  pro- 
positions. The  nature  of  Chemical  Attraction  is  expressed  in 
a  complex  definition  (Definite  numbers.  Production  of  Heat, 
Merging  of  elements).  There  may  be  real  predication  in 
declaring  these  three  facts  to  be  conjoined ;  and  their  con- 
junction may  be  resolved  into  higher  laws,  or  converted  from 
an  empirical  to  a  derivative  conjunction. 

The  propositions,  in  connexion  with  Chemical  action,  that 
have  in  the  highest  degree  the  character  of  real  concomitance, 
are  those  that  affirm  the  conditions,  arrangements,  or  situa- 
tions attendant  on  combination  and  on  decomposition. 

For  example,  Combination  requires  proximity  of  the  ele- 
ments, and  is  favoured  by  all  the  circumstances  that  aid 
proximity,  as  liquefaction ;  it  is  resisted  by  strong  cohesive  or 
adhesive  forces,  and  proceeds  as  these  are  released.  It  is 
brought  on  by  elevation  of  temperature  in  numerous  instances. 
It  is  induced  by  the  electric  spark  ;  which  may  operate  by 
mere  rise  of  temperature,  but  more  probably  by  polarLzing  the 
atoms.  It  is  promoted  by  concurring  combinations  ;  it  accom- 
panies decompositions.  Tliese  are  all  empirical  laws.  They 
are,  moreover,  statements  as  to  general  tendency,  and  need  to 
be  accompanied,  each  with  a  schedule,  stating  the  individual 
substances  and  situations  of  their  applicability. 

Many  other  laws  might  be  cited : — The  celebrated  law  of 
Berthollet,  regarding  the  double  decomposition  of  salts  ;  the 
laws  that  simple  substances  exhibit  the  strongest  affinities, — 
that  compounds  are  more  fusible  than  their  elements, — that 
combination  tends  to  a  lower  state  of  matter — fi-om  gas  down 
to  solid. 

As  Empirical  laws,  these  have  no  other  verification  but 
Agreement ;  they  are  only  surmised  to  be  laws  of  causation ; 
they  are  limited  to  adjacent  cases. 

11.  The  ultimate  generalizations  of  Chemistry  must  fall 
under  the  Law  of  Conservation  of  Force,  and  must  express 
the  most  generalized  conditions  of  the  re-distribution  of 
Chemical  Force. 

The  Law  of  Persistence  over-rides  every  phenomenon  of 


HYPOTHESES  IN  CHEMISTRY. 


485 


change,  but  it  must  be  accompanied  in  each  case  with  laws  of 
Collocation.  In  Chemistry,  there  must  be  indicated  the  pre- 
cise conditions  of  chemical  re-distribution,  whether  in  com- 
bination or  in  decomposition.  It  is  necessary  to  find  out,  in 
the  most  general  form,  the  situation  or  situations  that  bring 
about  chemical  change,  in  either  direction.  If  this  can  be 
comprehended  in  one  law,  that  will  be  the  highest,  the  ulti- 
mate law  of  Chemistry,  the  Chemical  appendage  of  the  Law  of 
Conservation.  The  Empirical  laws  above  quoted  will  then 
have  the  improved  character  attaching  to  Derivative  laws. 

12.  Chemistry  contains,  as  a  part  of  its  nature,  nume- 
rous Hypotheses.  These  are  mainly  of  the  class  named 
Representative  Fictions. 

To  express  in  the  most  general  terms  the  numerous  pheno* 
mena  of  combination  and  decomposition,  certain  arrangements 
of  the  component  elements  of  the  compounds  are  assumed 
hypothetically.  It  is  a/ac^  that  sulphate  of  potash  contains 
certain  proportions,  by  weight,  of  sulphur,  oxygen,  and  potas- 
sium ;  it  is  a  hypothesis  that  the  salt  is  made  up  in  the 
particular  way  shown  by  the  formula  KOjSOs,  being  a  binary 
compound  of  two  other  compounds. 

The  Atomic  Theory  of  Dalton  contained  a  generalization  of 
facts  embedded  in  Hypothesis.  The  facts  were  the  fixed  pro- 
portions of  bodies  combining  chemically ;  the  hypothesis,  that 
each  substance  is  composed  of  atoms,  and  that,  in  chemical 
union,  an  atom  of  one  substance  joins  with  one,  or  with  two, 
or  with  more  atoms  of  another ;  there  being  always  a  neat 
numerical  relation  without  remainder.  No  one  now  regards 
this  as  more  than  a  representative  fiction,  unsusceptible  of 
any  other  proof  than  its  facility  in  expressing  the  facts. 

The  Constitution  of  Salts  is  the  great  battle  ground  of 
chemical  hypotheses,  being  the  key  to  the  entire  structure  of 
chemical  representation.  There  is,  however,  a  perfect  under- 
standing as  to  the  nature  of  the  proof  to  be  offered  for  the 
rival  hypotheses,  namely,  the  suitability  to  comprehend  the 
greatest  number  of  chemical  re-actions,  or  combinations  and 
decompositions.  It  is  a  question  purely  chemical,  and  not  in 
anywise  logical  in  the  sense  of  demanding  attention  to  be  re- 
called to  neglected  logical  principles. 

As  examples  of  the  subordinate  hypothetical  points,  we  may 
quote  the  singular  idea  of  supposing  an  element  to  combine 
with  itself — hydrogen  with  hydrogen,  chlorine  with  chlorine^ 
and  so  on ;  a  very  great  stretch,  seeing  that  opposition  of  ele- 


486 


LOGIC   OF  CHEMISTRY. 


CHEMICAL   NOTATION. 


487 


ments  is  a  predicate  of  chemioal  nnioD.  A  better  example  of 
a  likely  hypothesis  is  the  proposal  to  assign  to  bodies  of  dif- 
ferent properties,  having  the  same  ultimate  constitution,  a  dif- 
ferent proximate  constitution ;  as  formic  ether  and  acetate  of 
methyl.  The  bold  hypothesis  of  Gerhardt  and  Griffin — to  re- 
gard as  two  substances,  iron  when  entering  into  proto  salts, 
and  when  entering  into  sesqui-salts,  and  the  same  with  all  other 
elements  producing  sesquioxides — was  considered  as  a  relief 
from  otherwise  inextricable  difficulties. 

The  hypothesis  of  the  Atom,  or  lowest  chemical  constituent 
is  now  coupled  with  another  hypothetical  entity — the  molecule 
representing  the  smallest  number  of  atoms  of  each  substance 
supposed  to  possess  separate  action.  Thus  the  molecule 
of  nitrogen  is  said  to  be  made  up  of  2  atoms  ;  the  phosphorus 
and  arsenicum  molecules,  4  atoms,  and  so  on. 

When  a  number  of  different  salts  are  in  the  same  solution, 
as  in  a  mineral  water,  it  is  a  matter  of  hypothesis  which  acid 
is  attached  to  which  base.     (IVliller's  Chemistry,  II.  824.) 

The  class  of  Scientific  Hypothesis  consisting  of  unverified 
theories,  does  not  require  special  mention  in  Chemistry.  Apart 
from  the  representative  fictions,  essential  and  permanent  in  the 
science,  there  are  no  hypothetic  forces  or  agents.  The  great 
prevailing  agent  or  cause  of  chemical  change  is,  and  can  only 
be,  a  molecular  aspect  of  the  great  primeval  force  named  under 
the  Law  of  Conservation.  Until  the  supplement  of  this  law, 
as  regards  chemical  transformation — the  universal  conditions 
or  collocations — be  worked  out,  there  will  be  many  hypotheti- 
cal collocatimiSy  which  will  be  susceptible  of  final  proof  op 
disproof. 

Nomenclature  and  Classijication  of  Chemistry, 

13.  The  Nomenclature  and  the  Classification  of  Chemi- 
stry involve  these  points  : — (1)  The  use  of  a  symbol  for 
each  elementary  substance ;  (2)  The  expression  of  the 
ultimate  constitution  of  compounds  ;  (3)  an  expression  of 
the  supposed  proximate  constitution  of  each  compound  in 
a  manner  suited  to  its  re-actions  with  other  bodies. 

(1)  The  symbolical  notation  has  the  advantage  of  affording 
a  brief  and  yet  full  expression  to  the  most  complicated  com- 
pounds, rivalling,  in  this  respect,  the  notation  of  Mathematics. 
It  also  enables  bodies  of  like  composition  to  be  readily  classed, 
and  their  class  indicated  to  the  eye. 

The  nomenclature  for  expressing  in  terms  the  various  bodiea 


18  made  up  of  the  names  of  the  elements — Oxygen,  Carbon, 
Iron,  Silver — and  of  a  systematic  mode  of  uniting  these  in 
compounds — carbonic  acid,  carburet  of  iron,  &c.  Only  binary 
compounds  are  stateable  in  this  way  ;  a  higher  combination  is 
expressed  in  some  supposed  binarj^  resolution — sulphuric  acid, 
acetate  of  potash,  chloride  of  formyl.  Substances  like  sugar, 
starch,  albumen,  are  given  in  their  familiar  names.  Hence 
double  naming  is,  in  Chemistry,  a  special  and  limited  process  ; 
and  has  no  analogy  to  the  names  of  species  in  Botany  and 
Zoology. 

(2)  The  notation  exhibits  the  ultimate  constitution  of  all 
compound  bodies,  by  stating  their  constituents  and  the  pro- 
portions of  each  ;  Ha  0  is  the  analysis  of  water ;  F  0,  protoxide 
of  iron  ;  Fg  O3,  peroxide  or  sesquioxide. 

(3)  The  symbols  are  farther  accommodated  to  give  the 
hypothetical  upbuilding  of  the  elements  in  complicated  com- 
pounds ;  as  in  the  theory  of  Salts.  The  ultimate  analysis  gives 
the  amount  of  oxygen  in  a  compound,  and  the  formula  states 
in  what  ways  the  oxygen  is  supposed  to  be  distributed ;  an 
oxygen  salt,  in  the  old  theory  was  a  binary  compound  of 
two  oxidized  radicles,  the  oxide  of  a  non-metal  (as  sulphur) 
and  of  a  metal  (as  iron) ;  sulphate  of  iron  (proto:::ide  j  S  O3  Fe  O. 
The  analytical  (or  Empirical)  formula  of  acetic  acid  is  C4  H4  O4 ; 
of  the  rational  or  hypothetical  formula,  there  are  no  less  than 
seven  renderings  (Miller's  Chemistry,  vol.  Ill ,  p.  6). 

14.  A  desideratum  in  Chemical  Nomenclature  is  the 
statement  of  the  structural  Heat  of  the  bodies. 

The  formula  Ha  0  is  given  indifferently  for  steam,  water, 
and  ice  ;  although  the  exact  difference  of  structural  heat  in 
the  three  admits  of  numerical  statement.  Calling  ice  Hs  O  ; 
we  may  call  water  H2  O  +  180°  ;  steam  H2  O  +  1180°,  on 
the  usual  reckoning  of  the  heat  of  boiling  and  of  evaporation. 

Farther,  when  Hydrogen  and  Oxygen  combine,  there  is 
a  great  evolution  of  structural  heat,  which  is  lost  to  the  com- 
pound ;  a  provision  might  be  made  for  indicating  the  exact 
figure,  which  has  been  found  out  by  experiment ;  a  certain 
minute  quantity  would  be  attached  to  Hj  O,  on  this  account, 
and  about  one  fourth  of  that  quantity  to  C  0^ 


CHAPTER  IV. 
LOGIC  OF  BIOLOGY. 

1.  Biology  is  the  Science  of  Living  Bodies — Plants  and 
Animals  ;  its  exact  definition  is  the  definition  of  Life. 

Definitio7i  of  Life. 

2.  Life  is  to  be  defined  by  a  generalization  of  what  is 
common  to  Living  Bodies. 

The  Denotation  of  the  term  Living  Body  is  well  fixed; 
there  is  scarcely  even  a  debateable  margin  between  the 
Organic  and  the  Inorganic  worlds. 

Choosing  Assimilation  as  a  characteristic  fact  of  bodily  life, 
and  Reasoning,  as  an  example  of  mental  life,  and  contrasting 
both  with  the  characters  of  dead  matter,  Mr.  Herbert  Spencer 
arrives  at  the  following  highly  complex  definition  : — 

1.  Life  contains  a  process  or  processes  of  change. 

2.  The  change  is  not  a  simple  or  individual  act,  but  a  series 
or  succession  of  changes. 

3.  Life  involves  a  plurality  of  simultaneous,  as  well  as  suc- 
cessive changes. 

4.  The  changes  are  heterogeneo^is,  or  various  in  character. 
6.   The  various  changes  all  combine  to  a  definite  result. 

6.  Finally,  the  changes  are  in  correspondence  with  external 
CO- existences  and  sequences. 

In  sum  : — Life  is  a  set  of  changes,  simultaneous  and  succes- 
sive, combined  to  a  definite  result,  and  in  correspondence  with 
external  circumstances.  Or,  in  a  briefer  form,  Life  is  the 
continuous  adjustment  of  internal  relations  to  external  rela- 
tions. 

So  carefully  has  the  comparison  been '  conducted,  that  no 
exception  could  be  taken  to  any  part  of  this  definition.  Every 
one  of  the  particulars  occurs  in  all  living  bodies,  and  in  no 
kind  of  dead  matter.  The  apparent  defect  of  the  definition  is 
omission  ;  it  does  not  express  or  seem  to  suggest  points  that 
strike  the  ordinary  observer.  For  example,  there  is  no  allusion 
to  the  organized  structure,  at  the  foundation  of  which  is  the 
peculiar  constituent  known  as  the  cell,  or  nucleated  corpuscle. 
Again,  there  is  no  mention  of  the  individual  and  independent 


^^Stiik 


ELEMENTS   OF  LIVING  BODIES. 


489 


existence  of  living  bodies ;   with  which  is  also  associated  the 
cycle  of  birth,  growth,  and  death. 

These  omissions,  real  or  apparent,  might  be  defended  or 
explained  on  one  of  three  different  grounds. 

First,  it  might  be  said,  that  the  facts  mentioned,  although 
present  and  conspicuous  in  many  or  in  most  living  bodies,  are 
not  found  in  all,  and  therefore  cannot  be  adopted  into  the 
genei*al  definition.  They  can  be  taken  notice  of  only  in 
defining  the  classes  or  subdivisions  of  the  whole  kingdom  of 
animated  nature.  This  remark  would  be  a  sufficient  justifica- 
tion, if  it  were  true  ;  but  it  is  not  true,  at  least  to  the  extent 
of  excluding  the  mention  of  the  circumstances  from  the 
definition. 

Secondly,  it  might  be  said,  that  the  definition  does  not  aim 
at  being  exhaustive,  but  only  at  being  discriminative ;  while 
it  is  based  on  essential  characters,  it  does  not  profess  to  give 
all  the  essential  characters.  Enough  is  given  to  prevent  us 
from  ever  confounding  a  plant  or  an  animal  with  a  stone ; 
but  there  is  no  intention  of  stating  every  feature  that  separates 
Hving  bodies  from  the  inanimate  world. 

To  this  the  obvious  reply  would  be,  why  should  all  the 
essential  characters  not  be  given  ?  There  is  no  apparent 
reason  for  omitting  in  the  statement  whatever  can  be  dis- 
covered as  common  to  the  whole  depai'tment  of  animated 
nature. 

Thirdly,  it  might  be  alleged,  that  the  aspects  in  question 
although  not  appearing  on  the  surface  of  the  definition,  are 
yet  implicated  on  it,  and  are  unfolded  in  the  due  course  of  the 
exposition.  The  definition,  it  may  be  said,  goes  to  the  root  of 
the  matter ;  while  all  else  branches  out  from  that,  and  is  duly 
unfolded  in  the  subsequent  exposition  of  the  science. 

In  order,  however,  to  bring  forward  at  once  whatever  can  be 
assigned  as  general  characters  of  living  bodies,  whether 
primary  or  derived,  we  shall  re -cast  the  definition,  and  dis- 
tribute it  under  the  heads — Constituent  Elements,  Structure, 
and  Functions. 

3.  I.  Living  bodies  are  constituted  from  elements  com- 
mon to  them  with  the  inorganic  world. 

The  chief  constituents  of  Living  bodies  are  these  four — 
Carbon,  Hydrogen,  Oxygen,  Nitrogen  ;  the  last.  Nitrogen, 
being  most  abundant  in  animals.  To  these  are  added,  in 
smaller  proportions.  Phosphorous,  Calcium,  Sulphur,  Chlorine^ 
Fluorine,  Sodium,  Potassium,  Iron,  Magnesium,  Silicon. 


1. 


490 


LOGIC  OF  BIOLOGY. 


The  various  properfciep,  Physical  and  Chemical,  belonging 
to  the  several  elements  are  found  operative  in  their  organized 
form.  All  the  mechanical  and  molecular  laws  are  traceable 
in  living  bodies. 

Chemically  considered,  organic  bodies,  are  exceedingly 
complex  compounds.  The  department  of  Organic  Chemistry 
is  devoted  expressly  to  these  compounds.  According  to  the 
chemical  reckoning,  a  single  atom  of  an  organic  substance,  as 
sugar,  starch,  albumen,  contains  hundreds  of  simple  chemical 
atoms ;  the  atom  of  albumen  is  said  to  bo  made  up  of  880 
atoms  of  the  four  chief  organic  elements. 

II.  With  reference  to  Structure. 

(1)  Living  bodies  possess  a  peculiar  structural  complexity, 
commonly  called  the  Orga)uzed  Structure,  Associated  with  oui 
notions  of  life  is  a  certain  mechanism,  or  machinery,  very 
various  in  its  extent  and  complication  in  individuals  ;  attain- 
ing in  the  higher  animals  a  degree  of  complicated  adjustment 
unequalled  in  any  other  department  of  nature.  Such  struc- 
tures as  the  eye,  the  ear,  the  brain,  of  human  beings  are,  in 
our  conceptions,  the  very  acme  of  structural  mechanism. 

It  is  now  known  that  the  ultimate  constituent  of  all  the 
variety  of  structures  is  a  microscope  element  called  a  cell^  or 
nucleated  corpuscle  ;  by  whose  aggregations  and  transforma- 
tions, tissues  are  formed,  which  tissues  make  up  the  organs. 
It  is  true  that  in  certain  low  forms,  both  plants  and  animals, 
the  cellular  structure  is  not  apparent,  and  therefore  its  visible 
peculiarities  —  namely,  the  bounding  pellicle  and  internal 
nucleus — are  not  absolutely  essential ;  still,  we  cannot  omit 
from  the  definition  an  arrangement  so  completely  bound  up 
with  all  living  nature,  the  few  apparent  exceptions  being 
equivocal. 

(2)  Another  prominent  feature  of  the  living  structure  is 
Individuality  f  or  individuation.  Living  matter  instead  of  exist- 
ing in  vast  continuous  masses,  like  rock,  is  separated  into 
distinct  individuals.  As  with  other  peculiarities,  however, 
there  is  an  ambiguous  margin  here  also.  In  animal  life  gene- 
rally, and  in  plant  life  generally,  we  have  no  misgiving  as  to 
individual  existence ;  men,  sheep,  forest  oaks,  are  all  distinct 
and  separate.  Still,  a  scientific  definition  must  grapple  with 
the  whole  field  of  cases,  having  merely  the  requisite  latitude 
of  a  small  doubtful  margin.  Mr.  Spencer  defines  the  indi- 
vidual, with  reference  to  his  definition  of  Life,  as  any  concrete 
whole  performing  within  itself,  all  the  adjustments  of  internal 


LIVING  STRUCTURE   IND   FUNCTIONS. 


491 


to  external  relations,  so  as  to  maintain  its  own  existence. 
This  definition,  to  a  certain  extent  anticipates  Function,  but 
so  does  any  adequate  statement  of  Structure  ;  the  separation 
of  Structure  and  Function  is  one  of  great  logical  convenience, 
but,  in  nature,  the  two  things  are  inseparable. 

With  Individuality  there  is  closely  associated,  in  our  con- 
ceptions of  living  beings,  the  Cycle  of  existence,  the  derivation 
of  one  living  being  from  others,  and  the  necessary  termination 
of  each  individual's  existence,  after  a  definite  career.  Here, 
too,  we  may  seem  to  anticipate  what  belongs  to  Function. 

(3)  We  may  not  improperly  state  in  connexion  with  struc- 
ture, and  as  following  on  Individuality,  a  circumstance  so 
notorious,  that  to  omit  it  from  the  comprehensive  statement  of 
life  would  appear  inexplicable,  namely,  the  vast  Variety  of 
Forms  and  Structures.  Uniformity,  comparatively  speakino-, 
pervades  dead  matter  ;  variety  is  the  characteristic  of  living 
substances.  The  different  forms  of  Plants  and  of  Animals 
count  by  thousands  ;  there  are  upwards  of  one  hundred 
thousand  species  of  Plants,  and  a  still  greater  number  of 
Animal  Species ;  while  of  every  one  of  these  distinct  species, 
there  is  an  indefinite  unceasing  multiplication  of  individuals, 
nearly,  although  not  absolutely  alike. 

One  of  the  chief  demands  of  Biological  science  is  to  find  an 
orderly  arrangement  for  such  a  host  of  various  forms.  This 
makes  Biology,  inter  alia^  a  science  of  Classification, 

III.  As  to  Functions. 

The  living  structure  is  naturally  active,  changing,  produc- 
tive, and  its  most  characteristic  points  must  have  reference  to 
these  activities.  Here  we  may  embrace  the  substance  of  Mr. 
Spencer's  definition,  in  two  principal  heads— Change,  and 
Adjustment  to  external  circumstances. 

(1)  A  definite  combination  of  changes,  simultaneous  and 
successive. 

(2)  An  adjustment  to  external  circumstances. 

(3)  It  naust  seem  unpardonable,  however,  not  to  bring  out 
into  prominent  statement  at  the  outset,  that  very  remarkable 
phenomenon  of  living  bodies,  to  which  there  is  no  exception, 
namely,  Assimilation,  or  the  power  of  an  existing  organized 
particle,  to  impart  its  own  organization  to  an  adjoining  particle 
having  the  proper  chemical  constitution.  This  magic  touch 
of  vitality,  has  only  a  faint  parallel  among  inanimate  bodies; 
combustion,  and  chemical  combinations  generally,  make  but  a 
small  approach   to  it.     Its  lesser  manifestations  are  in  the 


492 


LOGIC    OF  BIOLOGY. 


renewal,  by  nntrition,  of  the  living  tissues ;  its  culmination 
is  in  the  throwing  o£F  of  the  germ,  or  seed,  apparently  homo- 
geneous and  structureless,  but  possessed  of  interior  markings 
that  decide  whether  its  future  is  to  be  a  man  or  an  oak ;  a 
white  man,  or  a  negro ;  a  flat  nosed  or  an  aqulline-nosed  man 
or  woman.  We  may  not  be  able  to  consider  whether  this 
great  property  be  essential  and  fundamental,  or  whether  it 
be  derived  from  other  properties,  already  given  in  the  defini- 
tion. 

We  may  repeat  under  this  head,  the  peculiarity  above 
adverted  to,  under  individuality  of  structure — the  Cycle  of 
existence,  or  birth,  growth,  and  death. 

(4)  It  cannot  be  irrelevant  to  the  comprehensive  definition 
to  advert  to  the  connexion  of  Miiid  with  Living  Bodies. 
True,  this  is  not  a  concomitant  of  all  living  bodies,  yet  it 
appears  only  in  connexion  with  the  living  form.  When  we 
make  the  first  great  division  of  life,  into  Plants  and  Animals, 
we  obtain  the  more  precise  boundary  of  the  mental  manifesta- 
tions. Still,  at  the  very  outset,  we  are  interested  to  know 
that  this  characteristic  manifestation  appears  only  in  the 
department  of  living  structures. 

The  foregoing  definition  professes  to  leave  out  no  fact  that 
can  be  found  inhering  in  all  living  bodies.  The  first  requisite 
in  defining  is  to  be  exhaustive  ;  it  is  an  after  operation,  of 
great  scientific  interest,  to  trace  the  dependence  of  one  or 
more  properties  upon  the  others,  and  to  assign  what  appears 
to  be  the  ultimate  and  nnderivable  properties.  At  present, 
however,  all  such  derivation  is  but  tentative  and  hypothetical, 
and  therefore,  is  not  suitable  to  be  brought  forward  at  the 
commencement  of  the  subject.  Provisionally,  these  various 
peculiarities  are  to  be  held  as  distinct ;  no  one  being  assign- 
able as  a  derivative  of  another. 

Divisions  of  Biology, 

4.  The  Divisions  of  Biology  are  in  conformity  with  the 
Definitioa 

The  first  part  of  the  Definition  refers  to  the  Organic  Chemi- 
Btry  of  Life.  This  subject  is  partly  given  under  Chemistry, 
and  partly  as  the  Introduction  to  Biology. 

The  two  other  parts  of  the  definition  suppose  a  separate 
consideration  of  Structure  and  of  Function.  We  should  fully 
understand  the  reasons  and  the  limits  of  this  separation. 


STRUCTURE   AND   FUNCTION  VIEWED   SEPARATELY.     493 


These  two  facts  are  inseparable  in  the  reality.  But  as,  in 
less  complicated  subjects  than  Life,  we  have  often  to  make 
abstraction  of  some  qualities  to  the  exclusion  of  others  where 
there  is  no  actual  separation  possible,  so  in  the  present  case 
we  find  it  advisable  to  consider  Structure  by  itself,  before 
viewing  it  as  connected  with  Function. 

Yet  this  separation  may  be  carried  to  an  unjustifiable 
extreme.  As  soon  as  the  mind  has  perfectly  comprehended  a 
structural  arrangement,  we  are  prepared  to  enter  upon  the  uses 
or  functions  of  that  arrangement.  Indeed,  while  the  know- 
ledge of  the  structure  is  still  fresh,  the  knowledge  of  function 
should  be  imparted.  Function  completes  and  fixes  the  idea 
of  structure,  in  so  far  as  the  two  are  manifestly  connected. 
The  only  reason  for  not  following  up  the  account  of  structure, 
with  the  account  of  function,  for  every  distinct  living  organ, 
would  be  the  necessity  of  viewing  Function  as  a  connected 
whole,  and  therefore  not  to  be  entered  on  unless  it  could  be 
given  as  a  whole.  For  example,  the  Function  of  Digestion 
could  not  be  entered  on  till  the  entire  group  of  alimentary 
organs  were  structurally  described. 

The  separation  of  the  two  subjects  is  carried  to  a  question- 
able extreme  in  the  special  Biology  of  man ;  Anatomy  and 
Physiology  being,  by  present  convention,  treated  in  distinct 
works,  and  taught  by  distinct  teachers  in  the  schools.  The 
just  middle  plan  would  be  to  include  both  in  one  work,  and 
to  append  to  the  Anatomy  of  each  organ — Bones,  Muscles, 
Heart,  &c.— the  Physiology  or  function. 

In  the  usual  treatment  of  Plant  Biology,  Structural  Botany 
is  given  first.  Physiological  Botany  next  (in  the  same  treat- 
ise) ;  the  student  being  made  to  wait  for  the  account  of 
Function  in  any  organ  until  Structure  has  been  gone  through 
in  every  organ.  The  justifying  reasons  are  probably  these : — 
(1)  It  is  possible  to  carry  provisionally  the  whole  structure 
in  the  mind,  without  the  assistance  that  function  would  give ; 
and  (2)  there  is  a  convenience  in  treating  function  as  an  un- 
broken whole. 

In  Animal  Biology,  the  branch  called  Comparative  Anatomy 
takes  each  organ  apart,  giving  both  structure  and  function, 
and  exhausting  the  varieties  of  each  through  the  animal  series. 

Structure  has  to  be  viewed,  in  its  successive  modifications, 
through  the  cycle  of  the  individual  life.  This  is  called 
Embryology.  A  still  more  extended  view  is  the  considera- 
tion of  successive  structures  in  the  hereditary  line,  where 
there  may  occur  changes  requiring  to  be  taken  account  of. 


494 


LOGIC   OF  BIOLOGY. 


being  the  initial  step  of  the  new  biologic;il  department  called 
Evolution. 

It  is  proper  to  generalize  to  the  utmost  the  wide  variety  of 
structures,  and  to  exhibit  all  the  generalities  apart  as  giving 
a  mental  command  of  the  entire  field.  Such  generalities 
would  be  celled  General  Morphology,  and  General  Embryology. 

Function,  or  Physiology,  is  an  account  of  all  the  living  pro- 
cesses, in  the  most  convenient  order ;  all  those  changes  con- 
etituting  Life — changes  simultaneous  and  successive,  contri- 
buting to  a  definite  result,  and  adapting  each  organism  to  the 
environment.  Here  there  is  an  unlimited  scope  for  inductions, 
and  for  deductions,  confronting  and  correcting  one  another. 
The  high  generalities  of  Function  comprehending  all  Life,  if 
such  there  be,  would  form  a  General  Physiology. 

The  subject  of  Evolution  involves  the  mutual  actions  and 
modifications  of  Structure  and  Function.  It  deals  with  the 
general  truth  that  when  external  circumstances  demand  and 
prompt  an  increase  of  function  (as  when  an  animal  is  called  to 
exert  unusual  muscular  energy)  the  structure  is  liable  to  be 
increased,  and  thus  to  increase  the  function  apart  from  stimu- 
lation. This  is  one  way  of  the  supposed  re-action  of  Stracture 
and  Function.  Another  way  is  by  Mr.  Darwin's  Natural 
Selection,  or  Survival  of  the  Fittest.  The  carrying  out  of  these 
principles  is  the  substance  of  the  great  Biological  Hypothesis 
of  Development  or  Evolution. 

Biology  can  to  a  certain  extent  be  treated  as  a  whole,  there 
being  certain  things  common  to  living  beings — Constituents, 
Structure,  Fanction  and  Evolution ;  it  would  then  have  to  be 
divided,  as  has  always  been  usual,  into  Plant  Life  and  Animal 
Life  ;  each  of  these  subjects  being  subdivided  according  to  the 
plan  above  laid  down  for  the  whole. 

Remaining  Notions  of  Biology. 

The  general  definition  of  Life  has  been  seen  to  carry  with 
it  the  definitions  of  Organization,  Cell,  Protoplasm^  Assimi- 
lation, Individual,  Germ,  lieproduction,  Growth,  Death. 

The  specializing  of  the  structures  and  functions  introduces 
many  other  Notions. 

Plant — Animal, — The  greatest  line  of  demarcation  in  livint' 
bodies  is  between  Plants  and  Animals ;  these  are  the  two 
highest  genera  of  living  bodies,  a  perfect  dichotomy  of  the 
whole.  Allowing  for  a  doubtful  margin,  the  distinctive 
characters  are  numerous  and  important.  As  in  all  dichoto- 
mies, we  have  the  advantages  of  a  definition  by  Antithesis. 


PARTS  AND  PROCESSES   OF  PLANTS. 


495 


The  leading  characters  may  be  stated  in  contrast  thus  : 

Plant.  Animal. 

If  umber  and  complexity  of  Tissues,  Organs,  and  Functions, 
Small  Great 

Local  habitation. 

^^ed  Moveable  (Locomotion) 

Food  materials. 
Inorganic  Organic 

Mode  of  reception  of  Food. 
Absorption  Reception  into  a  mouth 

and  stomach 
Process  of  nutrition. 
Deoxidation  Oxidation, 

Tissue.  Organ.  Vessel— -These  are  comprehensive  parts  or 
constituents  of  the  organized  structure,  as  made  up  of  cells  • 
they  are  common  to  all  living  bodies,  and  admit  of  exact 
definition.  There  is  a  difierence  between  the  Tissue  and  the 
Organ;  one  Organ,  as  the  stomach,  may  contain  several 
tissues.  Each  Tissue  is  analyzed  into  a  distinct  cell  structure, 
which  is  its  defining  peculiarity  as  regards  structure,  to  which 
there  also  corresponds  a  certain  kind  of  activity  or  function. 
Thus,  the  nervous  tissue  is  made  up  of  nerve  fibres  and  nerve 
cells,  in  a  special  aggregation  ;  these  are  connected  with  the 
peculiar  activity  or  function  called  nerve  function,  or  the 
manifestation  of  nerve  force. 

The   view  of  Plant   Life   contains   the   definitions  of  the 
structural  'parts  of  the  plant. 

Cellular  Tissue       Integument  (Stomata,  Hairs,  Glands) 
vessels  Root 

Vascular  Tissue     Stem  ' 

Leaves 

Inflorescence  (Flower,  Fruit,  Germ). 
From  the  enormous  number  and  variety  of  plants,  a  great 
effort  is  needed  to  present  these  parts  in  their  widest  gener- 
ality;  while  the  general  idea  must  be  accompanied  with  a 
classified  detail  of  modifications. 

Definitions   must  also  be  given  of  the  processes  of  Plant 
Life, 

Osmose  Flowering 

Exhalation  Yigils  of  Plants 

Transpiration  Sexual  union 

Secretion  Impregnation 

Irritability  and  Contractility  Fecundation 

Defoliation  Germination 

Circulation,  sap,  capillarity  Propagation. 
22 


496 


LOGIC   OF  BIOLOGY. 


PROPOSITIONS   OP  ANIMAL   STRUCTUBE. 


497 


A  set  of  notions,  parallel  but  more  nnmerons  and  compli- 
cated, belong  to  the  description  of  Animal  Life  as  a  whole. 
The  modifications  of  the  ultimate  materials  are  described  as 
blastema  or  matrix,  crystals,  protoplasm,  granules,  homogeneous 
membrane,  vesicles,  nuclei,  nucleated  cells,  simple  fibres,  7iucleated 
fibres,  compound  fibres,  and  tubes.  These  are  compounded  into 
the  characteristic  Tissues — Celhdar,  Adipose,  Vascular,  Carti- 
laginous, Osseous,  Muscular,  Elastic,  Epithelial,  Nervous,  The 
Organs  are  Bones,  Muscles,  Alimentary  Canal,  Respiratory- 
Organs,  Heart  and  Blood  Vessels,  Sympathetics,  Skin,  Brain, 
Senses,  Reproductive  Organs.  The  Functions  follow  the 
Organs ;  and  in  several  instances,  give  these  their  distinctive 
names. 

The  Classification  of  Plants  and  of  Animals  gives  scope  for 
Definition  as  applied  to  the  several  grades. 

5.  In  these  detailed  Notions,  we  have  the  analysis  of  the 
Living  Organism — Plant  or  Animal. 

An  organism  is  by  its  very  nature  a  complexity.  In  a 
scientific  consideration  this  complexity  has  to  be  resolved  into 
the  related  parts — organs,  tissues,  constituents.  The  laws  of 
structure  are  laws  of  relations  of  the  parts  to  each  other ; 
and  if  our  analysis  has  hit  the  natural  partition,  it  is  the  basis 
of  our  subsequent  statements,  in  propositions,  of  the  natural 
relations.  It  the  analysis  is  inexact,  no  exact  propositions  can 
be  grounded  on  it. 

Propositions  of  Biology 

6.  The  Laws  and  Propositions  of  Biology  differ  in  their 
logical  character,  according  as  they  relate  to  Structure  op 
to  Function. 

First,  as  to  Structure. 

The  propositions  or  laws  of  Structure,  affirm  co-existence, 
as  order  in  place,  between  the  different  parts  of  living  bodies. 
Human  Anatomy  is  a  vast  congeries  of  such  propositions. 
How  far  the  co-existences  are  ultimately  dependent  on  Causa- 
tion, rests  with  the  theory  of  Evolution.  In  the  meantime, 
they  are  to  be  regarded  mainly  as  Co-existence  without  Causa- 
tion. 

These  propositions  may  be  special  to  individuals  and  limited 
groups  of  individuals  ;  or  they  may  be  generalized  over  very 
wide  areas.  The  narrow  class  is  exemplified  in  human  Ana- 
tomy, and  in  all  specific  descriptions  whether  of  plants  or  of 


•tiimals.  High  generalities,  realizing  the  scientific  ideal  of 
Biology,  are  not  wanting.  For  example,  in  Plants— all  the 
parts  are  homogeneous  in  structure;  or,  as  otherwise  expressed, 
the  flowers  are  modified  leaves  ;  the  monocotyledonous  mode 
of  germination  co-exists  with  the  endogenous  mode  of  growth  ; 
flowering  plants  are  generally  multiaxial ;  complexity  of  struc- 
ture is  accompanied  with  permanence  of  form.  In  Animals, 
we  have  the  anciently  observed  coincidence  of  ruminant  sto- 
mach, cloven  hoof,  and  horns ;  the  grouping  of  mammalian 
characteristics— mammae,  non-nucleated  red  blood-corpuscles, 
two  occipital  condyles,  with  a  well-ossified  basi-occipital,  each 
ramus  of  the  mandible  composed  of  a  single  piece  of  bone  and 
articulated  with  the  squamosal  element  of  the  skull. 

Viewed,  in  the  first  instance  at  least,  as  co-existences  with* 
out  causal  connexion,  these  propositions  must  be  verified  by 
agreement  through  all  nature,  and  held  as  true  only  to  the 
extent  observed. 

There  are  numerous  and  striking  co-existences  between 
Structure  and  External  circumstances,  the  so-called  Adapta- 
tions of  one  to  the  other ;  but  in  these  there  is  a  great  pre- 
sumption of  cause  and  effect ;  they  furnish  the  best  support  to 
the  doctrine  of  Evolution. 

There  are  likewise  laws  of  causation,  more  or  less  traceable, 
m  the  operation  of  all  the  outward  agents.  Thus,  Heat, 
Light,  Air,  and  Moisture,  are  essential  or  causal  conditions  of 
the  growth  of  plants.  Light  is  necessary  to  the  colour  of  the 
leaves.  The  oxygen  of  the  air  is  an  indispensable  condition 
of  all  animal  life.  Many  other  laws  of  causation  are  occupied 
in  expressing  the  agency  of  different  kinds  of  food,  of  medi- 
cines, &c. 

There  are  laws  of  canse  and  effect,  in  the  mutual  actions  of 
different  organs,  in  each  individual  plant  or  animal.  Thus, 
in  animals,  the  digestive  organs  affect,  and  are  affected  by 
the  circulation,  the  muscles,  and  the  brain. 

7.  Next  as  to  Function,  or  Physiology. 

The  propositions  here  affirm  Cause  and  Effect.  The  process 
of  Digestion,  for  example,  is  an  effect  of  the  contact  of  food 
material  with  the  complicated  alimentary  organs.  In  like 
manner,  every  organ  of  every  living  being  has  a  function, 
more  or  less  assignable. 

It  is  a  deduction  from  the  permanence  of  Matter,  established 
since  the  researches  of  Lavoisier  as  a  law  of  nature,  that  what- 
ever materials  exist  in  plants  and  in  animals,  must  be  sup- 


m 


498 


LOGIC  OF  BIOLOGY. 


plied  as  a  condition  of  their  growth.  Plants  being  constituted 
from  Carbon,  Oxygen,  Hydrogen,  Nitrogen  (in  small  portions), 
and  Saline  bodies, — must  find  all  these  elements  in  the  earth 
or  in  the  air.  The  animal  tissues  being  highly  nitrogenous, 
animals  must  have  nitrogenous  food.  The  gastric  jaice  con- 
tains hydrochloric  acid,  whence  the  necessity  of  salt  as  an 
article  of  food.' 

8.  The  law  of  the  Conservation  of  Force,  and  all  the 
subordinate  generalizations  of  Molecular  Physics  and 
Chemistry,  are  carried  up  into  Biology. 

The  law  of  Conservation  holds  true  in  organic  changes,  and 
is  a  deductive  key  to  the  phenomena.  Every  manifestation 
of  force  in  a  living  body — mechanical  energy,  heat,  decom- 
position of  compounds, — is  derivable  from  some  prior  force  of 
exactly  equivalent  amount. 

The  laws  of  Cohesion,  Adhesion  (in  all  the  forms — Solution, 
Capillary  Attraction,  Diffusion,  Osmose,  Transpiration),  Heat, 
Light,  Electricity,  and  the  laws  of  Chemical  combination  and 
decomposition,  are  carried  up  into  organic  bodies.  In  the 
present  advanced  state  of  knowledge  respecting  these  laws, 
there  are  many  deductive  applications  of  them  to  the  pheno- 
mena of  life.  The  complications  of  Biology  are  thus,  in  part, 
susceptible  of  being  unravelled  by  pure  deduction. 

So  far  as  concerns  Force,  or  energy,  in  any  shape,  there  is 
nothiug  special  to  living  bodies.  As  regards  Collocation, 
there  is  the  peculiarity  of  the  organized  structure.  It  is  not 
correct  to  speak  of  Vital  Force  in  any  other  sense  than  the 
molecular  and  chemical  forces,  operating  in  a  new  situation. 
It  would  be  strictly  proper  to  speak  of  a  Vital  Collocation  of 
elements,  under  which  the  molecular  forces  put  on  new 
aspects,  although  never  inconsistent  with  the  primary  law  of 
Conservation.  Thus  the  nerve  force  is  something  new,  not  as 
regards  its  derivation  from  an  antecedent  equivalent  of  force, 
but  as  regards  the  singularity  of  the  nerve  structure,  which 
leads  to  a  new  mode  in  the  manifestation  of  the  force. 

9.  In  the  department  of  Function,  there  are  necessarily 
many  Empirical  Inductions. 

Excepting  the  deductions  from  Physics  and  Chemistry, 
every  law  of  Biology  must  be  considered  as  empirical.  There 
are,  however,  some  empirical  laws  established  by  an  agree- 
ment so  wide  and  sustained  that  they  are  considered,  for  the 
present,  as  laws  of  nature.     Still,  no  such  laws  can  be  held  as 


PROPOSITIONS   OF  FUNCTION. 


499 


Bbsolntely  certain.  Notwithstanding  the  agreement  in  favour 
of  the  derivation  of  living  beings  from  germs  or  seed,  there  is 
yet  a  possibility  of  spontaneous  generation. 

The  following  are  examples  in  Plants.  Vegetable  cells 
absorb  fluids,  elaborate  secretions,  and  form  new  cells ;  they 
also  unite  to  form  vessels.  Roots  absorb  material  from  the 
soil,  in  part  by  osmotic  action.  The  sap  circulates  under  the 
influences  of  heat  and  light,  and  the  actions  going  on  at  the 
surfaces  of  the  loaves  and  of  the  roots.  In  flowering  plants, 
reproduction  is  performed  by  the  access  of  the  pollen  to  the 
ovules.  Fruit  succeeds  to  fecundation.  Seeds  germinate  in  the 
presence  of  heat,  moisture,  and  air,  with  absence  of  light. 

There  is  something  very  unsatisfactory  in  the  inductions  of 
Vegetable  Physiology.  Some  of  them  are  now  obvious  results 
of  the  law  of  Conservation  ;  as  for  example,  the  influence  of 
Heat  at  all  stages  of  vegetable  growth.  The  great  lack  is  in 
the  intermediate  steps  of  the  process  ;  what  happens  in  the 
interval  between  the  incidence  of  heat  and  air  in  the  leaves, 
and  the  elaboration  of  the  sap,  the  setting  free  of  oxygen,  &c. 
But  this  is  the  defective  part  of  our  knowledge  of  all  the 
organic  processes. 

In  the  functions  of  Animals,  there  are  numerous  empirical 
inductions.  Thus  the  conditions  of  Muscular  contractions  are 
well  known  by  experimental  research ;  they  are  the  presence 
of  blood,  and  the  stimulus  of  the  nerves.  That  blood  should  be 
necessary  is  a  consequence  of  the  law  of  conservation ;  muscular 
force  must  be  derived  from  some  prior  force.  That  non-azotized 
materials  are  sufficient  for  causing  muscular  energy  could  be 
known  only  by  experiment.  Again,  the  circumstances  affecting 
the  heart's  action,  are  empirical  inductions  ;  so  is  the  fact 
that  the  red  corpuscles  of  the  blood  carry  the  oxygen  for  the 
tissues.  The  processes  of  Digestion  are  stated  in  the  form  of 
empirical  inductions.  The  same  holds  of  Urination  and  Re- 
spiration. Farther,  the  multiplied  actions  concerned  in 
Impregnation,  Germination,  and  Growth,  are  ascertainable 
only  as  empirical  laws.  All  the  functions  of  the  Brain  and 
the  Senses  are  given  in  propositions  of  the  same  character. 

That  exercise  (within  limits)  strengthens  all  the  animal 
organs  has  long  been  established  as  an  Empirical  Law.  Mr. 
Darwin  is  dissatisfied  with  the  physiological  reason  or  deriva- 
tion of  the  law;  to  him,  therefore,  it  remains  empirical. 

These  empirical  inductions  are  to  a  certain  small  extent 
controlled  by  high  generalities,  and  are  in  so  far  derivative. 
The  law  of  Conservation  is  a  check  upon  many  of  them ;  and 


500 


LOGIC  OF  BIOLOGY. 


the  special  laws  of  Molecular  Physics  and  of  Cbemistry  are 
seen  at  work  in  some.  But  in  such  a  process  as  Digestion,  the 
recognized  physical  and  chemical  actions  are  thwarted  by 
deeper  forces,  of  which  we  have  only  an  empirical  statement. 
The  most  potent  instrumentality  of  deductive  explanations  at 
present  known  is  that  furnished  by  the  researches  of  Graham 
on  Transpiration,  Diffusion,  Osmose,  and  Capillarity. 

Animal  Mechanics,  and  the  propulsion  of  the  fluids  by  the 
heart's  action,  are  susceptible  of  a  complete  deductive  treat- 
ment, through  the  applications  of  Mechanics  and  Hydrostatics. 
This  is  well  exemplified  by  Dr.  Arnott,  in  his  *  Elements  of 
Physics.* 

Logical  Methods  of  Biology. 

10.  In  Biology,  the  facts  are  open  to  Observation  and 
to  Experiment ;  although  with  some  limitation  owing  to 
the  peculiarities  of  the  living  structure. 

The  difficulties  attending:  the  observation  of  livinsr  beino'3 
are  greatly  overcome  by  such  instruments  as  the  microscope, 
stethoscope,  laryngoscope,  ophthalmoscope,  &c.,  and  by  the 
chemical  examinations  of  the  various  products.  Accident 
sometimes  lays  open  the  interior,  as  in  the  case  of  Alexis  St. 
Martin,  through  whom  was  obtained  invaluable  results  as  to 
digestion. 

11.  Through  the  variety  of  the  cases  presented  by  Biology, 
there  is  great  scope  for  elimination  by  the  methods  of 
Agreement  and  Concomitant  Variations. 

The  means  of  varying  the  circumstances  by  the  comparison 
of  instances,  agreeing  and  yet  disagreeing,  is  very  extensive. 
From  the  number  of  different  vegetable  and  animal  species, 
each  structural  peculiarity  is  presented  under  the  greatest 
possible  variety  of  accompaniments.  And  this  is  only  one  part 
of  the  case.  In  every  individual  there  is  scope  for  additional 
comparisons  in  the  different  stages  of  its  existence,  the  method 
of  Embryology.  Lastly,  the  occurrence  of  monstrosities  still 
farther  contributes  to  the  desired  variation  of  circumstances. 
In  these  three  ways,  the  opportunities  of  plying  the  Methods 
of  Agreement  and  Concomitant  Variations  are  exceedingly 
multiplied. 

Thus,  an  examination  of  the  structure  of  the  eyes,  in  their 
rudimentary  types  in  the  lowest  animals,  and  in  their  succes- 
fiive  phases  of  growth  in  the  higher,  has  both  suggested  and 


CHANCE  AND   PROBABILITY. 


501 


proved  (as  some  believe)  that  an  eye  is  a  modified  portion  of 
the  skin. 

Mr.  Owen  enumerates  seven  different  modes  of  carrying  out 
comparisons  of  the  animal  structures  (Vertebrate  Animals, 
Vol.  I.  Preface). 

The  use  and  limits  of  the  Deductive  Method  in  Biology  have 
been  sufficiently  adverted  to  in  previous  remarks.  Some 
notice  may  be  taken  of  the  applications  of  Chance  and  Proba- 
bility. 

12.  There  are  many  biological  conjunctions  of  wide, 
but  not  of  uniform  concurrence.  Such  cases  must  be  dealt 
with  according  to  the  rules  for  the  Elimination  of  Chance. 

When  a  concurrence,  although  not  universal,  is,  neverthe- 
less, more  frequent  than  chance  would  account  for,  we  are 
bound  to  recognize  a  natural  tendency,  or  some  law  of  nature 
liable  to  be  defeated  by  other  laws.  For  example,  the  con- 
currence of  superiority  of  mental  power  with  superior  size  of 
brain,  although  liable  to  exceptions,  is  yet  very  general,  and 
far  more  than  chance  can  account  for.  Hence  we  must  regard 
this  as  an  established  law,  with  occasional  liability  to  be 
defeated.  We  are  not  at  liberty  to  predict  it  of  every  instance, 
but  only  with  a  probability  proportioned  to  the  observed  fre- 
quency as  compared  with  the  failures. 

13.  It  is  a  result  of  the  great  complicacy  of  vital  pro- 
cesses, that  many  inductions  are  but  approximately  true  ; 
and,  therefore,  are  to  be  reasoned  on  according  to  the 
principles  of  Probable  Evidence. 

The  prevalence  of  approximate  generalizations  is  a  mark  of 
the  increased  complicacy  of  the  Biological  processes,  as  com- 
pared with  the  processes  in  Phj^sics  and  in  Chemistry. 

The  best  that  can  be  done,  in  this  state  of  things,  is  to  ob- 
tain statistics  of  the  actual  occurrence  of  certain  conjunctions. 
There  is  a  large  department,  of  modem  creation,  termed  Vital 
Statistics,  which  enables  us  to  reason  on  vital  phenomena  with 
the  degree  of  probability  belonging  to  each  case.  It  is  thus 
that  we  can  infer  the  proportions  of  mortality  at  different  ages, 
and  the  proportion  of  male  to  female  births.  When  Agricul- 
tural Statistics  shall  have  been  continued  for  a  sufficient  time, 
the  recurrence  of  good  and  bad  harvests  will  be  capable  of 
being  stated  with  numerical  probabihty. 

14.  Many  of  the  propositions  of  Biology  are  defective  in 
numerical  precision. 


602 


LOGIC  OF  BIOLOGY. 


In  Physical  and  Chemical  facts,  it  is  usually  possible  to 
measure  numerically  the  degree  of  the  qualities.  •  Thus  most 
of  the  properties  of  a  mineral  can  be  stated  with  numerical 
precision ;  others,  as  colour,  and  fracture,  can  be  referred  to 
a  known  type.  But  when  we  say  a  certain  amoont  of  exercise 
strengthens  the  organs,  while  a  greater  amount  weakens  them, 
we  leave  the  estimate  very  vague.  Change  of  air  is  said  to 
invigorate  the  powers,  but  there  are  no  precise  reckonings, 
either  in  the  general  or  in  particular  cases,  of  how  much  invi- 
goration  may  be  expected  from  a  definite  change.  So,  the 
influence  of  altered  circumstances  on  breeds  and  on  races  is 
given  in  vague  indeterminate  language,  and  must  be  takea 
with  great  latitude. 

Hypotheses  of  Biologif. 

15.  The  character  of  the  science  requires  the  utmost 
aids  that  can  be  afforded  by  well-contrived  Hypotheses. 

Biology  has  all  the  difficulties  of  Molecular  Physics  and 
Chemistry  as  regards  the  impalpable  nature  of  the  constituent 
parts  in  living  bodies,  and  its  own  additional  complications 
from  the  organized  struct  are. 

The  hypotheses  of  Biology  are  of  all  the  varieties  enu- 
merated in  the  general  chapter  on  the  subject  (Induction, 
chap.  XIII.).  Some  assume  a  real  cause,  as  the  Development 
Hypothesis ;  others  assume  unreal  or  unknown  agencies,  as 
the  supposed  adherence  to  Type  or  plan;  a  third  class  would 
claim  to  be  Representative  assumptions. 

Of  the  first  class,  we  may  cite,  as  instances  involving  the 
smallest  amount  of  peril  in  the  assumption,  the  unverified 
deductions  from  general  laws  of  the  inorganic  world,  such  as 
the  molecular  and  chemical  laws.  These  powers  of  cohesion, 
adhesion,  solution,  osmose,  &c.,  are  assumed  as  operating  in 
the  living  body,  but  the  deduction  from  them  is  not  sufficiently 
exact  to  be  fully  verified.  Hence  there  is  much  that  is  hypo- 
thetical in  the  theories  of  oxidation,  of  animal  heat,  of  secre- 
tion, &c.  From  the  known  chemical  inertness  of  Nitrogen, 
Mr.  Herbert  Spencer  draws  some  remarkable  inferences  in 
explanation  of  the  vegetable  and  animal  processes  (Biology, 
I.  8). 

Development  Hypothesis. — This  renowned  speculation,  with 
all  its  boldness,  has  the  characters  of  a  legitimate  hypothesis ; 
it  assumes  a  real  agency,  a  vera  causa ;  its  difficulties  lie  in 
showing  that  the  supposed  agent  is  equal  to  the  vastness  of 
the  results. 


HYPOTHESES. 


603 


Properly  speaking  there  is  no  rival  hypothesis.  The  Special- 
Creation  view  is  a  phrase  that  merely  expresses  our  ignorance. 
Its  power  of  explanation  is  confined  to  making  a  comparison ; 
it  assigns  to  the  living  species  that  have  successively  appeared 
in  the  course  of  ages  the  same  mode  of  origin  as  the  earliest 
species  of  all,  and  as  the  whole  framework  of  the  universe  ;  an 
origin  that  must  for  ever  be  inconceivable  to  the  human  miad« 
As  the  physical  theorists  who  speculate  upon  cosmical  develop- 
ment— the  formation  of  suns  and  planets — start  with  the 
assumption  of  matter  spread  out  over  a  great  amplitude  of 
space,  and  coming  together  by  gravity,  so  the  biological  theo- 
rists assume  a  primeval  start,  either  of  living  broods,  or  of 
matter  ready  to  become  organized  under  particular  circum- 
stances. Now  the  value  of  any  scientific  explanation  of  life  is 
measured  by  its  capability  of  tracing  the  whole  of  organized 
nature  to  the  fewest  primitive  assumptions. 

The  modification  of  plants  and  animals  in  the  course  of 
generations  is  a  fact.  It  happens  even  in  the  same  external 
circumstances ;  while  under  alteration  of  circumstances,  the 
changes  become  vastly  greater.  Now,  if  any  means  can  be 
assigned  whereby  some  of  the  modified  forms  are  kept  alive 
while  all  the  others  perish,  the  deviations  are  rendered  per- 
manent. Mr.  Darwin  provides  an  instrumentality  of  this 
nature  in  what  he  calls  Natural  Selection,  or  the  preservation 
of  the  fittest  in  the  struggle  of  life.  It  has  been  his  endeavour 
to  accumulate  a  vast  multitude  of  facts  showing  the  principle 
in  operation,  many  of  them  inexplicable  on  any  other  supposi- 
tion. Herbert  Spencer,  Huxley,  Hooker,  Wallace,  and  others, 
have  contributed  to  the  support  and  elucidation  of  the  hypo- 
thesis. 

The  occurrence  of  allied  species  in  the  same  geographical 
area,  and  the  wide  difierences  in  character  of  the  species  in 
localities  widely  apart,  are  adapted  to  the  doctrine  of  deve- 
lopment and  not  to  any  other  view  as  yet  provided.  Again, 
says  Mr.  Darwin — 'How  inexplicable  is  the  similar  pattern  of 
the  hand  of  a  man,  the  foot  of  a  dog,  the  wing  of  a  bat,  the 
flipper  of  a  seal,  in  the  doctrine  of  independent  acts  of 
creation  !  how  simply  explained  on  the  principle  of  the  natural 
selection  of  successive  slight  variations  in  the  diverging 
descendants  from  a  single  progenitor!'  In  the  course  of 
time  and  change,  certain  parts  originally  useful  have  become 
superfluous ;  and  their  retention  in  the  useless  condition  ifl 
intelligible  only  on  a  hypothesis  of  descent. 

So  long  as  the  Development  Hypothesis  tallies  with  a  very 


504 


LOGIC   OF  BIOLOGY. 


large  number  of  facts,  and  is  not  incompatible  with  any,  it  is 
a  legitimate  and  tenable  bypotbesis ;  and  its  worth  is  propor- 
tioned to  the  extent  of  the  phenomena  that  it  explains,  com- 
pared with  those  that  it  fiails  to  explain. 

Hypothesis  of  Reproduction. — The  reproduction  of  each  living 
being  from  one  or  from  two  others,  through  the  medium  of  a 
small  globule  which  contains  in  itself  the  future  of  a  definite 
species,  is  the  greatest  marvel  in  the  whole  of  the  physical 
world  ;  it  is  the  acme  of  organic  complication. 

Mr.  Herbert  Spencer  and  Mr.  Darwin  have  recently  pro- 
mulgated hypotheses  to  represent  this  process.  (Spencer, 
Biology,  I.,  253  ;  Darwin,  Domestication,  II.,  357).  The  two 
views  have  a  good  deal  in  common,  and  might  be  taken 
together.  Mr.  Darwin's,  however,  ventures  farthest,  and 
may  be  here  quoted  as  exemplifying  a  biological  hypothesis. 
He  prepares  the  way  by  generalizing  all  the  different  modes 
of  reproduction — whether  unsexual  or  sexual.  The  nnsexual 
modes,  as  buds  and  fissure,  are  to  be  held  as  identical  with 
the  processes  for  maintaining  each  organ  in  its  integrity,  for 
the  growth  or  development  of  the  structure,  and  for  the 
restoration  of  injured  parts.  And  it  seems  to  be  a  tenable 
supposition  that  the  sexual  mode  of  reproduction  is  a  mere 
modification  of  the  same  general  fact. 

The  hypothesis  then  is  that  each  egg,  or  seed  (of  ihQ  female) 
and  each  spermatozoon,  or  pollen  grain  (of  the  male)  is  already 
a  vast  aggregation,  a  world  in  itself.  It  is  made  up  of  a  host 
of  smaller  bodies,  which  may  be  called  gemmules,  with  all  the 
properties  of  growth  or  reproduction  commonly  attributed  to 
cells  in  general ;  this  host  is  different  in  each  species.  For 
every  separate  part  of  the  animal  or  plant  to  be  formed,  down 
to  a  feather,  there  are  distinct  gemmules  of  the  type  of  that 
part,  and  unfolding  to  produce  it  by  ordinary  growth.  Every 
animal  contains  circulating  through  it  the  undeveloped  gem- 
mules of  all  its  organs,  and  parts  of  organs  ;  a  complete  set  is 
bound  up  in  the  ovum  of  the  animal  (or  plant),  and  by  due 
expansion  reproduces  the  new  individual  complete  at  all  points. 
Something  must  be  assumed  as  determining  them  to  fall  into 
their  places ;  but  that  there  is  no  absolute  fixity  in  this  respect, 
Mr.  Darwin  shows  by  the  frequent  occurrence  of  misplaced 
organs  ;  this,  he  thinks,  favours  the  view  of  the  multitudinous 
gemmules,  and  refutes  any  hypothesis  of  a  formed  microcosm 
existing  in  the  seed,  to  which  supposition  there  are  many  other 
hostile  facts. 

To  grasp,  reconcile,  and  generalize  the  facts,  is  an  ample 


HYPOTHESES. 


605 


jnatification  of  this  bold  venture ;  by  the  nature  of  the  case, 
we  can  never  hope  to  penetrate  the  precise  operation,  nor  yet 
to  arrive  at  a  supposition  that  shall  exclude  every  other.  It 
is,  however,  an  important  appendage  to  whatever  hypothesis 
may  be  formed  of  the  great  vital  fact  named  Assimilation. 


CHAPTER  V. 
LOGIC  OF  PSYCHOLOGY. 

1.  Psychology,  or  the  Science  of  .Mind,  comprises  both 
Mind  proper,  and  its  alliance  with  Matter,  in  the  animal 
body. 

Definition  of  Mind, 

2.  The  ultimate  antithesis  of  all  knowledge  is  called  the 
antithesis  of  Object  and  Subject. 

The  object  world  coincides  with  the  property  called  Exten- 
sion ;  whence  the  Subject,  or  Mind,  is  definable  by  antithesis 
as  the  Unextended.  A  tree  is  extended  ;  a  pleasure,  a  thought^ 
a  desire,  have  nothing  in  common  with  extended  things. 

3.  By  the  method  of  Particulars,  Mind  is  definable  as 
possessing  the  three  attributes  named  Feeling,  Volition, 
and  Intellect. 

Feeling  is  exemplified  by  pleasures  and  pains  ;  Volition  is 
action  prompted  by  Feelings  ;  Thought,  or  Intellect,  contains 
the  processes  known  as  Memory,  Reason,  Imagination,  &c. 

All  our  emotions  are  included  under  Feeling ;  our  sensa- 
tions are  partly  Feelings  and  partly  Intellectual  states. 

The  positive  definition  of  the  Mind  is  also  a  Division,  and 
must  conform  to  the  laws  of  Logical  Division. 

Concomitance  of  Mind  and  Body. 

4.  To  the  Definition  of  Mind,  we  must  add  the  Con- 
comitance of  the  Body. 

The  concomitance  of  Mind  and  Body  is  a  conjunction  alto- 
gether unique.  The  extreme  facts  of  human  experience — the 
subject  and  the  object,  mind  and  extended  matter — are  found 
in  union.     We  cannot  say  with  certainty  whether  the  nnionis 


606 


LOGIC   OF  PSYCHOLOGY. 


a  case  of  causation,  or  a  case  of  co-inheiing  attributes.     It 
stands  apart. 

5.  The  union  of  Mind  and  Body  must  hold  throughout 

While  many,  from  Aristotle  downwards,  have  held  that 
portions  of  the  mind  are  unconnected  with  bodily  processes, 
no  one  denies  that  mind  is  to  some  extent  dependent  on  the 
body.  But  all  have  failed  in  every  attempt  to  draw  a  line 
between  the  functions  that  are  dependent,  and  those  that  are 
supposed  independent  of  bodily  organs. 

6.  The  concomitance  of  the  two  radically  distinct 
phenomena  gives  the  peculiar  characteristic  of  the  science. 
Every  fact  of  mind  has  two  sides. 

Every  feeling  has  its  mental  side  known  to  each  one's  own 
consciousness,  and  its  physical  side,  consisting  of  a  series  of 
physical  effects,  some  superficial  and  apparent,  others  deep 
and  intricate. 

It  depends  upon  circumstances  whether,  and  how  far,  these 
physical  adjuncts  should  be  brought  forward  in  the  scientific 
exposition  of  the  mind.  On  the  one  hand,  if  they  are 
unvarying  in  their  concomitance,  they  can  hardly  be  excluded 
without  impairing  our  knowledge  of  the  mental  part.  On 
the  other  hand,  it  is  a  bare  possibility  that  the  mental  pheno- 
mena, being  radically  distinct  and  unique,  may  be  studied 
better  by  making  entire  abstraction  of  the  physical  accompani- 
ments. Moreover,  much  depends  upon  the  degree  of  insight 
actually  possessed  respecting  the  nervous  system  and  the 
various  organs  related  to  the  mind.  It  might  be  expedient  at 
one  stage  of  knowledge  to  drop  these  from  tlie  view,  and  at 
another  stage  to  take  them  up. 

In  point  of  fact,  until  the  present  century,  only  a  very  small 
number  of  philosophers  gave  systematic  attention  to  the 
physical  implications  of  mind  ;  the  chief  being  Plato,  Aristotle, 
Hobbes,  and  Hartley.  In  spite  of  the  crudity  of  their  know- 
ledge of  physiology,  they  all  (with  perhaps  the  exception  ot 
Plato)  gained  most  valuable  psychological  hints  by  means  of 
that  knowledge.  The  physiology  of  the  present  century 
having  placed  the  whole  subject  on  a  new  vantage  ground, 
the  attention  to  the  physical  side  may  be  expected  to  be  much 
more  rewarding. 

Thus,  on  one  side.  Psychology  is  a  department  of  Animal 
Biology,  and  subject  to  biological  laws.  The  all-pervading 
law  of  Persistence  of  Force  extends  to  the  physical  concomi- 


DEPINrnON  OF  MENTAL  PROPERTIES. 


507 


lants  of  mind,  and  is   pregnant  with   consequences  of  the 
utmost  practical  value. 

On  the  other  side,  Psychology  presents  a  unique  phenome- 
non— individual  self-consciousness — to  which  there  is  no 
forerunner  in  any  of  the  previously  enumerated  sciences. 
Still,  the  methods  and  spirit  of  scientific  enquiry,  as  exhibited 
in  these  other  sciences,  are  of  value  in  the  study  of  mind  in 
its  psychical  side.  States  of  consciousness  have  degrees  of 
intensity  and  duration ;  they  are  single  or  compound ;  they 
aid  or  thwart  one  another  ;  they  have  their  laws  of  emergence, 
increase,  decline ;  in  all  which  particulars  they  observe 
analogies  to  physical  forces  ;  so  that  the  intellectual  habits  of 
accurately  estimating  physical  agencies  may,  with  due  allow- 
ances, be  of  service  in  dealing  with  the  complications  of  mind. 

The  two-sidedness  of  the  phenomena  appears  in  language. 
The  terms  of  mind  had  all  an  objective  origin ;  and,  while 
some  of  them  have  now  an  almost  exclusively  subjective 
meaning — as  pleasure,  pain,  feeling,  thought,  sweetness,  fear, 
conscience,  remorse, — others  have  also  an  objective  reference, 
as  shock,  emotion,  excitement,  avidity,  irritation.  In  these 
last,  the  language  is  ambiguous ;  we  cannot  always  tell 
whether  the  physical  or  the  mental  is  aimed  at.  There  is, 
morover,  a  liability  to  represent  the  mental  fact  as  a  physical 
fact. 

Other  Notions  of  Psychology, 

Consciotisness. — The  most  difficult  word  in  the  human  voca- 
bulary. It  concentrates  in  itself  all  the  puzzles  of  metaphysics. 
If  it  were  strictly  synonymous  with  Mind,  it  would  be  defined 
accordingly.  But  the  object,  or  extended  world,  is  inseparable 
from  our  cognitive  faculties ;  so  that  a  word  that  expresses 
every  conscious  state  whatever  is  wider  than  mind,  strictly  so 
called  ;  it  comprises  both  matter  and  mind.  Hence,  if  *  con- 
sciousness '  be  the  name  for  all  sentient  states,  it  is  the  widest 
word  that  we  can  employ,  in  fact,  there  is  no  meaning  corre- 
sponding to  it ;  like  Existence,  it  is  a  fictitious  addition  of  the 
two  highest  genera.  To  state  these  separately,  we  must  have 
the  double  epithets  Subject-consciousness  and  Object-con- 
sciousness ;  which,  however,  give  only  the  meanings — Object 
and  Subject. 

Sensation. — A  word  with  several  distinct  meanings.  In  the 
first  place,  it  may  either  cover  the  physical  operations  con- 
nected with  the  exercise  of  our  senses,  or  it  may  be  restricted 
to  the  purely  mental  state  arising  therefrom.      In  the  next 


608 


LOGIC   OF  PSYCHOLOGY. 


ESSENTIAL  AND   REAL  PREDICATION. 


509 


place,  inasmuch  as  the  senses  give  us  feelings  in  the  purest 
form  (pleasures  and  pains)  and  also  intellectual  discrimina- 
tions, the  ground  work  of  our  ideas, — sensation  may  be  used 
for  either  class.  In  the  third  place,  there  is  a  contrast  of 
Sensation  with  Perception,  or  between  the  immediate  effect 
on  the  mind,  and  the  associated  effects  ;  colour  and  visible 
magnitude  are  sensations,  distance  and  true  magnitude  are 
perceptions. 

The  special  modes  of  sensation,  together  with  muscular 
feeling,  are  ultimate  states  of  the  mind,  to  be  defined  solely 
by  individual  reference.  Resistance,  Motion,  Warmth,  Diges- 
tive Sensibility,  Taste,  Smell,  Touch,  Hearing,  Sight, — as 
states  of  feelino:,  must  be  known  by  independent  experience. 

Emotion. — The  emotions  are  a  department  of  the  feelings, 
formed  by  the  intervention  of  intellectual  processes.  Several 
of  them  are  so  characteristic  that  they  can  be  known  only  by 
individual  experience  ;  as  Wonder,  Fear,  Love,  Anger.  These 
stand  very  near  the  ultimate  elements  of  human  feeling. 
Many,  however,  are  evidently  derived ;  such  are,  in  an  emi- 
nent degree,  the  -Esthetic  and  the  Ethical  emotions. 

Phases  of  Volition. — The  definition  of  the  Will,  or  Volition, 
is  a  part  of  the  definition  of  mind  as  a  whole.  Will,  as  con- 
trasted with  Feeling,  is  a  unity,  indivisible.  Yet,  there  are 
various  aspects  or  modifications  of  it,  that  receive  names. 
Motive  is  the  feeling  that  prompts  the  will  in  any  one  case ; 
the  motive  to  eat  is  the  pain  of  hunger,  or  the  pleasure  of  eat- 
ing, or  the  pain  of  defective  nutrition.  Deliberation  supposes 
conflicting  motives.  Resolution  is  a  volition  with  the  action 
adjourned.  Desire  is  ideal  volition,  either  as  preparatory  to 
the  actual,  or  in  lieu  of  it.  Belief  is  preparedness  to  act, 
for  a  given  end,  in  a  given  way. 

Intellectual  States. — In  the  Intellect,  we  have  three  fun- 
damental processes — Discrimination,  Similarity,  Retentiveness 
or  Revivability  ;  all  requiring  actual  experience  in  order  to  be 
understood.  Discritninationis  another  word  for  the  fundamental 
fact  called  Relativity  and  also  Contrast.  Similarity,  or  agree- 
ment in  difference,  is  a  distinct  fact  of  the  mind  ;  the  sensi- 
bility corresponding  to  it  is  unique ;  and  it  is  one  of  the  most 
iterated  of  human  experiences.  Eetentiveness  and  Kevivahilify 
describe  a  great  characteristic  of  our  mental  nature,  for  which 
we  have  other  designations,  as  Idea,  Memory,  Recollection  ;  it 
can  be  defined  only  by  reference  to  actual  experience  ;  al- 
though the  figurative  words — retention,  revival,  resuscitation, 
seem  to  be  a  definition  bv  the  medium  of  other  notions. 


The  complex  intellectual  faculties — Reason,  Imagination, 
&c.,  are  defined  each  by  its  proper  department  of  exercise; 
thus.  Reason  is  the  power  of  drawing  conclusions  from  pre- 
mises, or  the  scientific  faculty.  To  this  definition  may  be 
appended,  as  a  real  predicate,  the  derivation  from  the  ultimate 
intellectual  elements  just  named. 

Psychology  contains  scope  for  Classification,  both  according 
to  Logical  Division,  and  according  to  Ramification  or  Compo- 
sition. The  ultimate  sensibilities — namely,  the  Senses,  the 
elements  of  Intellect,  and  the  Simple  Emotions — are  classified 
as  genera  and  species,  and  according  to  Logical  Division. 
The  compound  faculties  and  sensibilities,  as  the  popularly 
named  Intellectual  Powers,  and  the  Complex  Emotions,  are 
classified  solely  by  Ramification ;  their  classes  do  not  comply 
with  Logical  Division. 

Propositions  of  Mind, 

7.  The  complexity  of  many  of  the  Notions  of  Mind 
gives  rise  to  Essential  Predications. 

Mind  itself  being  defined  (positively)  by  the  union  of  three 
distinct  and  irresolvable  characteristics,  there  may  be  proposi- 
tions affirming  the  concomitance  of  these  three  facts;  as 
Feeling  is  accompanied  with  Volition  and  with  Intelligence. 
When  we  say  that  Mind  (as  a  whole)  feels,  wills,  remembers, 
we  give  a  verbal  or  essential  predication. 

So  with  many  other  notions.  Such  simple  feelings  as  fear, 
love,  anger,  if  defined,  would  have  a  plurality  of  circumstances. 
That  such  circumstances  are  united,  may  be  a  real  predica- 
tion ;  but  when  any  one  of  them  is  predicated  of  the  name, 
the  proposition  is  essential.  *  Anger  makes  one  delight  in 
retaliation  '  is  a  purely  verbal  predication. 

Our  common  talk  on  mind  is  full  of  Essential  propositions. 
His  vices  were  condemned,  his  virtues  praised.  Prudence 
keeps  a  man  out  of  difficulties.  The  strongest  motive  deter- 
mines action. 

8.  The  conjunction  of  Mind  and  Body  is  a  real  predi- 
cation ;  it  being  understood  that  the  definition  of  Mind  is 
restricted  to  subjective  facts. 

This  holds  throughout  the  detail  of  feelings,  volitions,  and 
thoughts.  When  the  name  for  an  emotion  is  the  subject  of  a 
proposition,  and  the  physical  accompaniments  are  affirmed, 
the  predication  is  real : — *  Fear  depresses  the  vital  organs  *  is 


610 


PSYCHOLOGY   OF  LOGIC. 


LAWS   OF  MIND. 


511 


an  affirmation  of  concomitance.  *  The  hope  of  the  reward 
quickened  his  speed  '  conjoins  a  motive  to  the  will  (a  feeling) 
with  the  bodily  part  of  a  volantary  act. 

9.  The  three  leading  functions,  given  as  the  Definition 
of  Intellect  (Discrimination,  Agreement,  Eetentiveness), 
are  unfolded  in  predications. 

That  Mind  discriminates  is  an  Essential  proposition ;  yet  the 
fall  account  of  the  fact  of  Discrimination,  Relativity,  or  Con- 
trast, demands  numerous  prepositional  statements,  many  of 
them  real.  Not  to  re-iterate  the  double-sidedness  of  every 
mental  fact,  the  conditions,  circumstances,  and  limitations  of 
each  of  these  leading  properties  are  enounced  in  propositions 
that  are  in  no  sense  verbal. 

(1)  Thus,  we  speak  of  the  law  of  Belativity,  expressed  as 
the  concomitance  of  consciousness  with  change  of  impression. 
This  is  the  general  statement ;  and  constitutes  a  real  predication 
by  virtue  of  the  distinctness  of  the  two  facts— change  of  im- 
pression (physical,  in  great  part),  and  consciousness  (strictly 

mental). 

(2)  RetentivenesSy  Bevlvahilitijj  Contiguous  Association,  are 
names  for  a  fundamental  property  of  mind,  which  in  its  expo- 
sition takes  the  form  of  a  law.  A  certain  condition  or  situa- 
tion has  to  be  assigned  (the  reception  of  present  impressions), 
and  to  this  is  attached  as  a  real  predicate,  the  property  of 
being  retained,  revived,  remembered.  The  various  modifying 
circumstances  (engagement  of  attention,  physical  vigour,  <fcc.) 
are  real  propositions  in  subordination  to  the  main  principle : 
It  is  a  grand  generalization,  resuming,  explaining,  and  ren- 
derino"  precise  the  media  axiomata  of  acquisition,  as  regards 
intellectual  growths,  emotional  growths,  and  volitional  growths, 
Under  it  are  given  numerous  affirmations  as  to  the  derivation 
of  complex  phenomena  from  simpler,  the  unfolding  of  thoughts 
and  emotions,  and  the  evolution  of  the  mature  mind  from  its 
primary  elements.  This  is  commonly  called  the  Analysis  of 
the  Mind.  The  proof  of  such  assertions  rests  partly  on  the 
consciousness  of  the  hearer,  and  partly  on  indirect  reasonings. 
Thus,  the  proof  that  Beauty  is  a  compound,  and  not  a  simple 
Emotion,  is  that  we  can  consciously  identify  its  constituents. 
The  same  with  the  Moral  Sense.  The  indirect  proofs  are,  the 
absence  of  the  Feeling  prior  to  certain  opportunities  of  mental 
association.     (See  §  12.) 

(3)  The  Law  of  Similarity,  or  Agreement  in  Difference,  is, 
for  the  same  reasons,   an   inductive  generalization  of  real 


ooncomitanca  *  Present  states  of  feeling,  &c.,  tend  to  revive 
their  like  among  former  states,  notwithstanding  a  certain 
amount  of  difference.'  As  before,  there  are  required  many 
subsidiary  propositions  to  express  all  the  qualifying  circum- 
stances of  this  wide  generality. 

Another  important  law  of  the  mind  is  sometimes  described 
as  the  law  of  the  Fixed  Idea,  namely,  that  ideas  tend  to  act 
themselves  out ;  as  when  the  sight  of  yawning  makes  us  yawn, 
merely  by  giving  us  the  idea  of  the  act. 

10.  There  may  be  laws  of  the  rise,  continuance,  and 
subsidence  of  Feelings. 

The  connotation  of  each  distinct  mode  of  feeling,  whether 
sensation  or  emotion,  indicates  both  its  character  as  feeling, 
and  its  mental  antecedent.  The  laws  connecting  mind  and 
body,  predicate  its  physical  side  ;  the  laws  of  Relativity  and 
of  Retentiveness  contain  additional  predicates.  To  all  these 
may  be  added  inductions  as  so  the  rise,  continuance,  and  sub- 
sidence of  Feeling ;  which  laws,  like  every  other,  have  a  physical 
side,  and  may  possibly,  on  that  side,  be  generalized  into  still 
higher  laws. 

Like  all  sciences  where  simple  elements  contribute  to  form 
compounds,  Psychology  contains  affirmations  respecting  the 
composition  of  feelings  and  other  states.  The  assertion  is 
made,  for  example,  that  Beauty,  Conscience,  Imagination,  are 
not  simple  facts,  but  are  compounded  of  certain  assignable 
elements. 

Among  the  ordinary  predications  respecting  living  beino's, 
we  may  mention  the  passing  of  the  various  capabilities  into 
action.  This  extends  to  mind.  I  walk,  speak,  reason,  wonder, 
desire,  &c.,  are  examples ;  to  all  such  belongs  the  reality  of 
predication. 

Logical  MetJwds  of  Psychology, 

11.  In  Psychology,  special  importance  attaches  to  the 
ultimate  Analysis  of  the  phenomena. 

In  all  sciences,  we  desiderate  an  accurate  and  thorouo-h- 
going  analysis  of  the  phenomena.  It  is  only  an  ultimate 
analysis  that  can  be  the  groundwork  of  the  most  general  pre^ 
positions  respecting  them. 

In  proportion  to  the  difficulty  of  ascertaining  and  proving 
the  facts  in  detail,  is  the  value  of  an  ultimate  analysis,  whereby 
we  can  reduce  to  a  minimum   the   number  of  independent 


512 


LOGIC   OF   PSYCHOLOGY. 


LOGICAL  METHODS  IN  MIND. 


513 


assertions.  When  we  know  the  component  parts  of  an  Emo- 
tion, for  example.  Beauty,  the  Moral  Sentiment,  or  Veneration, 
we  can  apply  our  experience  of  the  parts  to  correct  and  con- 
firm our  experience  of  the  totals. 

12.  The  proof  of  a  Psychological  Analysis  is  (1)  the 
feeling  of  identity  between  the  compound  and  the  parts. 
This  must  be  a  matter  of  individual  self-consciousness. 

That  the  Moral  Sentiment  contains  a  feeling  of  obedience 
to  authority,  under  dread  of  punishment,  is  proved  by  each 
one's  being  conscious  of  the  presence,  in  the  compound,  of 
that  special  element. 

13.  An  Analysis  is  proved  (2)  by  the  identity  of  the 
consequences  and  collaterals  of  a  feeling.  This  will 
afford  an  Objective  proof. 

That  the  Religious  Sentiment  contains  an  element  of  Fear, 
is  proved  by  identity  in  the  Expression  and  the  Actions 
dictated  by  the  state. 

14.  The  greatest  difficulty  is  felt  in  establishing  the 
sufficiency  of  an  Analysis. 

This  is  a  difficulty  in  all  cases  where  there  is  great  com- 
plexity in  the  phenomena.  We  may  identify  the  presence  of 
certain  elements,  without  being  able  to  show  that  these  are 
the  whole.  Where  the  quantity  of  the  elements  can  be 
measured,  as  in  Chemistry,  we  can  prove  the  analysis  by 
casting  up  their  sum.  Where  quantity  is  not  exactly  esti- 
mable, as  in  many  biological  facts,  and  in  nearly  all  psycho- 
logical facts,  this  check  is  indecisive. 

For  example,  some  have  maintained  that  Benevolence  is 
exclusively  made  up  of  self- regarding  elements.  Others, 
while  admitting  the  presence  of  these  elements,  deny  that 
they  account  for  the  whole.  Owing  to  the  vagueness  of  our 
estimates  of  quantity  in  mind,  the  dispute  cannot  be  decided 
by  a  process  of  summation  in  ordinary  cases.  We  must 
proceed  by  vaiying  the  circumstances,  and  by  finding 
instances  where  self-regarding  elements  are  either  wanting,  or 
so  small  in  amount,  as  to  be  obviously  unequal  to  the  effect 
produced.  Such  an  instance  is  found  in  the  pity  called  forth 
by  the  punishment  of  great  criminals. 

15.  The  Inductions  of  Mind  bring  into  play  the  Experi- 
mental Methods. 


The  great  Law  of  Concomitance  of  Mind  and  Body  must  be 
proved  by  the  Method  of  Agreement.  We  must  show  that 
the  whole  of  the  facts  of  mind— Feelings,  Volitions,  Thoughts, 
are  at  all  times  accompanied  by  bodily  processes.  The  case 
has  something  of  the  peculiarities  of  the  Law  of  Causation. 
We  can  prove  the  concomitance  in  a  vast  number  of  cases ; 
while  in  many  mental  exercises,  as  in  meditative  reflection, 
the  physical  processes  almost  escape  detection  from  their 
subtlety.  These  instances,  however,  although  unable  to 
confirm  the  proposition,  are  not  opposed  to  It;  and  they 
do  nothing  to  invalidate  the  force  of  the  unequivocal  in- 
stances. 

We  can  do  more  than  establish  a  law  of  concomitance  of 
mind  and  body  generally.  We  can,  by  the  methods  of  Elimi- 
nation, ascertain  the  exact  bodily  processes  connected  with 
mental  processes.  On  this  determination,  we  can  bring  to 
bear  all  the  Experimental  Methods. 

The  Law  of  Relativity  is  established  by  Agreement,  and,  in 
a  remarkable  manner,  by  Concomitant  Variations. 

The  Intellectual  Laws,  called  Retentiveness  and  Similarity, 
are  established,  both  in  general  terms,  and  as  respects  their 
peculiar  conditions,  by  all  the  methods. 

16.  From  the  circumstance  that,  in  Psychology,  we  have 
attained  to  laws  of  high  generality,  there  is  great  scope  for 
the  Deductive  Method. 

While  every  one  of  the  great  laws  above  enumerated  is 
fruitful  in   deductive  applications,  the  instance  that  perhaps 
best  exemplifies  the  Deductive  Method  of  enquiry,  considered 
as  a  supplement  to  Induction,  is  the  Law  of  Conservation  or 
Correlation,  applied  to  Mind,  through  the  physical  supports. 
By  this  law,  every  mental  act  represents  a  definite,  although 
not  numerically  expressible,  physical  expenditure,  which  must 
be  borne  by  the  physical  resources  of  the  system.     The  deduc- 
tive  consequences   of    this   fact   are   innumerable.       A   few 
instances  may  be  briefly  suggested.     Great  mental  labour  or 
excitement  is  accompanied  by  corresponding  physical  waste, 
which  is  so  much  subtracted  from  the  total  of  the  physical 
forces  available  for  the  collective  necessities  of  the  system. 
Again,  great  expenditure  in  one  mode  of  mental  exertion,  if  not 
at  the  expense  of  the  more  properly  bodily  functions,  is  at  the 
expense  of  other  mental  functions  ;  and  so  on.     Now  to  such 
cases,  we  may  apply  the  deductive  process,  in  all  its  stages ; 
there  is  a  prior  Induction,  there  may  be  a  process  of  Calcula- 


t  flfv 


514 


LOGIC   OF  PSYCHOLOGY. 


HYPOTHESES. 


515 


tion  so  far  as  the  case  admits  ;  there  should  be  a  Verification, 
both  from  isolated  facts  and  from  empirical  laws. 

These  Deductive  applications  are  a  valuable  check  upon  the 
loose  empiricisms  so  abundant  in  the  treatment  of  mmd,  and 
are  the  best  testimony  to  the  use  of  a  science  of  psychology, 
in  spite  of  its  imperfections.  There  are  empirical  generaliza- 
tions on  the  points  just  alluded  to,  namely,  the  incompatibility 
of  great  expenditure  in  one  direction  of  effort,  with  great 
expenditure  in  other  directions.  Now,  by  the  Law  of  Conser- 
vation, such  empiricisms  receive  their  definite  limitations,  and 
the  exceptions  are  fully  accounted  for. 

17.  The  Psychological  mystery  of  the  union  of  Mind 
and  Body  is  the  severest  test  of  logical  Explanation. 

Enough  was  said  in  this  head,  under  the  chapter  relating  to 
Explanation. 

Empirical  and  Derivative  Laws  in  Mind. 

18.  There  are  in  Mind  many  Empirical  Laws,  but,  as  a 
consequence  of  the  attainment  of  high  generalities,  there 
are  also  Derivative  Laws. 

From  the  complication  of  the  physical  adjuncts  of  mind, 
considered  as  the  culmination  of  Biology,  we  may  expect 
many  of  the  Inductions  to  be  purely  empirical,  and  as  such 
narrowly  limited  in  time,  place,  and  circumstances. 

The  phenomena  of  Dreaming  can  be  stated  only  as  Empirical 
Laws,  with  a  certain  aid  from  hypothesis. 

We  have  only  pure  empiricisms  to  express  the  operation  of 
stimulating  drugs  upon  the  emotional  states  ;  whereas  the 
laws  that  state  the  operation  of  food  or  mutrimont  can  be 
derived. 

Hence,  a  very  great  number  of  the  inductions  of  mind  may 
be  traced  as  Derivations  of  these  higher  laws,  whereby  they 
attain  a  greater  certainty  and  compass  of  application.  All 
the  rules  for  aiding  memory  are  easy  deductions  from  the 
great  law  of  Retentiveness.  The  effects  of  Novelty,  and  Con- 
trast, are  derived  from  the  Law  of  Relativity. 

Strictly  speaking,  the  supreme  laws  of  mind — Relativity; 
Retentiveness,  Similarity,  &c.,  are  but  a  high  order  of  em- 
piricisms. They  are  not  ultimate  laws  of  nature,  lika 
Gravity  and  the  Persistence  of  Force.  They  are,  however, 
exliaustively  verified  through  the  whole  of  mind ;   and  are 


applicable  in  accordance  with  the  extent  of  their  verification. 
We  properly  treat  them  as  the  highest  or  ultimate  laws  of  the 
department,  and  employ  them  deductively  in  tracing  out 
derivative  laws. 

Hypotheses  in  Mind. 

19.  The  principal  examples  of  Hypotheses,  in  the  logical 
sense,  are  to  be  found  in  the  great  problems  of  analysis — 
namely,  Innate  Ideas,  External  Perception,  and  the  Will. 

Perhaps  the  instance  most  in  point  is  Perception.  On  this 
subject,  there  prevails  the  assumption  of  an  independent 
material  world  and  a  series  of  independent  minds,  brought 
into  mutual  contact ;  an  assumption  that  has  the  great  recom- 
mendation of  easily  and  simply  expressing  all  the  common 
phenomena.  It  has,  however,  the  serious  drawback  of  being 
self-contradictory  ;  whereas  the  view  that  avoids  the  con- 
tradiction is  lumbering  and  unmanageable  in  its  application  to 
express  the  facts,  and  hence  the  backwardness  to  receive  it,  as 
a  substitute  for  the  other. 

This  is  an  extreme  case  of  a  hypothesis  believed  solely  be- 
cause it  squares  with  the  appearances.  Not  only  is  there  an 
absence  of  proof  otherwise,  but  there  is  flagrant  self-contra- 
diction, which  ought  to  be  considered  as  a  complete  disproof. 

Among  the  unexplained  phenomena  of  mind,  we  are  to  in- 
clude Dreaming.  One  hypothesis  on  this  subject  is  a  real 
cause,  namely,  the  partial  activity  or  wakefulness  of  the  brain. 
It  is  a  fact  well  established  that  the  brain  may  be  either  alive 
or  dormant  in  all  degrees.  Now  if  we  assume  wakefulness  in 
certain  partSy  and  dormancy  in  others,  we  may  account  for 
many  of  the  appearances  of  dreaming,  sonnambulism,  and 
mesmerism.  The  hypothetical  element  is  the  selection  of  the 
parts,  namely,  the  senses,  and  the  centres  of  voluntary  move- 
ment. The  coincidence  of  the  facts  with  what  would  follow 
on  this  assumption  is  a  considerable  probability  in  favour  of  the 
hypothesis. 

It  is  a  well-known  fact  that  when  a  chain  of  ideas  has  often 
passed  in  succession,  and  when  the  last  link  of  the  chain  is 
more  important  than  the  intermediate  links,  we  pass  at  once 
from  the  first  to  the  last,  the  others  not  appearing  in  conscious- 
ness at  all.  The  oblivion  has  been  the  occasion  of  various 
hypotheses.  (1)  According  to  Stewart,  the  intermediate  steps 
are  passed  so  rapidly  as  to  be  forgotten.  (2)  According  to 
Hamilton,  it  belongs  to  the  class  of  latent  mental  processea 


516 


LOGIC   OF  CHARACTER. 


(3)  According  to  J.  S.  Mill,  there  is  a  direct  association  formed 
between  the  first  and  the  last,  and  the  others  disappear  alto- 
gether from  the  chain.  All  the  three  suppositions  refer  to 
real  agencies ;  all  might  operate  in  the  case  supposed.  Con- 
sequently, the  decision  turns  upon  whether  the  elTect  of  any 
one  is  exactly  equal  to  the  effect  observed.  Allowing  for  the 
standing  difficulty  of  computing  mental  forces,  we  may  say 
that,  on  the  whole,  the  last  most  nearly  coincides  with  the 
phenomenon. 

The  exact  character  of  the  human  mind  at  birth  is  a  hypo- 
thesis of  the  second  class  of  scientific  hypothesis,  a  fictitious 
representation  that  has  no  gi'oundwork  but  fitness  to  express 
the  subsequent  manifestations. 

The  minds  of  other  human  beings  and  of  animals  are  con- 
ceived by  us  hypothetically  as  expressing  the  appearances  upon 
the  analogy  of  our  own  conscious  experience. 

Chance  and  Probability  in  Mind, 

20.  The  complications  of  .the  phenomena  of  Mind  pre- 
vent us  from  attaining  laws  of  universal  application.  In 
many  instances,  we  must  state  our  propositions  as  more 
or  less  Probable. 

The  influence  of  Education  is  not  in  all  instances  certain. 
The  Law  of  Retentiveness  is  sure  in  its  operation,  but  its 
various  complicated  conditions  may  not  always  be  complied 
with.  A  training  in  good  conduct,  in  most  cases,  but  not  in 
all,  makes  a  good  moral  character ;  a  training  in  vice  is 
generally,  but  not  uniformly,  perverting.  Adversity,  in  many 
instances,  but  not  in  all,  improves  the  disposition. 

LOGIC   OF  CHARACTER. 

21.  The  Scie:^ce  of  Character  has  reference  to  the 
proportionate  development  of  the  sensibilities  and  powers 
in  different  Individuals.  It  presupposes  the  Science  of 
Mind. 

Human  beings  in  general  have  certain  susceptibilities  to 
Feeling,  powers  of  Volition,  and  aptitudes  of  Thought ;  all 
which  possess  degree,  and  may  be  unequally  manifested  in 
different  persons.  Hence,  an  individual  mind  is  not  suffi- 
ciently described  by  its  participation  of  our  universal  mental 
nature  ;  but  must  be  represented  according  to  the  proportion- 
ate development  of  the   several   Feelings,  (&c.,  common   to 


BASIS  OF  THE  SCIEIflCE   OF  CHARACTER. 


517 


humanity.     We  are  all  liable  to  Fear ;  we  all  possess  Tender 
Affection  ;  but  some  more,  some  less. 

It  is  impossible  to  state  these  pecaliarities  of  character 
except  in  the  language  applicable  to  mind  universally  ;  or  to 
analyze  a  character  without  having  first  analyzed  the  mind. 

The  basis  of  any  Science  of  Character  must,  therefore,  be 
the  ultimate  analysis  of  the  Mind.  There  should  be  ascer- 
tained, as  far  as  possible,  the  native  and  irresolvable  Feelings, 
and  the  attributes  of  Volition  and  of  Thought.  K  a  mind 
were  like  a  mineral,  the  statement  of  the  degrees  of  these 
various  fundamental  attributes  would  be  the  account  of  a 
character.  But  the  mind  is  a  thing  of  indefinite  growth, 
adaptation,  acquisition ;  its  first  cast  is  greatly  altered  before 
the  end ;  and,  as  what  we  usually  desiderate  is  the  character 
of  a  full-grown  man  or  woman,  we  must  provide  an  account 
of  the  acquired,  as  well  as  of  the  native  powers. 

The  proper  view  to  take  of  Phrenology  is  to  regard  it  as  a 
Bcience  of  Character,  accompanied  with  a  theory  of  external 
indications.  It  furnishes  a  professedly  ultimate  Analysis  of 
the  Mind.  It  farther  endeavours  to  connect  each  mental 
power  or  susceptibility  with  a  local  habitation  in  the  brain, 
outwardly  manifested  by  the  shape  of  the  head.  This  addi- 
tion, although  highly  convenient,  is  not  necessary  to  constitute 
a  science  of  character. 

22.  In  the  description  of  characters,  there  is  obviously 
wanted  a  scale  of  degree. 

The  difficulties  attending  the  quantitative  eptiimate  of  mind 
are  a  serious  drawback  in  the  science  of  character.  Yet  it  is 
impossible  not  to  make  the  attempt  to  distinguish  more  and 
less  in  the  various  mental  attributes. 

The  ordinary  mode  of  procedure  is  this.  In  each  separate 
peculiarity — emotional,  volitional  and  intellectual — we  form 
an  estimate  of  the  general  average  of  persons  known  to  us. 
Above  and  below  this  average,  we  use  the  indefinite  adjectives 
of  quantity, — much,  great,  very  great,  small,  very  small,  defi- 
cient, and  so  on. 

The  scale  of  Phrenology  includes  a  wide  range  of  degrees, 
probably  beyond  what  can  be  practically  discriminated  and 
agreed  upon. 

Our  most  correct  appreciations  of  quantity  in  mind,  rest 
npon  an  objective  basis.  Thus,  a  slow  learner  can  be  com- 
pared with  a  moderate  or  a  quick  learner,  through  the  lengths 


518 


LOGIC  OF  CHAKACTER. 


INFLUENCES  ON  CHARACTER. 


519 


\ 


^^ 


of  time  required  by  each  for  a  given  amount  of  acqui- 
sition. This  objective  method  admits  of  a  considerable 
amount  of  precision,  and  is  the  chief  hope  of  attaining 
quantitative  accuracy  in  the  Science  of  Mind. 

23.  The  native  Elements  of  Character  would  be  con- 
veniently represented  under  the  three  heads — Activity, 

^    Feeling  (Emotional),  Intellect. 

The  detailed  account  of  these  elements  is  the  adaptation  of 
+he  psychological  analysis  of  the  mind,  to  the  statement  of  the 
basis  of  character. 

The  mental  elements  might  be  prefaced  by  an  account  of 
the  important  physical  organs  implicated  in  mental  processes, 
so  far  as  regards  their  physical  characteristics.  The  Brain, 
the  Muscular  System,  the  Digestive  System,  &c.,  of  each 
individual,  might  be  regarded,  in  the  first  instance,  from  the 
objective  side,  or  as  viewed  by  the  physiologist  and  physician. 
These  organs  have  all  bearings,  direct,  or  indirect, on  character. 

In  recounting  the  native  elements  of  Activity,  Feeling,  and 
Thought,  we  need  to  single  out  for  special  consideration  the 
Intellectual  Retentiveness,  as  being  the  expression  of  the 
possibilities  of  growth,  acquisition,  or  education.  This  is  the 
foremost  law  of  mind,  with  reference  to  the  moulding  or 
Formation  of  Character,  the  means  of  transforming  the  various 
native  tendencies  into  an  artificial  cast.  The  educability  of  a 
character  needs  to  be  looked  at  by  itself ;  a  thing  only  to  be 
determined  by  actual  experiment  of  the  progress  in  given  cir- 
cumstances. The  schoolmaster,  after  a  certain  length  of  pro- 
bation, judges  whether  a  pupil  will  succeed  in  Mathematics,  in 
Language,  or  in  Drawing. 

24.  In  estimating  Character,  whether  in  fact  or  in 
expectation,  we  must  never  drop  out  of  sight  the  Law  of 
(Conservation,  under  the  guise  of  the  Limitation  of  the 
Powers. 

The  accurate  judgment  of  an  individual  either  as  exhibited 
at  any  one  time,  or  as  regards  the  possibilities  of  transforma- 
tion, must  depend  upon  the  precision  of  our  allowance  for  the 
Limitation  of  the  Powers.  Dealing  with  persons  averagely 
constituted,  we  cannot  expect  a  development  above  average 
in  one  region  without  a  falling  off  in  some  other  ;  and  so  on, 
through  all  varieties  of  assumption  as  to  the  extent  of  the 
powers  on  the  whole,  and  as  to  the  proportions  of  each. 


25.  The  subordinate  laws  of  Character  are  the  statement 
of  the  operation  of  Circumstances  on  the  Formation  of 
Character.  These  must  be  handled  in  detail,  under  the  con- 
fluent lights  of  actual  experience  and  of  the  superior  laws. 

The  circumstances  that  influence  character  are  various  and 
inexhaustible.  They  afford  a  wide  exemplification  of  Induc- 
tion coupled  with  Deduction— Empirical  Laws  transferred 
into  Derivative.  They  also  exemplify  the  prevailing  laxity  in 
the  use  of  the  method  of  Agreement. 

The  leading  circumstances  are  such  as  these  : — 

I.  The  physique  of  the  individual,  viewed  from  its  purely 
physical  side  ;  the  comparative  strength  or  weakness  of  the 
different  physical  organs.  A  whole  series  of  consequences 
to  the  character  follow  from  the  purely  physical  endowments. 
Great  muscular  strength  gives  a  certain  direction  to  the  activi- 
ties and  pursuits,  whatever  be  the  proper  mental  tendencies. 

II.  The  physical  treatment  of  the  system,  in  all  that  regards 
nourishment  and  the  adjuncts  of  health.  The  consequences 
of  these  are  the  greater  or  less  total  of  foice,  to  be  distributed 
among  the  various  functions,  including  the  supports  of  mind. 
Climate,  town  or  country  life,  poverty  or  affluence,  indulgence 
or  temperance,  are  obvious  elements  of  this  computation. 

III.  Natural  surroundings,  as  they  affect  the  mind  —  the 
activities,  feelings,  or  intelligence.  Differences  have  often  been 
pointed  out  as  between  mountaineers  and  tenants  of  the  plains, 
between  sea-faring  nations  and  those  in  the  interior  of  conti- 
nents, between  rural  and  urban  populations.  Not  much 
precision  has  as  yet  been  gained  in  the  expression  of  those 
differences.  But,  if  studied  by  the  doable  method  of  induction 
and  deduction,  they  may  yield  important  lasvs. 

It  is  a  clear  deductive  truth  that  variety  of  impressions  must 
enlarge  the  compass  of  the  intellect.  It  is  not  so  obvious  what 
will  be  the  effects  on  the  feelings ;  the  aesthetic  sensibilities, 
for  example,  are  not  quickened  by  nature  alone  ;  they  usually 
need  another  stimulus.  Incessant  familiarity  with  scenes  of 
grandeur  has  less  effect  (on  the  Law  of  Relativity)  than  alter- 
nation of  these  with  others  of  a  tamer  sort. 

rV.  Modes  of  Industry,  or  habitual  occupation,  give  a 
notorious  bent  to  the  character.  The  effects  of  occupation  or 
profession  have  been  a  subject  of  frequent  observation  ;  many 
of  the  consequences  being  apparent.  The  soldier,  the  sailor, 
the  tiller  of  the  ground,  the  trader,  the  priest,  have  each  the 
Btamp  of  their  calling, 

23 


520 


LOGIC   OF  CHARACTEB. 


V.  The  Surrounding  Society  moulds  the  individual  as  to 
feelings,  and  as  to  modes  of  thinking,  in  ways  too  numerous 
to  exhaust,  but  yet  capable  of  being  stated  with  remarkable 
precision.  The  inductive  empiricisms  on  the  one  hand,  and 
the  deductive  principles,  on  the  other,  conspire  to  express  the 
remarkable  assimilation  of  the  individual  to  the  society; 
while  it  is  not  difficult  to  point  out  its  limitations,  the  circum- 
stances being  given.  The  religious,  ethical,  and  political 
opinions  of  each  person  are,  in  the  great  mass  of  cases,  the 
exact  reflex  of  what  prevails  in  the  society  about  him. 

VI.  The  express  Education  given  by  the  schoolmaster 
should  be  added  to  the  moulding  influence  of  general  society. 
This  element  admits  of  being  clearly  stated.  A  people 
sent  regularly  to  school  like  the  Scotch,  or  the  Germans, 
acquires  a  distinct  superiority  of  intellectual  and  moral 
character.  Under  this  head,  attention  must  be  paid  to  the 
educational  influence  of  Institutions  ;  as,  for  example,  an 
established  church. 

VII.  The  amount  of  Liberty  permitted  to  individuals  by 
the  state,  and  by  society,  has  a  vast  influence  on  character. 
The  revolutions  that  have  achieved  enlargements  of  individual 
freedom,  as  the  Protestant  Reformation,  are  experiments  of 
Difierence,  showing  the  impetus  given  to  progress  by  Liberty. 

Political  freedom  is  not  exactly  the  same  thing  as  Self- 
government,  but  is  not  complete  without  that  addition.  This 
too  is  an  instrumentality  for  moulding  the  character. 

VIII.  Many  Social  Institutions,  Laws  and  Customs,  apart 
from  the  general  fact  of  Freedom  with  Self-government, 
exercise  on  character  an  influence  that  may  be  studied  and 
assigned.  The  tenure  and  descent  of  Property,  the  Marriage 
Laws,  improved  means  of  Communication,  are  obvious  in- 

From  the  foregoing  remarks,  will  sufficiently  appear  the 
Notions,  the  Propositions,  and  the  logical  Methods  of  the 
science  of  Character.  It  will  be  advisable,  farther,  to  note 
the  heads  of  Classification  ;  which  will  serve  as  an  important 
preparation  for  the  Logic  of  Politics. 

Classification  of  Characters, 

26.  The  classification  of  Characters  is  not  a  proper 
classification  according  to  the  Natural  History  mode. 

We  could  not,  except  by  a  useless  fiction,  arrange  charac- 
ters in  Orders,  Gen-rfi  and  Species.     The  real  distinction  be- 


PECULIABITIES  OF  CHAEACTER. 


521 


tween  characters  is  expressed  by  the  higher  or  lower  deoree 
of  some  one  or  more  of  the  ultimate  elements  of  character. 
And  we  do  not  find  characters  agreeing  in  a  plurality  of 
common  attributes,  excepting  so  far  as  the  elevation  of  one 
peculiarity  implies  the  depression  of  some  others  ;  and  hence 
we  have  no  basis  of  generic  or  specific  agreements.  The  only 
possible  way  of  giving  an  exhaustive  account  of  characters  is 
to  assume  by  turns  a  higher  degree  of  each  peculiarity- 
Active,  Emotional,  Intellectual,  and  to  state  the  appearances 
connected  with  that ;  whence  by  obverse  inference  we  could 
gather  the  concomitants  of  the  low  degree  in  each  case. 
Thus,  we  could  indicate  the  general  consequences  of  an  unusual 
pitch  of  Natural  or  Spontaneous  Energy  ;  of  the  Emotional 
Temperament  on  the  whole,  and  of  any  of  the  special  suscep- 
tibilities to  Feeling  or  Emotion,  as  Organic  Sensibilitv,  Sio-ht. 
Tender  Emotion.  J*      o   ^ 

There  is  no  limit  to  the  possible  modes  and  varieties  of 
character  arising  out  of  the  conjunctions  of  different  faculties 
in  excess  or  in  defect.  These  conjunctions,  however,  must  be 
governed  by  the  laws  of  their  elements;  so  that  their  explana- 
tion is  purely  deductive,  under  the  check  of  actual  cases. 

27.  The  details  of  Character  are  thus  the  account  of  the 
separate  peculiarities,  followed  by  the  analysis  and  expla- 
nation of  such  select  conjunctions  as  are  often  found,  and 
are  of  practical  importanca 

Under  the  head  of  Action,  we  have  important  varieties — as 
indolence,  general  or  partial,  fitfulness  of  energy,  and  steady 
persistence.  The  Emotional  character  is  yet  more  varied  • 
under  it  we  have  the  dispositions  expressed  by  sensual,  sensu- 
ous, sociable,  reverential,  irascible,  egotistical,  and  so  on. 
The  aspects  of  Intellect  are  more  numerous  still ;  general 
ability,  general  stupidity,  aptitude  for  language,  for  science, 
tor  art,  for  business,  and  many  other  still  more  special  modes. 
The  attributes  involved  under  Conscience  are  a  very  mixed 
product.  That  predominance  of  the  Love  of  Gain— manifested 
from  ancient  times  by  the  Jews,  and  in  modern  times  by  the 
English,  and  the  peoples  sprung  from  them — ought  to  bo 
traceable  to  constitutional  foundations  coupled  with  circum- 
stances.   The  sense  of  Dignity,  united  with  respect  for  the 

Forms  of  Law,  and  the  regard  to  the  Practical  and  Concrete 

as  combined  in  the  ancient  Roman— ofier  an  interesting  subject 
for  analysis  and  explanation. 


522 


LOGIC   OF   MINERALOGY. 


The  distinctive  characters  of  the  Sexes  are  to  be  sought 
by  the  same  analytic  procedare.  These  refer  us  to  physical 
foundations,  as  well  as  to  mental  elements  and  to  the  opera- 
tion of  circumstances,  ^ 

The  problems  of  character  take  a  practical  shape  in  Educa- 
tion ;  being  an  enquiry  into  the  means  of  moulding  character 
according  to  prescribed  types— Active,  Emotional,  Intellectual. 
The  experience  of  the  educator  is  the  verification  of  the 
deduced  maxims. 

Under  the  Logic  of  Politics,  there  will  be  a  further  occasion 
for  applying  the  science  of  character. 


CHAPTER  YI. 
SCIENCES  OF  CLASSIPICATIOK. 

Mineralogy. 

1.  Mineralogy  is  a  Concrete,  Descriptive,  Classificatory 
science,  referring  to  the  solid  inorganic  constituents  of  the 

globe. 

A  Mineral  is  defined  as  a  solid  homogeneous  body, 
having  a  definite  chemical  composition  and  a  definite 
onjstalline  form. 

Mineralogy  brings  forward  no  new  laws  or  operations.  It 
merely  applies  mathematical,  physical,  and  chemical  laws  to 
the  inorganic  solid  constituents  of  the  globe.  Moreover,  it  is 
not  so  much  engaged  in  tracing  physical  sequences  as  in 
arranging  and  classifying  the  multitudinous  materials  we  find 
in  the  earth's  crust.  Its  laws  are  laws  of  co-existence,  as 
Co-inherence  of  Attribute. 

The  science  of  xMineralogy  is  in  close  connexion  with 
Chemistry.  Had  Chemistry  attained  its  present  advanced 
shape  at  an  earlier  period,  there  might  have  been  no  separate 
science  of  minerals.  But  for  the  comprehensive  treatment  of 
all  material  elements  whatsoever,  under  Chemistry,  there 
might  be  an  objection  to  the  exclusiveness  of  Mineralogy,  m 
refusing  to  take  account  of  liquid  and  gaseous  bodies,  as 
water  and  air.  Yet,  seeing  that  all  these  are  sufficiently  given 
in  Chemistry,  there  is  no  need  for  repeating  them  in  another 


siftftA^JArf^iA  iSi^Mii^ 


MINERALS  DEFINED. 


523 


fcience  ;  and  Mineralogy  retains  its  special  and  restricted 
scope,  which  is  to  treat  of  substances  presenting  form  as  well 
as  definite  composition. 

The  chief  advantage  of  detaching  Mineralogy  from  Chemis- 
try is  to  enable  minerals  to  be  more  fully  described  in  their 
minute  varieties,  and  to  be  more  comprehensively  classified. 
The  separation  relieves  Chemistry  of  a  burden,  and  allows  a 
fresh  start  in  the  process  of  classifying. 

Definition  of  a  Mineral. — Into  the  definition  of  a  mineral, 
two  main  facts  enter,  and  these  dictate  the  whole  plan  of  the 
science : — Chemical  Composition  and  Crystalline  Form.  As 
regards  the  first  point,  minerals  are  either  simple  bodies  or 
chemical  compounds ;  and  as  chemical  compounds,  they  must 
be  homogeneous  substances,  and  not  conglomerations  of 
difforeut  material  like  a  piece  of  pudding  stone  or  of  granite ; 
such  conglomerates  are  not  minerals  but  roclis ;  quartz  is  a 
mineral,  gneiss  is  a  rock. 

As  regards  the  second  part  of  the  definition,  minerals  have 
a  definite  Form ;  a  fact  associated  with  their  homogeneous 
character.  The  simple  substances  in  their  purity,  and  the 
definite  chemical  compounds,  when  in  their  highest  degree  of 
consolidation,  assume  definite  crystalline  shapes;  and  the 
occurrence  of  these  shapes  is  a  further  guarantee  of  the  homo- 
geneous nature  of  the  material,  allowance  being  made  for 
the  property  called  isomorphism,  or  the  existence  of  similar 
forms  in  diflerent  materials,  which  permits  of  their  crystallizing 
together. 

The  definition  excludes  clay,  sand,  and  soils,  these  bring  for 
the  most  part  heterogeneous,  as  well  as  formless. 

The  deposits  from  organic  bodies,  as  coal,  amber,  and 
mineral  resins,  are  improper  minerals  ;  they  have  neither 
parity  nor  form. 

I.  Arrangement  of  Mineral  Characters. 

2.  The  exhaustive  statement  of  Characters,  in  Minera- 
logy, is  substantially  the  same  as  in  Chemistry. 

Under  the  Logic  of  Chemistry,  we  discussed  the  guiding 
principle  of  arrangement  of  characters,  namely,  to  follow  the 
expository  order  of  the  properties  :  from  which  was  deduced 
the  following  sequence. 

I.  Crystalline  Form, 

II.  Optical  properties,  including  Refraction,  Double  Refrac- 
tion and  Polarization  ;  Colour  j  Lustre. 


524 


LOGIC  OF  MINERALOGY. 


BASIS  OF  MINERAL  CLASSIFICATION. 


525 


ni.  Specific  Gravity.  m         •       i?i 

IV.  Cohesive  properties,  namely,  Hardness,  Tenacity,  Elas- 
ticity.    To  these  three  heads  are  reducible  Brittleness,  Dqo 

tility.  Malleability. 

V.  Adhesion.  This  means  the  cohesive  union  of  different 
substances,  without  chemical  affinity  ;  the  leading  cases  are 
solutions,  alloys,  and  cements.  It  might  be  the  head  for 
entering  the  composition  of  those  bodies  that  are  treated  as 
alloys  and  not  as  chemical  compounds.  The  isoraorphous 
unions  are  of  this  nature. 

VI.  Relations  to  Heat.  Rate  of  Dilatation  by  increased 
temperature  ;  Melting  and  Boiling  points  ;  Conduction  of 
Heat ;  Specific  Heat ;  Radiation,  Absorption,  Refraction,  and 
Polarization  of  Heat.  This  is  the  exhaustive  array  of  proper- 
ties having  reference  to  heat  ;  and  probably  includes  more 
than  the  mineralogist  is  ever  accustomed  to  state,  they  being 
unknown  for  the  greater  number  of  minerals. 

VIL  Relations  to  Electricity  .—Magnetic  property  ;  Con- 
duction or  Isolation  of  Electricity  (Frictional  and  Voltaic)  ; 
place  in  the  Electric  series,  from  Electro-positive  to  Electro- 
negative ;  place  in  the  Thermo-Electric  series. 

VIII.  Chemical  properties.  The  mineralogist  is  not  sup- 
posed to  transcribe  the  whole  chemistry  of  each  substance. 
For  his  purposes  a  selection  is  made  of  chemical  re-actions 
useful  in  mineral  testing. 

Occasionally  minerals  have  Taste  and  Odour. 

How  far  any  of  these  properties  can  be  related,  by  general 
laws  of  Causation  or  of  Co-existence,  with  any  other  proper- 
ties, is  an  important  enquiry  falling  under  Molecular  Physics, 
and  is  not  especially  the  business  of  the  mineralogiatk  Such 
laws  of  connexion  as  may  be  established,  simplify  the  study  of 
minerals,  by  making  one  property  the  index  of  another.  That 
there  are  such  laws  is  certain  ;  several  have  been  noticed  in 
former  connexions  (Book  IIL,  Chap.  III.  §  3).  These  laws, 
however,  do  not,  as  yet,  dispense  with  the  separate  statement 
of  the  properties  above  given,  although  they  may  give  to 
several  of  them  a  derivative  character. 

The  fact  of  there  being  laws  of  connexion  of  the  properties 
has  an  important  bearing  on  the  next  head. 

XL  The  Maximum  of  Affinity  of  Minerals,  as  guiding  their 

Classification. 
8.  It  has  to  be  seen  what  classification  of  minerals  best 
complies  with  the  golden  rule. 


To  bring  together  things  that  have  in  common  the  greatest 
number  of  leading  attributes,  is  the  first  condition  of  a  classi- 
fication. Now  we  have  above  enumerated  eight  different 
groups  of  mineral  charactera  ;  and  the  question  arises,  wh'ch 
of  all  these  should  be  the  groundwork  of  the  arrangement  into 
classes. 

There  are  two  suppositions  that,  if  true,  would  facilitate 
the  decision.  First,  if  by  the  discovery  of  laws  of  mutual 
connexion,  any  one  of  the  groups  of  properties  were  a  key  to 
one  or  two  other  groups,  there  would  be  a  reduction  of  the 
total  number  of  alternatives.  Thus,  if  Crystallization  were 
related  to  the  modes  of  Cohesion,  or  if  Electrical  and  Chemical 
properties  were  found  to  be  allied,  we  should  be  able  to  assume 
one  of  the  allied  members  as  representing  both. 

Again,  if  any  one  group  of  properties,  by  intrinsic  import- 
ance, and  apart  from  the  association  with  another  group,  had 
an  obvious  and  marked  predominance,  such  group  would  be 
properly  chosen  to  give  the  lead  in  the  classification.  In  this 
point  of  view,  for  example,  the  Crystalline  arrangement  might 
be  fairly  preferred  to  either  Heat  or  Electricity. 

On  both  grounds,  preference  is  to  be  given  to  these  two 
characters ;  namely,  Chemical  Composition  and  Crystalline 
Form.  Accordingly,  these  are  employed  a**  the  groundwork 
of  classification.  Minerals  are  first  divided  according  to  their 
Chemical  Composition ;  and  farther  subdivided  according  to 
their  Crystallization.  In  the  mineral  collection  of  the  British 
Museum,  arranged  by  Mr.  Maskelyne,  no  other  property  is 
employed  as  a  basis  of  division. 

In  the  older  classifications,  other  characters  were  made  use 
of  The  system  of  Mohs  proceeded  on  Gnjstalline  form,  Hard- 
nesSf  and  Specific  Gravity.  Now,  Hardness^  which  we  may 
otherwise  express  as  cohesive  energy,  must  be  a  result  of  the 
molecular  forces  and  arrangements  accompanying  chemical 
constitution  and  crystallization,  and,  from  this  circumstance 
alone,  is  peculiarly  unsuited  to  be  a  primary  foundation  of 
classes.  Again,  Specific  Gravity  may  likewise  be  viewed  as  a 
result  of  the  molecular  arrangements,  under  which  the  ulti- 
mate particles  attain  to  greater  or  less  proximity. 

The  arrangement  of  Weiss  is  in  its  chief  basis  chemical ;  his 
primary  division  into  Orders  is  governed  by  chemical  compo- 
fiition  purely: — Oxidized  Stones,  Saline  Stones,  Saline  Ores, 
Oxidized  Ores,  Native  Metals,  Sulphuretted  Metals,  Inflam- 
mables. In  subdividing  the  Orders  into  Families,  he  brings 
into  play  other  considerations.     Thus,  importance  in  the  com- 


fi^i 


526 


LOGIC   OF  MINERALOGY. 


MINERAL  COMPOUNDS. 


627 


position  of  rocks,  or  in  the  geological  stratification  of  the  glohe, 
determines  such  families  as  Quartz,  Felspar,  Mica,  Hornblende, 
Garnet.  Again,  the  precious  stones,  or  gems,  notwithstanding 
diversity  of  chemical  composition,  have  a  remarkable  agree- 
ment in  such  characters  as  hardness,  tenacity,  high  specific 
gravity  without  metallic  aspect,  transparency,  vivid  colours. 
We  may,  however,  fairly  doubt  whether  either  of  those  two  cir- 
cumstances is  enough  to  justify  miueralogists  in  departing  from 
the  arrangement  according  to  the  great  primary  attributes — 
Composition  and  Form.  In  such  cases,  a  supplemental  arrange- 
ment should  be  made  for  the  specific  object  in  view,  without 
distorting  the  one  principal  scheme.  The  geologist,  to  prepare 
for  describing  the  stratification  of  the  earth's  crust,  may  select, 
and  array  for  his  own  purpose,  the  predominating  mineral 
constituents.  And,  with  a  view  to  the  popular  interests  of  the 
subject,  the  mineralogist  may  bring  together  into  one  group 
all  the  substances  that  combine  the  most  highly  fascinating 
properties  of  external  appearance. 

The  arrangement  in  the  British  Museum  can  be  briefly  re- 
ferred to,  as  carrying  out  the  scheme  according  to  Composition 
and  Form. 

The  first  division  is  into  Native  Ele:jents,  or  Simple  Bodies, 
and  Compounds. 

In  arranging  the  Native  Elements^  there  is  an  inversion  of 
the  usual  order  in  Chemistry ;  the  Metals  precede  the  Non- 
metals.  This  is  owing  to  the  predominance  of  the  fact  of 
Solidity  in  the  mineralogical  view  of  the  earth's  constituents. 
The  native  metals,  therefore,  come  first  of  all ;  and  in  deciding 
their  arrangement  among  themselves,  no  farther  chemical 
circumstance  is  taken  into  account ;  the  reference  is  solely  to 
Crystalhzation. 

Under  the  first  System  of  Crystallography,  the  Cuhic,  are 
arranged,  Copper,  Silver,  and  Gold.  Under  the  fourth  System, 
the  Hexagonal  or  Rhombohedral,  are  the  isomorphous  metals, 
Arsenic,  Antimony,  and  Bismuth  ;  and  the  same  forms  brings 
into  continuity  with  these  the  rare  metal.  Tellurium. 

The  Non-metallic  native  elements  are  Carbon  and  Sulphur  ; 
Carbon  being  found  in  the  two  mineral  forms — Diamond  and 
Graphite. 

Compotind  Minerals.  —  The  native  metals  occur  often  as 
alloys  ;  and  these  are  included  with  the  simple  minerals  ;  an 
alloy  is  not  a  chemical  compound.  The  chemical  combination 
of  the  metals  takes  place  chiefly  with  the  non-metals  ;  the 
prominent  instances  of  combination  with  other  metals,  are  the 


compounds  with  the  Arsenides — Arsenic,  Antimony,  Bismuth. 
Accordingly,  the  Arsenides,  &c.,  are  the  commencing  division 
of  compound  minerals ;  the  subdivisions,  as  in  the  native 
elements,  being  according  to  form.  The  three  elements 
Tellurium,  Selenium,  and  Sulphur,  are  chemically  grouped 
together,  under  the  name  *  thionid '  elements,  and  their  com- 
pounds with  the  metals — Tellurides,  Selenides,  Sulphides — 
are  next  in  order  ;  there  being  subordinate  arrangements 
according  to  the  crystalline  systems,  which  are  nearly  all 
represented.  There  are  also  divisions  according  to  still  higher 
compounds,  as  when  Arsenides,  &c.,  unite  with  Sulphides ; 
which  higher  compounds  succeed  in  order  to  the  simple  com- 
pounds. 

The  next  division  comprises  compounds  of  the  Metals  with 
the  non-metallic  group — Chlorine,  Iodine,  Bromine,  Fluorine— 
the  *  halogens.'  Under  these  fall  certain  conspicuous  substan- 
ces— Common  Salt,  Calomel,  Sal  ammoniac,  Fluor  Spar,  &c. 

The  remaining  first  rank  Division  of  compound  minerals  is 
the  Compounds  of  Oxygen — a  division  of  enormous  extent,  and 
progressive  complication.  The  chief  subdivisions  are  there- 
fore chemical,  the  distinctions  of  crystalline  form  being  reserved 
for  the  final  subdivisions.  Commencing  with  bodies  having 
the  lowest  equivalents  of  oxygen — the  Monoxides,  we  are  led 
to  the  higher  equivalents — the  Sesquioxides  and  Binoxides ; 
under  each  of  these  heads,  the  farther  subdivision  is  according 
to  crystalline  systems.  Next  are  the  Oxygen  Salts,  of  which 
the  Carbonates  are  an  extensive  group  of  minerals,  divided  by 
their  crystalline  forms  into  Prismatic,  Rhombohedral,  and 
Oblique.  After  these  come  the  Silicates,  a  large,  varied,  and 
important  class  of  minerals,  subdivided  chemically  in  the  first 
instance,  and  by  crystalline  form  in  the  end.  To  these  succeed 
Borates  and  Nitrates.  The  final  groups  ai^  Phosphates  and 
Arseniates,  which,  in  consequence  of  the  isomorphisms  of  cor- 
responding compounds  of  Phosphorus  and  of  Arsenic,  cannot 
be  classified  apart. 

If  it  be  the  fact  that  the  two  properties — Chemical  Compo- 
sition and  Crystalline  Form — have  a  commanding  prominence 
in  minerals  overshadowing  the  others,  or  else  carrying  these 
along  with  them,  the  foregoing  classification  is  in  the  highest 
degree  natural  or  philosophical,  being  accordant  with  the  rule 
of  the  maximum  of  resemblance. 

4  The  Chemical  Composition  and  the  Crystalline  form 
also  give  the  proper  boundaries  of  Species. 


lv| 


fv 


528 


LOGIC  OF  MINERALOGY. 


The  question  as  to  the  boondaries  of  species  presents  BO 
theoretical  difficulties  on  the  above  scheme.  Every  native 
element,  and  every  definite  chemical  compound,  would  consti* 
tute  a  well-marked  species,  an  Infima  Species,  or  lowest  kind. 
If  the  same  element,  or  the  same  compound,  has  two  allotropic 
forms,  as  Carbon,  these  are  distinct  mineral  varieties,  but 
would  not  be  proper  species. 

The  practical  difficulties  attending  mineral  species  arise 
from  combinations  not  chemical,  where  the  elements  may  be 
in  all  proportions ;  as  in  the  isomorphous  compounds,  the 
alloys,  and  the  admixture  of  foreign  ingredients  generally. 
Such  instances  are  proper  varieties,  and  receive  distinctive 
names  and  separate  descnptions  whenever  the  difiference  is  of 
a  marked  kind. 

III.  Classification  ly  Grades. 

5.  The  Gi-ades  in  Mineral  Classification  are  used  merely 
for  arrangment,  and  not  for  shortening  the  description  of 
Mineral  Species. 

In  the  scheme  of  Weiss,  there  are  three  grades — Orders, 
Families,  and  Species ;  an  irrelevant  and  illusive  semblance  of 
the  classification  in  Botany  and  in  Zoology,  where  the 
several  gradations — the  Orders,  Families,  &c. —  are  each  ac- 
companied with  a  definition,  or  enumeration  of  common 
characters.  A  Mineral  Order,  on  the  other  hand — as  Oxidized 
Stones,  Native  Metals — is  accompanied  with  no  definition,  and 
suggests  no  common  characters  beyond  what  is  gathered  from 
the  name.  So  with  the  Families.  The  family  *  Quartz '  in 
the  order  *  Oxidized  Stones  '  is  not  defined  as  a  family  ;  there 
are  no  characters  assigned  as  common  to  all  the  species  of 
the  quartz  family.  There  is  a  title  OXIDIZED  STONES,  a 
sub-title  Quartz;  and  then  commences  the  enumeration  of 
species ;  so  that  each  specific  description  contains  all  the 
characters  of  that  species,  exactly  as  if  it  stood  alone  in  the 
world.  The  Gradation,  therefore,  is  a  Division,  but  not  a 
Classification. 

In  the  scheme  of  the  British  Museum,  the  division  begins 
with  the  dichotomy  of  Native  Minerals  and  Compounds.  The 
Native  Minerals  are  not  again  divided  formally ;  they  are 
simply  arranged  in  the  order  of  crystalline  systems.  The 
Compounds  involve  various  subdivisions,  which  could  easily 
be  laid  out  in  the  tabular  form.  As  there  is  no  systematic 
treatise  on  Mineralogy  based  on  the  scheme,  we  do  not  know 


UNIFORMITY  IN  STATEMENT  OF  CHARACTEKS.        529 

whether  the  gradation  could  be  properly  converted  into  a 
system  of  Orders  and  Families,  in  the  proper  sense,  with  an 
enunaeration  of  the  characters  of  those  orders  and  families ; 
but,  in  all  likelihood,  no  such  attempt  would  be  made.  Neither 
Chemistry  nor  Mineralogy  can  gain  much  by  straining  the 
parallel  of  Botany  and  Zoology  in  this  respect 

IV.  Marking  of  Agreement  and  Difference, 

6.  The  exhibition  of  Agreement  and  Difiference  in  Mineral 
description  is  gained  in  the  following  ways. 

(1)  By  observing  a  uniform  plan. 

(2)  By  proximity  of  species  according  to  the  maximum 

of  agreement. 

(3)  By  select  comparisons, 

(4)  By  select  contrasts. 

From  the  absence  of  defining  characTiers  m  the  higher  divi- 
sions (except  as  indicated  by  the  significance  of  the  names) 
the  best  means  of  stating  agreements  is  wantin g.  If  the  nature 
of  the  case  does  not  permit  of  the  operation  of  giving  characters 
to  Orders  and  Families,  we  must  proceed  by  other  ways. 

(1.)  A  uniform  plan  in  the  statement  of  the  characters  gives 
a  facility  of  comparing  any  one  species  with  any  other.  This 
is  carried  out  in  works  on  Mineralogy,  although  not  with  all 
the  aids  that  typography  might  afibrd. 

(2.)  It  necessarily  follows  from  a  good  classification  that  the 
species  placed  in  close  proximity  have  the  most  numerous 
points  of  agreement,  or  the  fewest  points  of  difference.  When 
native  metals  are  arranged  in  crystalline  forms,  the  contiguous 
species  have  a  very  large  amount  of  similarity,  and  compara- 
tively few  dissimilarities.  This  produces  on  the  reader  the 
effect  of  a  classification  by  grades,  with  agreements  stated  at 
each  grade. 

(3)  The  mind  receives  great  assistance  from  separate  tables 
of  agreements,  on  select  properties.  Thus,  it  is  convenient  to 
tabulate  the  minerals  falling  under  distinct  crystalline  forms; 
those  having  the  same  specific  gravity ;  the  same  hardness, 
&c.  This  is  a  great  supplemental  aid  to  the  mental  comparison 
of  individuals. 

(4)  Select  contrasts.  When  important  minerals  are  nearly 
allied,  and  apt  to  be  confounded,  they  should  be  brought  into 
direct  comparison,  through  a  statement  of  the  agreeing  feat- 
ures, and  a  tabular  contrast  of  the  differences.  For  example. 
Platinum  and  Palladium  have  a  very  close  resemblance,  and 


630 


LOGIC   OP  MINERALOGY. 


CHARACTERS   FROM   PARTS   OF   PLANTS. 


631 


mi^ht  have  their  agreeing  characters  given  together,  and  their 
differences  formally  contrasted. 

V.  Index  Classifications  of  Minerals. 

7.  For  the  ready  determining  of  Minerals,  recourse  may 
be  had  to  Index  Tables. 

The  properties  apparently  most  suitable  are — Crystal- 
lization ;  Transparency,  Lustre  and  Colour ;  Specific 
Gravity ;  Hardness  ;  Chemical  and  Blow-pipe  re-actions. 

Of  the  two  chief  modes  of  constructing  an  Index — a  succes- 
sion of  Dichotomies,  and  Tabulations — the  first  is  exemplified 
in  Botany,  the  second  seems  adapted  to  the  present  state  of 
Mineralogy.  The  thing  requisite  is  to  tabulate  all  known 
minerals  according  to  every  one  of  these  properties,  so  that 
-when  any  one  property  is  ascertained,  a  reference  to  the  table 
for  that  property  will  show  what  group  it  belongs  to,  and 
thereby  limit  the  search.  The  discovery  of  a  second  property, 
in  like  manner,  gives  a  reference  to  a  second  table,  and 
reduces  the  choice  still  farther. 

The  first  table — Crystalline  Forms — would  be  arranged  in 
the  order  of  the  crystalline  systems,  and  the  important 
varieties  of  each,  and  would  also  be  adapted  as  far  as  possible 
to  the  indications  of  the   goniometer,   which    measures   the 

angles. 

The  Oj^liccd  properties,  Transparency,  Translucency,  Lustre, 
Colour,  might  demand  several  tabulations — one  for  modes  of 
Transparency  and  Translucency,  another  for  Lustres,  a  third 
for  Colours.  There  are  doubts,  however,  as  to  the  practical 
utility,  for  purposes  of  discrimination,  of  the  table  of  colours; 
since,  although  colour  is  an  important  mark  in  pure  substances, 
the  admixture  of  colouring  matters  is  so  frequent  as  to  render 
the  test  misleading. 

A  Table  of  Specific  Gravities  would  be  useful  as  a  means  of 
testing.  Many  substances  are  well  marked  by  specific  gravity. 
The  different  varieties  of  the  important  group  of  Dolomites, 
or  magnesian  lime  stone,  are  most  conveniently  distinguished 
by  this  test. 

Hardness  being  reduced  to  a  scale  of  degrees,  and  being 
easily  tested,  is  a  valuable  aid  to  discrimination  ;  for  which 
end  there  should  be  a  table  of  minerals  according  to  degrees 
of  Hardness. 

With  a  view  to  Blow-pipe  and  Chemical  testing,  there  are 
needed  corresponding  tables  for  each  characteristic  appear- 


ance; as  fusibility  or  infusibility,  solubility  in  acids,  &o. 
This  is  merely  a  modification  of  the  methods  of  Practical 
Chemistry. 

Each  of  the  Index  tables  might  contain  columns  for  the 
other  important  index  properties,  so  as  to  give  all  the  charac- 
ters at  a  glance. 

These  tables  farther  point  out  Agreements  among  minerals, 
and  furnish  one  of  the  modes  given  for  that  purpose  under  the 
preceding  head.  Their  use  in  suggesting  Laws  of  Co-existence 
or  of  Causation,  among  the  properties  of  bodies,  is  sufficient 
to  give  them  a  place  among  the  Arts  of  Discovery. 

BOTANY. 

I.  Arrangement  of  Plant  Characters, 
8.  The  arrangement  of  the  characters  of  Plants  follows 
the  expository  order  of  the  parts  of  the  Plant. 

This  is  the  principle  already  exemplified  in  Mineralogy,  and 
applicable  to  all  sciences  of  classification. 

In  a  complete  system  of  Botany,  the  First  Divis'on — Struc- 
tural and  Morphological  Botany — enumerates  the  parts  of 
Plants  as  a  whole  ;  giving  a  generalized  and  methodical 
account  of  all  the  structures  found  in  all  known  plants. 

Commencing  with  the  constituent  Tissues  of  Plants,  this 
division  includes — Cells  and  Cellular  Tissue ;  Vessels  and 
Vascular  Tissue ;  the  Contents  of  the  Vegetable  Tissues — 
starch,  gum,  sugar,  oils,  resins,  &c. ;  the  Integumentary 
Tissues — as  hairs,  glands,  and  other  appendages. 

Plants  differ  in  the  modes  of  these  constituent  Tissues. 
Thus,  the  Acoiyledons  are  cellular  plants  without  vessels,  or  else 
vascular  plants  with  scalariform  vessels  ;  the  Monocotyledons 
and  Dicotyledons  are  vascular  plants  with  spiral  vessels  and 
stomata. 

The  Organs  or  parts  of  Plants  are  divided  into  Nutritive 
and  Reproductive.  The  nutritive  are  the  Hoot,  Stem,  and 
Leaves  ;  the  reproductive,  the  Flowers,  and  Fruit.  An  enume- 
ration is  given  of  all  the  different  forms  assumed  by  each  organ 
throughout  the  entire  assemblage  of  vegetable  species.  There 
might  be,  under  each  separate  peculiarity,  a  tolerably  exhaus- 
tive reference  to  the  plants  possessing  it.  By  such  means  the 
information  respecting  species  is  repeated  in  a  different  form. 

To  this  department  of  general  Botany  succeeds  Vegetable 
Physiology,  which,  however,  has  only  an  indirect  bearing  on 
the  Classification  of  plants.     Any  peculiarity  of  function  in  an 


I    I 


632 


LOGIC   OF  BOTAmr. 


individual  species  would  be  stated  under  the  or^n  concerned. 
Thus,  some  cellular  plants,  as  Oscillator iaSy  bave  undulating 
movements  in  the  cells  ;  and  some,  as  Confervce  and  Diato^ 
maceoBf  conjugate,  that  is.  unite  their  cells  in  reproduction, 
by  means  of  an  interposed  tube. 

The  next  great  division,  called  Taxological  Botany,  embraces 
the  Classification  of  Plants,  with  the  Description  of  each. 
The  principles  of  Classification  will  be  considered  under  the 
subsequent  heads.  The  order  of  Description  is  the  order  of 
the  parts  in  Structural  Botany,  as  above  quoted  : — Cellular 
Tissue,  Vascular  Tissue,  Contents  of  Cells  ;  Root,  Stem, 
Leaves,  Flower,  Fruit. 

In  referring  to  a  work  of  Botany  for  the  description  of  any 
given  plant,  we  shall  not  find,  as  in  Mineralogical  treatises, 
a  consecutive  and  exhaustive  account  of  characters.  Two  cir- 
cumstances stand  in  the  way  of  such  a  description. 

In  the  first  place,  the  system  of  (jrades,  which  is  inoperative 
in  Mineralogy,  is  thoroughly  worked  in  Botany.  Hence  to 
exhaust  the  characters  of  a  species,  we  must  ascend  through 
all  the  grades,  collecting  the  characters  of  each,  and  uniting 
them  in  one  series.  The  characters  of  the  *  Common  Haw- 
thorn* are  distributed  .(1)  nnder  the  species  so  named,  (2)  under 
the  genus  *  Hawthorn  '  (Grati^gtis)^  (3)  under  the  family 
*  Rose  *  Bosacece),  (4)  under  the  clasSj  *  Dicotyledon.*  By 
assembling  the  common  characters  of  the  class,  the  family, 
the  genus,  and  the  species,  in  the  proper  order,  we  should 
have  a  full  description  of  the  Hawthorn. 

In  the  second  place,  most  works  on  Botany  do  not  profess 
to  exhaust  the  known  character  of  species,  or  to  give  under 
each  species  the  whole  of  the  information  that  exists  respect- 
ing it ;  so  that  even  after  collecting  the  characters  from  all 
the  gradations,  we  have  not  the  full  knowledge  of  the  species. 
The  reason  is,  partly,  that  botanical  treatises  are  usually  con- 
fined to  the  humbler  function  of  determining  or  identifying 
plants ;  partly,  that  the  full  information,  while  very  volumi- 
nous, is  seldom  asked  for  ;  and  partly,  it  is  to  be  feared,  from 
vacillating  between  the  two  ends — determination  and  informa- 
tion. 

II.   The  Maximum  of  Affinity  of  Plants  as  guiding  their 

Classification. 

9.  In  considering  the  characters  of  plants,  with  a  view 
to  classification,  we  find  the  order  of  description  to  be  also 
the  order  of  relative  importance. 


CONCOMITANCE  OP  TISSUES  AND   OKGANS. 


533 


The  circumstance  that  most  of  all  gives  importance  to  a 
character  is  the  number  of  other  characters  that  go  along 
with  it.  Supposing  all  the  characters  of  equal  intrinsic 
value,  any  one  that  represents  three  others  is  four  times  the 
value  of  one  that  represents  only  itself. 

There  is  a  correspondence  or  concomitance  of  characters  in 
the  fundamental  parts  of  plants — Elementary  Tissues,  Nutri- 
tive Organs,  and  Reproductive  Organs — which  facilitates 
natural  groupings.  When  we  assume  as  a  basis  any  one  of 
this  class  of  characters,  we  secure  at  once  a  large  amonnt  of 
Agreement.  Isolated  characters,  as  Colour  and  Odour,  give  no 
help  to  classification. 

Now  it  is  found  that  the  Elementary  Tissues  are  the  most 
important  in  this  view ;  next  are  the  Nutritive  Organs  ;  and 
lastly,  the  Reproductive  Organs.  Certain  forms  of  the  Ele- 
mentary Tissues  are  accompanied  with  definite  modes  in  the 
Organs,  both  nutritive  and  reproductive.  By  the  Tissues 
alone.  Plants  are  divided,  in  the  first  instance,  into  Cellular 
and  Vascular ;  the  Cellular  comprising  the  lower  tribes,  a» 
Lichens,  Seaweeds,  and  mushrooms ;  the  Vascular,  the  higher 
flowerless  plants  and  the  flowering  plants.  Thus,  the  dis- 
tinction marks  the  lower  and  higher  in  organization. 

In  the  Nutritive  organs,  the  embryo  is  the  part  of  greatest* 
importance  ;  on  it  rests  the  grand  ternary  division  into  Acoty- 
ledons.  Monocotyledons,  and  Dicotyledons,  which  represents 
numerous  and  important  differences,  and  is,  therefore,  in  the 
highest  degree  a  natural  or  scientific  division.  Second  in 
importance  to  the  embryo,  or  seed,  is  the  root,  on  which  is 
based  a  triple  division — Heterorhizal,  Endorhizal,  and  Exo- 
rhizal.  After  the  root  comes  the  stem,  by  which  is  marked  the 
great  division  into  Exogenous  and  Endogenous,  together 
with  the  farther  division  into  Acrogenous  and  Thallogenous. 

In  the  Reproductive  System,  the  stamens  and  the  pistils 
occupy  the  first  place ;  these  were  the  chief  basis  of  the  Linnean 
Artificial  or  Index  system.  They  are  the  essential  organs  in 
the  Phanerogamia,  or  flowering  plants  ;  and  have  an  analogue 
in  Cryptogamia,  or  flowerless  plants.  Next  to  these  in  value 
is  the  fruit ;  and  after  it,  the  floral  envelopes  ;  and  finally,  in 
flowering  plants,  are  found  the  inflorescence  and  bracts. 

Thus,  by  classing  according  to  the  characters  that  carry  with' 
them  the  greatest  number  of  other  characters,  there  is  gained 
the  maximum  of  affinity  on  the  whole.  On  the  great  leading 
divisions  this  is  effectually  secured.  The  difficulties  arise  in 
disposing  of  the  families  or  Natural  Orders,  of  which  a  large 


534 


LOGIC   OF  BOTANY. 


SPECIES   OF  PLANTS. 


535 


number  is  included  in  the  immediately  superior  classes  (or 
Bub-classes) ;  66  Natural  Orders  are  contained  in  the  first  sub- 
class of  the  Dicotyledons  (Thalamifiora)).  It  is  impossible  to 
arrange  these  upon  any  one  principle  of  succession  or  contig- 
uity;  whence  such  devices  as  circular  arrangement,  double 
placing,  &c.  After  describing  any  one  Natural  Order,  Lindley 
exhibits  it  diagramatically  in  the  centre  of  four  other  orders 

right,  left,  above,  beneath — so  as  to  show  its  alliances  on 

different  sides. 

A  still  greater  difficulty  is  presented  by  the  transition 
classes,  which,  with  reference  to  the  others,  are  denominated 
aberrant,  as  departing  from  a  recognized  assemblage  of 
characters.  At  the  end  of  the  enumeration  of  a  class  is  some- 
times given  detached  an  anomalous  or  aberrant  member, 
which,  however,  by  the  very  fact  of  its  isolation,  is  a  new 
class.  The  genus  Spleenwort  (in  the  Fern  family)  is  a  re- 
markably well-characterized  and  natural  genus ;  yet  a  few 
species  are  scarcely  to  be  distinguished  from  some  species  of 
Shieldfern  and  Polypody,  except  by  the  sori. 

III.  Classification  hy  Grades, 

10.  Botany  is  the  happiest  example  of  Classification  by 
Grades. 

It  is  a  peculiar  circumstance  in  Botanical  classification,  that 
the  higher  divisions  are  made  upon  the  more  fundamental 
characters  (the  Tissues) ;  that  the  next  sub-divisions  are  upon 
characters  next  in  order  of  importance  (the  Roots,  &c.)  The 
Natural  Orders  or  Families  are  characterized  by  general 
structure,  but  especially  the  Flowers  and  the  Fruit,  The 
characters  of  the  Genus  are  a  continuation  of  those  in  the 
Order.  In  the  Species,  the  difierential  marks  embrace  Stem, 
Leaf,  and  Flowers.  The  tendency  of  this  arrangement  is 
to  reduce  to  comparative  insignificance  the   distinctions   of 

Species. 

For  practical  purposes,  great  interest  attaches  to  the  various 
products  or  deposits  in  plants — starch,  sugar,  gum,  oil,  resins, 
&c.  These  special  products  often  prevail  through  Natural 
Orders,  while  sometimes  they  attach  to  Genera,  and  sometimes 
to  Species. 

The  motives  for  settling  the  lowest  Species,  as  distinguished 
from  Varieties,  were  formerly  stated.  Constancy  or  perma- 
nence of  characters  is  one  of  the  conditions.  Thus  the  Water 
Ranunculus  assumes  many  striking  variations  of  form,  which 


have  been  regarded  as  specific  distinctions ;  but  from  their 
inconstancy,  and  their  dependence  upon  situation,  they  are 
more  correctly  deemed  Varieties.  So,  Colour  is  a  character 
that  must  be  generally  withheld  from  specific  marks,  and 
given  as  a  variety. 

ApluraUtij  of  important  characters  is  the  best  workable  test 
of  a  species.  The  sweet  orange  and  the  bitter  orange  are  re- 
garded as  Varieties  ;  the  lemon  is  held  to  be  a  distinct  Species ; 
the  points  of  difierence  between  the  sweet  and  bitter  orange 
are  fewer  than  the  difierences  between  the  orange  and  the 
lemon. 

In  the  inferior  forms  of  Plants,  the  specific  marks  are  often 
very  limited  in  number,  although  they  may  refer  to  organs 
high  in  the  scale.  Thus,  in  the  Ferns,  the  limitation  of  both 
genera  and  species  has  always  been  a  matter  of  difficulty.  The 
chief  reference  is  the  fructification,  or  the  arrangement  of  the 
seed ;  a  character  of  high  fixity  and  permanence  in  plants 
throughout.  In  grasses  too,  the  limits  of  the  numerous  genera 
are  not  clearly  fixed,— a  proof  of  the  fewness  of  available 
characters. 

The  apparatus  of  Grades  necessarily  collapses  when  the 
organization  is  not  of  a  sufficiently  high  order  to  allow  of  a 
series  of  halting  places  with  important  community  of  attri- 
butes. The  eight,  ten,  or  twelve  steps  of  descent  that  may  be 
interpolated  in  the  more  elaborately  organized  Blcotijledonous 
Orders,  are  reduced  to  three  or  four  in  the  Grasses  and  Ferns  ; 
while  it  may  be  difficult  to  maintain  even  that  number  in  the 
Fungi,  Lichens,  and  Sea-weeds. 

IV.  Marking  of  Agreement  and  Difference, 

11.  The  system  of  Grades  so  far  provides  for  the  state- 
ment of  Agreements. 

We  have  frequently  called  attention  to  Agreement  and 
Difierence  as  the  fundamental  facts  of  all  knowledge.  The 
more  thorough  the  provision  for  exhibiting  these  two  facts, 
the  better  will  the  subject  matter  be  known  and  understood. 

By  forming  a  class,  we  indicate  a  community  of  attributes  ; 
and  everything  should  be  done  to  exhibit  the  Agreement 
plainly.  The  tabular  form  is  more  particularly  suited  to 
characters  that  can  be  expressed  shortly.  It  is  a  grand 
mistake  to  suppose  that  the  forms  and  typography  of  ordinary 
composition  are  suited  to  the  generic  and  specific  descriptions 
of  plants  or  of  minerals.     The  different  heads  of  the  descrip- 


536 


LOGIC  OF   BOTANY. 


STATEMENT   OF  DIFFERENCES. 


537 


tion  are  seized  with  difficalty  when  scattered  indiscriminately 
over  the  printed  lines— sometimes  at  the  beginning,  and  some- 
times  at  the  middle  or  ab  the  end.  Any  remark  on  a  character, 
by  way  of  commentary,  or  explanation,  involving  the  composi- 
tion  of  one  or  more  sentences,  shonld  be  prmted  m  the  compact 
form  of  ordinary  composition :  but  the  broken  nnsentenced 
description  of  characters  should  be  exclusive  y  tabular  Such 
expressions  have  already  the  reality  of  a  table,  and  to  deprive 
them  of  the  form,  in  order  to  make  them  seem  composition  is 
to  withhold  the  only  advantageous  mode  of  presenting  them 
to  the  mind.  Thus  to  take  the  genus  Ranunculus  described  as 

below'''^  •— —  - 

The  first  sentence,  containing  a  very  general  remark,  may 
stand  as  it  is,  out  of  the  tabular  form  :  *  Annual  or  perennial 
herbs,  sometimes  entirely  aquatic ;'  this  should  be  coupled 
with  the  sentence  that  comes  after  the  description,  as  to  the 
geographical  spread  of  the  genus.  The  proper  descriptive 
characters  are  strictly  matter  for  a  table,  thus : 

Leaves,  entire,  or  more  or  less  divided. 

Flowers,  usually  yellow  or  white. 

Sepals,  6,  very  rarely  reduced  to  three. 

Petals,  5  or  sometimes  more,  each  with,  &a 

Stamens,  usually  numerous. 

Carpels,  numerous,  without  awns,  &c. 
As  tabular  arrangements  are  hard  reading,  they  may  be 
relieved  and  lightened  by  remarks  and  illustrations,  or  by 
adding  information  that  properly  takes  the  form  of  regular 
composition. 

12.  Considerable  nicety  attends  the  exhibition  oi  Differ- 
ences, there  being,  except  in  dichotomies,  no  regular 
method. 

Numerous  examples  have  already  been  given  of  stating 
difierence  by  pointed  contrast.  When  more  than  two  things 
are  compared,  this  is  impracticable.  Still,  the  value  of  the 
pointed  contrast,  as  appealing  to  the  most  fundamental  sensi- 
bility of  the  human  mind,  should  never  be  lost  sight  of.  We 
may,  for  example,  select  for  comparison  among  the  numerous 

♦  Annual  or  perennial  herbs,  sometimes  entirely  aquatic.  Leaves  entiw 
or  more  or  less  divided.  Flowers  usually  yellow  or  white.  Sepals  6, 
very  rarely  reduced  to  3.  Petals  6,  or  Bometimes  more,  each  with  a 
thickened  hollow  spot  at  the  base,  often  covered  by  a  minute  scale. 
Stamens  usually  numerous.  Carpels  numerous,  without  awns,  ma  globu- 
Iw  or  oblong  head,  each  containing  a  single  ovule  attached  near  its  base. 


cpecies  of  a  genus  all  the  twos  that  are  most  liable  to  be  con- 
founded. 

If  the  differing  species  of  a  genus,  or  the  differing  genera  of 
a  family,  differed  throughout ;  that  is,  if  no  two  agreed  in  any- 
thing but  in  the  common  features  of  the  higher  class,  the 
pointed  contrast  would  still  be  effective.  Thus  three  objects 
might  be  contrasted  on  a  single  feature,  differing  in  all  the 
three.  The  actual  case,  however,  is  that  differing  species  have 
many  partial  agreements  ;  of  six  species,  three  may  agree  in 
some  one  point,  four  in  another,  and  so  on.  In  this  state  of 
things,  we  might  carry  out  a  little  farther  the  exhibition  of 
Agreements.  We  might  give  Nos.  1,  3,  4,  6,  as  agreeing 
in  certain  features ;  2,  4,  5,  as  agreeing  in  others.  An 
additional  plan  is  to  modify  the  statement  of  the  generic  agree- 
ments thus  : — Feature  A  is  possessed  by  all  except  No.  2  ; 
Feature  B  is  possessed  by  I,  4,  6  ;  Feature  C  by  2,  4,  6, 6,  and 
so  on  (adopting  the  tabular  iform). 

For  example,  Lindley  constitutes  an  *  Alliance  *  or  Sub-class, 
Berberales,  in  which  he  places  seven  Natural  Orders,  dis- 
tinguished by  the  Flowers,  Stamens,  P  stils,  &c. ;  but  with 
partial  agreements,  thus — 

Flowers ;  regular  and  symmetrical.     All  the  seven,  except 

FumariaceaB. 
Placenta ;  axile  in  four  (naming  them),  parietal  in  two, 

sutural  in  one. 
Stamens ;  alternate  in  four,  opposite  in  <}hree. 
Every  device  that  brings  clearly  into  the  view  either  Agree- 
ments or  Differences  is  vital  to  the  understanding  and  the  re- 
collecting of  the  characters  of  the  various  classes.  Whenever 
there  is  occasion  or  scope  for  the  exhibition  of  agreement  and 
difference,  the  manner  of  it  should  be  prominent  and  even 
ostentatious  ;  often  the  best  course  is  to  detach  the  statement 
from  the  ordinary  form  of  composition,  and  to  put  it  in  tabular 
array  or  contrast,  as  already  exemplified. 

It  is  a  rule  of  good  exposition  not  to  mix  up  the  description 
of  characters  with  reflections  and  theories  as  to  their  causes 
or  explanations.  This  applies  especially  to  all  subjects  where 
the  descriptions  are  long  and  complicated.  The  follovCing  is 
an  improper  mixture  of  the  two  modes — *  The  odours  of  flowers, 
as  well  as  their  colours,  vary  much.  The  sources  of  odours  in 
flowers  are  very  obscure.  They  are  often  traced  to  the  presence 
of  fragrant  volatile  oils  in  resins.  The  effluvia  are  of  such  a  subtle 
nature  as  to  elude  chemical  analysis.  Some  flowers  are  odori- 
ferous only  in  the  evening.      This  is  the  case,  &c."     The  seii- 


HJ 


538 


LOGIC  OF  ZOOLOGY. 


COMPARATIVE  ANATOMY  AND  ZOOLOGY. 


539 


tences  in  italics  should  have  been   withlield  until  the  facts 
respecting  the  prevalence  of  odours  had  been  first  stated. 

V.  Index  Classification  of  Plants. 

13.  From  the  circumstance  of  passim^  throu^rh  the 
Liiinaean  classificatiou,  so  well  adapted  to  the  ready  deter- 
mination of  plants,  Botany  adbrds  the  best  example  of 
an  Index  Classification. 

We  may  retain  for  this  purpose  the  Linnasan  system  in  its 
literal  form  ;  or  we  may  have  recourse  to  the  modified  schemes 
of  recent  Botanical  writers.  The  principle  is  the  same.  We 
commence  with  certain  characters,  having  alternative  modes  ; 
and  the  key  or  index  informs  us  what  classes  each  mode  points 
to.  A  second  character  is  then  examined,  its  alternatives 
found,  and  the  corresponding  classes  discovered.  (See  Lind- 
ley's  Vegetable  Kingdom,  Bentham's  British  Flora,  &c.) 

LOGIC   OF  ZOOLOGY. 

14.  The  dilTiculties  of  Zoological  Classification  relate 
to  the  multitude  and  the  complication  of  the  Animal  King- 
dom. 

The  multitude  of  the  objects  to  bo  arranged,  and  the  com- 
plication of  even  the  lowest  forms,  distinguish  Zoology  from 
all  other  classificatory  sciences.  There  are  certain  partial 
compensations.  As  compared  with  Minerals,  the  organs  of 
Animals  present  numerous  relations  of  concomitance  ;  and  as 
compared  with  Plants,  the  Animal  Kingdom  falls  in  a  remark- 
able degree,  under  a  lineal  series^  or  consecutive  development. 

I.  CJiaracters  of  Animals. 

15.  We  must  look  for  the  characters  of  Animals  in  the 
division  of  the  animal  system  into  constituent  Organs. 

The  Animal,  like  the  Plant,  is  made  up  of  Tissues  and 
Organs,  which  have  a  certain  amount  of  sameness,  with 
variety,  throughout  the  entire  Animal  Kingdom.  The  enu- 
meration of  these  belongs  to  Biology  ;  Connective  tissue, 
Elastic  tissue,  Adipose  tissue.  Cartilage,  Bone,  Muscle,  Nerve, 
Vascular  tissue.  Blood  corpuscles,  &c.  In  Zoology,  however, 
the  Tissues  are  viewed  mainly  in  the  Organs  ;  and  Zoological 
characters  are  characters  of  organs.  There  is  not  the  same 
use  made  of  distinction  of  Tissue,  as  we  have  seen  in  Botany. 
The  basis  of  Zoological  Classification  is  the  division  of  tho 


Animal  system  into  Organs.  These,  with  their  functions,  may 
be  variously  arranged,  there  being  two  natural  groups  ;  (1) 
the  Vegetative  Organs  and  Functions  (Nutritive  and  Repro- 
ductive) —  Digestion,  Absorption,  Circulation,  Nutrition, 
Secretion,  Excretion,  Respiration,  Generation,  Development  ; 
(2)  the  higher  Animal  Organs  —  Locomotion,  the  Senses, 
the  Brain. 

In  all  these  various  organs,  characters  may  be  sought; 
there  being  none  but  what  are  subject  to  variation  throughout 
the  Animal  series.  The  Anatomy  of  Vertebrates  comprises 
the  following  parts :— Skeleton,  Muscles,  Brain  and  Senses, 
Teeth,  Alimentary  Canal  and  Appendages,  Absorbents,  Circu- 
lation, Respiration,  Urinary  organs.  Skin,  Generative  Organs. 

The  Blood  is  also  a  source  of  distinction  in  the  larger  divisions 

as  between  Vertebrate  and  Invertebrate,  Warm-blooded  (Birds 
and  Mammals)  and  Cold-blooded  (Fishes  and  Reptiles).^ 

The  grand  separation,  common  to  all  classificatory  sciences, 
between  the  General  and  the  Special  Departments,  in  the 
Animal  Kingdom,  gives  birth  to  the  two  subjects, — Compara- 
tive Anatomy  and  Zoology.  As  in  Mineralogy,  and  in  Botany, 
these  should  repeat  and  support  one  another,  giving  the  same 
information  in  two  different  forms. 

The  Comparative  Anatomy  arrangement,  besides  settling 
the  selection  and  the  order  of  Zoological  characters,  is  a  mos^ 
powerful  instrument  of  generalization.  The  exhibition  of  each 
successive  organ  in  all  varieties  and  modifications,  discloses 
many  aspects  otherwise  hidden ;  and  places  the  more  general 
and  fundamental  peculiarities  in  a  strong  light.  Much  of 
the  insight  that  we  at  present  possess  regarding  the  brain  is 
due  to  Comparative  Anatomy.  Too  great  pains  cannot  be 
given  to  the  perfecting  of  the  Comparative  Method  ;  and  the 
grand  secret  is  the  lucid  presentation  of  agreements  and  of  dif- 
ferences. 

16.  There  being,  in  Animals,  a  number  of  distinct 
organs,  a  search  is  made  for  Laws  of  Concomitance  be- 
tween them. 

It  is  a  part  of  Biology,  and  an  indispensable  aid  to  Zoology, 
to  find  out  the  correspondences  or  laws  of  concomitance 
between  the  different  organs — Moving  Organs,  Nervous 
System,  Digestion,  Reproduction,  &c. 

These  laws  occur  under  various  aspects.  Some  are  empiri- 
cal generalizations,  such  as  the  coincidence  of  the  ruminant 
characteristic  with  the  cloven  foot  and  horns  on  the  frontal 


11 


,  i 


i 


I' 


m 


540 


LOGIC   OF  ZOOLOGY. 


BASIS   OF  CLASSIFICATION. 


541 


bone.  Other  coincidences  are  mutually  related,  and  are  part 
and  parcel  of  the  development  of  the  species ;  as  the  advance 
of  the  brain  with  the  muscular  system,  the  reproductive 
organs,  and  the  organs  generally.  The  fact  of  increase  of 
organization  as  a  whole  implies  laws  of  concomitant  advance- 
ment of  all  the  leading  organs.  The  connexion  between  an 
animaFs  organs  and  its  circumstances  or  conditions  of  life  is 
not  a  law  of  co-existence,  but  of  mutual  implication ;  it  does  not 
give  us  two  independent  facts,  but  the  same  fact  on  two  sides. 
AH  references  to  the  element  of  each  species — water,  air, 
earth,  the  body  of  another  animal — are  to  be  held  as  merely 
illustrating  the  nature  of  the  organs. 

The  best  established  laws  of  concomitance  in  the  animal 
organs,  on  which  depends  the  existence  of  a  science  of  Zoo- 
logy, aa  distinguished  from  a  Comparative  Anatomy  of  ani- 
mals, are  liable  to  exceptions.  Sometimes  a  single  species 
will  mar  the  unanimity  of  an  entire  Division,  like  Amphioxus 
among  fishes.  It  is  clear,  however,  that  such  exceptions  are 
to  be  mentioned,  and  then  disregarded.  They  do  not  even 
prevent  us  from  supposing  that  the  characters  whose  con- 
junction  they  violate  are  united  by  cause  and  eflfect ;  for 
although  causation  permits  no  exceptions,  it  may  be  ocasionally 
counteracted. 

The  more  we  can  exhaust  the  relations  of  correspondence 
or  concomitance,  and  the  more  precisely  we  can  express  them, 
the  better  are  we  prepared  for  the  great  classifying  operation 
that  makes  up  Zoology.  The  full  import  of  the  remark  will 
appear  under  the  next  head. 

It  might  seem  superfluous  to  insist  on  preserving  a  regular 
order  in  the  statement  of  Characters  throughout  the  whole 
scheme — whether  in  iiie  Comparative  Anatomy  or  in  the 
Zoology, — seeing  no  one  can  follow  out  comparisons  that  are 
not  uniformly  expressed. 

II.   T7Le  Maximum  of  Ajjinity  as  giving  the  Classes. 

17.  The  choice  of  Classes  follows  the  maximum  of  agree- 
ments in  the  several  organs. 

The  existence  of  Laws  of  Concomitance  indicates  the  possi- 
bility of  finding  animal  groups  that  agree  in  two,  three,  or 
more  organs,  or  important  modifications  of  organs.  The 
zoologist  grasps  at  this  circumstance,  in  order  to  form  his 
leading  classes. 

In  appeai-ance,  but  only  in  appearance,  there  is  another 


principle  of  grouping.  Some  one  organ  is  chosen  as  the  basis 
of  classification  ;  for  example,  the  Reproductive  system,  which 
gives  the  name  to  Mammalia*  In  reality,  however,  such  choice 
is  made  not  on  account  of  the  organ  by  itself,  bat  on  account 
of  the  number  of  its  alliances. 

An  extreme  supposition  will  place  this  fact  in  a  clearer 
light.  Let  us  imagine  that  every  one  of  the  leading  organs, 
or  systems, — Nervous,  Reproductive,  &c. — was  wholly  uncon- 
nected in  its  modifications  with  every  other  organ ;  that  the 
nervous  system  might  vary  through  all  possible  modes 
without  any  corresponding  variaition  in  anything  else.  Under 
such  circumstances,  we  might  have  a  comparative  anatomy  of 
each  organ,  but  no  concurrence  of  organs.  Zoology  would 
be  incompetent  and  non-existent.  The  only  possible  classifi. 
cation  would  be  according  to  the  Comparative  Anatomy  of  the 
several  organs.  We  might  assign  a  superior  dignity  to 
same  one  organ,  as  the  Brain,  and  give  it  a  priority  in  arrange- 
ment, and  a  preference  in  study ;  but  after  the  entire  animal 
kingdom  had  been  exhaustively  arranged  under  thecomparative 
anatomy  of  the  Nervous  System,  the  same  operation  would 
have  to  be  repeated  under  the  other  systems  ;  the  work  would 
then  be  finished  ;  being  substantially  the  present  science  of 
Comparative  Anatomy,  without  the  relief  that  is  at  present 
afforded,  to  the  overwhelming  mass  of  details,  by  laws  of 
Concomitance. 

Accordingly,  the  justification  of  preferring  one  organ  as  the 
classifying  basis,  is  avowedly  its  alliances.  The  taxonomic 
value  of  the  *  placenta  *  in  Mammalia  is  the  number  of  charac- 
ters that  it  carries  along  with  it.  *  Man,  the  Apes,  the  Inseo- 
tivora,  the  Cheiroptera,  the  Rodentia, — are  all  as  closely  con- 
nected by  their  placental  structure  as  they  are  by  their  general 
affinities'  (Huxley).  The  real  motive  to  the  groupiug  is  not  the 
placental  structure,  hut  the  general  affinities. 

We  may  make  another  illustrative  supposition.  If  all  the 
organs  were  strictly  co-equal  in  development  and  in  modifica- 
tions; if  the  Nervous  System,  the  Muscular  System,  the 
Reproductive  System,  &c.,  were  all  modified  in  strict  concomi- 
tance, there  would  be  no  such  thing  as  a  preference  organ 
whereupon  to  base  classification ;  the  Reproductive  organs 
could  be  no  more  a  clue  to  the  *  general  affinities  *  than  the 
digestion,  or  the  respiration.  There  would  be  no  mention  of 
a  special  basis ;  general  affinity  would  alone  be  prominent. 

It  would  appear,  however,  that  the  constituent  systems  of 
the  animal  organization  are  not  co-equal  and  concomitant  in 


W'l 


642 


LOGIC  OF  ZOOLOGY. 


AGKEEMENT  AND  DIFFERENCE. 


543 


their  changes ;  some  carry  with  thera  more,  and  some  less,  of 
general  affinity  or  concomitance.  Taking  the  whole  Animal 
Kingdom,  we  tind  that  the  Nervous  System  is  by  far  the  most 
important  basis  of  classification  ;  the  reason  being  that  the 
organs  generally  cannot  advance  without  a  corresponding  rise 
in  the  regulating  and  co-ordinating  organ.  There  cannot  be 
an  extension  of  the  muscular  apparatus  without  an  extension 
of  the  brain  ;  while  the  muscular  apparatus  itself  implicates 
many  other  parts  of  the  system. 

Next  to  the  Nervous  System  is  that  part  of  Reproduction, 
embracing  the  mode  of  Development  of  the  animal  from  the 
germ  upwards.  We  have  already  seen  how  far  this  governs 
the  divisions  and  sub-divisions  of  the  Mammalia  ;  their  very 
name  is  founded  on  it. 

If,  for  the  sake  of  illustration,  it  were  asked  what  would  be 
the  worst  organ  for  classifying  upon — the  one  that  undergoes 
the  greatest  degree  of  unconnected  or  isolated  variation, — the 
answer  would  probably  be  the  Heart. 

III.  Classification  hj  Grades. — Species. 

18.  It  beiiis;  assumed  that  each  class  is  formed  on  the 
maximum  of  affinities,  the  number  of  grades  is  regulated 
by  the  occurrence  of  a  succession  of  suitable  groupings. 

The  grades,  or  halting-places,  ar3  a  relief  to  the  burden  of 
numerous  common  characters ;  but  there  is  no  need  to  con- 
stitute them  where  the  amount  of  resemblance  is  inconsider- 
able. 

In  the  higher  Vertebrates,  a  succession  of  six,  seven,  or  more 
grades  is  admissible  and  advisable  ;  while  the  attempt  to  con- 
stitute Natural  Orders,  Genera  and  Species,  iu  the  Protozoa, 
is  misplaced  and  savours  of  pedantry. 

In  Mammalia,  the  distinctions  of  Species  may  be  nnraerons 
and  important ;  profound  differences  separate  the  Lion  and 
the  Tiger,  the  Horse  and  the  Ass.  In  Birds,  on  the  other 
hand,  the  species  often  turn  upon  small  and  nice  peculiarities. 
Of  the  three  hundred  species  of  Parrots,  it  is  impossible  that 
there  can  be  specific  differences  either  numerous  or  important ; 
the  Psittacos  erithacus,  for  example,  is  distinguished  as  grey^ 
with  tail  red  I  The  domesticated  varieties  of  the  horse,  dog, 
and  cat,  have  wider  differences  than  many  species,  or  even 
genera,  of  the  lower  animal  tribes.  The  differences  between 
a  Negro  and  a  Caucasian  {varieties  of  the   Species — Man)  pro- 


bably  surpass  in  number  the  distinctions  between  two  Natural 
Orders  of  Infusoria. 

Iu  some  cases,  there  occurs  a  single  character  so  bold  and 
remarkable  as  to  satisfy  our  utmost  demands  for  a  specific 
distinction.  Such  is  the  extraordinary  electrical  organ  in  cer- 
tain fishes.  The  species  of  the  Gymnotus  named  electricus,  is 
sufficingly  marked  by  this  single  feature,  in  whose  presence 
the  describer  abstains  from  all  further  specification. 
IV.  Marking  of  Agreement  and  Difference, 

19.  Zoology  depends  greatly  on  the  rule  of  parallel 
array  for  Agreements,  and  of  pointed  contrast  for  Differ- 
ences. 

^  The  characters  of  classes,  high  or  low,  should  be  thrown 
mto  the  form  most  advantageous  to  the  reader,  that  is,  the 
tabular  arrangement,  with  appended  remarks  and  comment- 
aries in  ordinary  typography. 

For  example,  the  characters  of  Aves  (reckoned  sufficient  for 
discrimination,  although  inadequate  as  information)  are  these:— 
Reproduction : — oviparous 
Respiration :— air-breathing 
Heart:— four  cavities,  as  in  the  Mammalia 
Integument : — feathers 
Teeth  :— wanting ;  substitute  horny  jaws 
Locomotive  Orga^is  .—the  anterior  limbs  are  wings. 
Besides  these  characters  much  is  to  be  said  as  to  the  points 
of  community,  in  the  Nervous  System,  the  Digestive  System 
and  other  parts. 

For  the  statement  of  Difference  we  may  select  Mr  Huxley's 
primary  division  of  Birds  into  three  classes  ;  an  instance  where 
tlie  pointed  contrast  may  be  extended  to  three  members  :— 

SAUKUBJ;  RATITJ;  CABINATJl 

Metacarpal  Bones 
Not  ankylosed         Ankylosed  Ankylosed 

Caudal  Vertehrce  and  Tail 
Longer  than  body         Shorter  Shorter 

Crest  of  Sternum 

None  Present 

Barbs  of  the  Feathers 

Disconnected      Connected. 
There  are  several  other  characters  of  the  second  and  third 
classes,  and  no  more  of  the  first.     Hence,  we  might  have  put 
the  first  against  the  two  others  as  a  whole,  and  then  worked 
oat  the  present  contrast  upon  these  two, 
2i 


I 


f 


544 


LOGIC   OF  ZOOLOGY. 


Not  merely  in  the  formal  exhibition  of  generic  and  epecifio 
characters,  but  in  every  incidental  comparison  of  one  class 
with  another,  the  statement  of  Agreements  and  of  DiiTerences 
should  always  be  clear,  emphatic,  and  ostentatious. 

V.  Index  Classification, 
20.  An  Index  Classification  for  Zoology  might  choose 
between  the  two  alternatives— the  tahdar  and  the  diclhotom- 

ous. 

The  Tabular  method  has  already  been  suggested  for  Mine- 
ralogy, and  will  again  be  brought  up  for  Diseases.  The 
Pichotomous  method  is  carried  to  perfection  in  Botany. 

A  tabular  plan  could  be  based  upon  Comparative  Anatomy  ; 
there  being  given,  under  every  peculiar  mode  of  each  organ,  a 
complete  list  of  all  animals  possessing  that  mode.  Thus, 
there  would  be  a  table  of  the  species  conforming  to  each 
grouping  of  the  Teeth,  so  that  the  discovery  of  such  grouping 
in  any  given  specimen  would  decide  the  animal  as  one  of  the 
list.  A  second  character  being  noted  as  present  in  the  speci- 
men would  direct  to  a  second  list,  where  the  animal  must 
appear ;  the  choice  is  now  narrowed  to  such  as  are  common 
to  both  lists.  A  third,  and  a  fourth  character,  being  followed 
out  in  the  same  way,  would  reduce  the  choice  to  still  smaller 
limits ;  and  eventually  the  enquirer  would  be  guided  to  the 

proper  Species. 

The  dichotomous  method  of  Botany,  if  fully  adapted  to 
Zoology,  as  it  might  obviously  be,  would  be  still  better. 

The  want  of  an  Index  is  less  felt  in  Zoology  because  of  the 
better  marked  specific  distinctions,  at  least  until  we  descend 
to  the  inferior  tribes,  where  there  are  numerous  specie^, 
slightly  marked.  It  would  be  pre-eminently  necessary  for 
Birds,  among  Vertebrate  animals,  and  for  the  Invertebrate 
Orders  generally.  It  is  less  necessary  for  Mammalia^  except 
in  a  coUeotioQ  of  anusually  vast  extent. 


CHAPTER  VIL 

LOGIC  OF  PRACTICE. 

1.  The  Practical  Sciences  are  defined  by  their  several 
Ends. 

Medicine  is  the  practical  science  having  for  its  end  Health. 
Grammar  and  Rhetoric  have  for  ends  the  perfection  of  the 
instrument  of  Language. 

2.  There  is  one  crowning  end,  the  sum  of  all  other  ends, 
namely,  Happiness  or  Well-being. 

People  desire  Health  in  order  to  be  happy.  There  can  be 
no  end  beyond  human  enjoyment— the  gaming  of  pleasure 
and  the  averting  of  pain. 

3.  The  final  end  of  all  pursuit  must  be  assumed  or 
granted  ;  it  cannot  be  proved. 

No  proof  can  be  offered  of  the  position  that  Happiness  is 
the  supreme  end  of  human  conduct.  We  must  be  satisfied 
with  the  fact  that  mankind  make  it  the  end.  As  all  proof 
consists  in  referring  the  point  in  question  to  something  more 
fundamental,  there  must  be  at  last  something  taken  for 
granted  on  its  own  account.  Such  is  Happiness,  the  highest 
crowning  end.  Men  desire  Happiness,  either  for  themselves 
or  for  others,  as  the  goal  of  all  endeavour. 

4.  There  is,  however,  a  want  of  perfect  unanimity  as  to 
the  final  end.  Some  even  deny  that  Happiness  is  the  end; 
while  there  may  be  great  difference  of  opinion  as  to  the 
nature  of  the  happiness  to  be  sought. 

The  end  set  up  by  some,  as  the  final  end  of  all,  is  Virtue. 
To  those  that  embrace  this  view  consistently,  there  is  no 
reply ;  there  is  no  possible  appeal  from  a  fundamental  end. 

We  may,  however,  enquire  whether  any  class  of  persons  do 
consistently  and  thoroughly  maintain  virtue,  and  not  happi- 
ness, to  be  the  sole  end  of  all  endeavours.  Wherever  there  is 
inconsistency,  an  argument  is  possible. 

Now,  in  reply  to  the  setting  up  of  Virtue,  or  mere  self- 
denial,  as  an  end,  we  may  urge,  first-,  that  the  conduct  of  man- 
kind  shows  that,  in  the  great  mass  of  cases,  they  regard  virtue 


if',' 


*. 


546 


LOGIC   OF  PRACTICE, 


as  a  means  to  happiness.  The  virtue  of  Howard  consisted  not 
in  the  fatigues  and  privations  suffered  from  his  journeys,  and 
from  visiting  squalid  dungeons  ;  it  was  in  the  amount  of  human 
misery  that  he  relieved. 

Secondly,  the  position  that  Virtue  is  an  end  is  almost 
uniformly  coupled  with  the  assertion  that,  in  the  long  run, 
Virtue  is  Happiness ;  which  is  merely  another  way  of  assign- 
ing Happiness  as  the  end. 

Thirdly,  the  thorough  carrying  out  of  the  position  that 
Virtue,  in  the  form  of  ascetic  self-denial,  which  is  Virtue 
dissociated  from  Happiness,  is  the  ethical  end,  would  be  tanta- 
mount to  abolishing  the  difference  between  good  and  evil, 
with  which  virtue  itself  is  identified.  Virtue,  in  the  sense  sup- 
posed, flourishes  in  misery  ;  the  more  miserable  we  are,  the 
greater  scope  we  have  for  virtue  ;  the  more  miserable  we 
make  other  people,  the  more  scope  we  give  them  for  virtue. 

Again,  Happiness  may  be  allowed  as  the  end,  and  yet  there 
may  be  wide  differences  of  view  in  the  interpretation  of  the 
end.  The  partizans  of  virtue  may  re-appear  on  this  ground, 
affirming  that  Happiness  is  only  to  be  found  in  Virtue  or 
Duty,  not  in  enjoyment  and  in  the  absence  of  pains.  The 
reply  proceeds  as  before;  are  these  reasoners  thoroughly 
consistent  with  themselves  ?  If  they  are,  they  cannot  be 
refuted ;  if  they  are  not,  they  may. 

Great  variety  of  opinion  may  be  held  as  to  the  beings  whose 
happiness  is  to  be  sought..  Are  we  to  seek  our  own  happiness 
solely,  or  the  happiness  of  others  solely,  or  partly  the  one  and 
partly  the  other  ?  How  far  are  we  to  extend  our  regards — 
to  our  own  kinsmen,  to  our  fellow  citizens,  io  humanity  in 
general,  to  the  lower  animals  ?  In  none  of  these  points  is 
argument  possible,  unless  where  people  are  inconsistent,  which 
they  need  not  be.  We  cannot  reason  a  person  into  the  adop- 
tion of  other  people's  happiness  as  an  end,  unless  such  person 
has  already  of  his  own  accord  embraced  some  doctrine  that 
involves  this,  as  for  example,  the  profession  of  Christianity. 
Neither  can  we  offer  any  reason  for  extending  sympathy  to 
the  lower  animals.  An  education  of  the  feelings  is  the  only 
mode  of  enlarging  people's  sympathies.  No  man  can  be  argued 
oat  of  a  consistent  selfishnesa 


CHAPTER  VIIL 
LOGIC  OF  POLITICS. 

1.  Politics,  in  the  largest  sense,  refers  to  the  action  of 
human  beings  in  Society. 

The  notion  of  Society  can  be  gained  only  by  each  one's 
individual  experience.  The  first  example  of  it  is  the  Family, 
which  contains  a  plurality  of  persons  in  mutual  co-operation,* 
withcommand  andobedience.  The  earliest  notions  of  authority, 
law,  command,  obedience,  punishment,  superior,  inferior,  ruler] 
subject, — are  gained  from  the  various  aspects  of  the  small 
domestic  circle. 

The  larger  aggregations  of  the  school,  village,  parish,  town- 
ship, church,  &c.,  repeat  all  those  aspects  of  the  family,  while 
dropping  the  incidents  special  to  the  family. 

2.  The  science  of  Politics,  as  a  whole,  is  either  Theoreti- 
cal or  Practical. 

Under  the  Theoretical  Science  of  Politics  must  be  described 
the  structure  or  organization  of  Political  Society ;  this  being 
equally  essential  as  a  preparation  for  the  Practical  Science. 
All  the  leading  terms  of  Politics  must  be  defined  ;  all  the  parts 
of  the  Political  system  explained.  To  this  preliminary  branch, 
Sir  G.  C.  Lewis  applies  the  designation  *  Positive  Politics,* 

In  the  second  place,  the  Theoretical  Science  traces  cause 
and  effect  in  political  institutions,  as  facts  of  the  order  of 
nature ;  in  the  same  way  as  Physics  and  Chemistry  describe 
cause  and  effect  in  inorganic  bodies,  and  Biology  in  living 
bodies.  The  theoretical  department  of  Society  would  state, 
upon  evidence  of  fact,  conjoined  with  reasonings  from  human 
nature,  what  are  the  consequences  of  given  institutions.  To 
quote  from  Sir  George  Lewis  : — 

*  It  assumes  that  we  know  what  a  state  is  ;  what  are  its  functions ; 
what  are  the  conditions  necessary  for  its  existence ;  by  what  in- 
Btruinents  it  acts ;  what  are  its  possible  relations  with  other  states. 
Starting  from  this  point,  it  inquires  how  certain  forms  of  govern- 
nient,  and  certain  laws  and  political  institutions,  operate  ;  it  seeks, 
from  observed  facts  and  from  known  principles  of  human  nature, 
to  determine  their  character  and  tendency ;  it  attempts  to  frame 
propositions  respecting  their  probable  consequences,  either  uni- 


?»'■ 


< 


4 


548 


LOGIC   OF  POLITICS. 


SCIENCES  COMPBISED  IN  POLITICS. 


549 


versally,  or  in  sorae  hypothetical  state  of  circumstances.  Thus  it 
may  undertake  to  determine  the  respective  characters  of  monarchy, 
aristocracy,  and  democracy  ;  it  may  show  how  each  of  these  forms 
of  government  promotes  the  happiness  of  the  community,  and 
which  of  them  is  jyreftrable  to  the  other  two.  It  may  inquire  into  the 
operation  of  certain  modes  of  preventing  crimes — as  police, — of 
criminal  procedure,  and  of  legal  punishment,  such  as  death,  trans- 
portation, imprisonment,  pecuniary  fines, — and  it  may  seek  to 
determine  the  characteristic  advantages  and  disadvantages  of  each, 
in  certain  assumed  conditions.  It  may  inquire  into  the  operation 
of  different  systems  of  taxation — of  laws  respecting  trade  and 
industry — of  modes  of  regulating  the  currency — of  laws  regulating 
the  distribution  of  property  with  or  without  will — and  other 
economical  relations.  It  may  lay  down  the  conditions  which 
render  it  expedient  to  govern  a  territory  as  a  dependency ;  or 
which  tend  to  promote  the  prosperity  of  a  new  colony.  It  may 
define  the  circumstances  which  ensure  the  permanence  of  national 
confederacies,  and  it  may  inquire  what  are  the  rules  of  interna- 
tional law  which  would  tend  to  promote  the  uninterrupted  main* 
tenance  of  peace. 

*  It  seeks  to  lay  down  general  theorems  respecting  the  operation 
and  consequences  of  political  institutions,  and  measures  thera  by 
their  utility  or  their  capacity  for  promoting  the  welfare  of  the 
national  community  to  which  they  are  applicable.  Propositions 
of  this  sort  may  lead  (though  not  by  so  direct  a  road  as  is  often 
supposed)  to  preceptive  maxims  ;  but  they  are  themselves  merely 
general  expressions  of  fact,  and  they  neither  prescribe  any  course 
of  conduct,  nor  do  they  predict  any  specific  ocxjurrence ;  though, 
from  the  generality  of  their  form,  they  may  relate  as  much  to  the 
future  as  to  the  past.* 

The  Theoretical  Science  of  Society  is  sometimes  expressed 
as  the  *  Philosophy  of  History/  or  the  accounting  upon  general 
principles  of  cause  and  effect  for  the  actual  course  of  political 
events,  the  growth  of  institutions,  the  progress  and  decay  of 
nations.  History,  in  the  ordinary  signification,  recounts  these 
things  in  the  detail ;  the  Philosophy  of  History  generalizes  the 
agencies  at  work,  and  endeavours  to  present  the  whole  as  fol- 
lowing out  certain  great  leading  ideas.  A  few  writers  have 
aimed  at  establishing  such  generalities — Vico,  Montesquieu, 
Millar,  Condorcet,  Auguste  Comte,  &c. 

Practical  Politics  consists  of  maxims  of  political  practice. 
Here  we  have  to  suppose  an  end, — the  welfare  of  the  com- 
munity, or  any  other  mode  of  stating  the  political  end. 

This  necessarily  appears  with  more  or  less  prominence  in  all 
political  treatises.  Aristotle's  work  is  a  search  after  the  hcsi 
government.  Machiavers  treatises  are  preceptive  or  practical. 
Locke  does  not  formally  enquire  after  the  best  constitution. 


bnt  nnder  the  guise  of  what  is  necessary  to  a  state,  he  insinuates 
certain  political  forms,  and  certain  legislative  principles. 

Sound  method  requires  that  a  writer  should,  in  the  first 
instance;  separate  the  Theoretical  from  the  Practical. 

3.  The  entire  department  of  Political  Science  at  the  pre- 
sent day  comprises  several  sciences. 

It  has  been  found  practicable  and  convenient  to  withdraw 
from  the  wide  region  of  human  society,  certain  subjects  that 
can  with  advantage  be  cultivated  apart,  and  thus  to  reduce  the 
complication  of  political  enquiries. 

(1)  The  first  of  these  is  Jurisprudence.  This  is  a  distinct 
branch  bearing  on  the  form  of  Law,  as  apart  from  its  substance. 
It  teaches  how  laws  should  be  expressed,  with  a  view  to  their 
satisfactory  interpretation  by  the  Courts  ;  it  embraces  evidence, 
and  the  principles  and  procedure  for  the  just  administration 
of  the  laws.  It  does  not  consider  the  choice  and  gradation  of 
punishments,  but  explains  how  they  should  be  legally  defined, 
so  as  to  be  applied  in  the  manner  intended  by  the  legislator. 

(2)  International  law  is  the  body  of  rules  agreed  upon  by 
independent  nations  for  regulating  their  dealings  with  each 
other,  both  in  peace  and  in  war.  It  includes,  for  example, 
questions  as  to  the  Extradition  of  Criminals,  and  the  rio-ht  of 
Blockade  at  Sea. 

(3)  Political  Economy,  or  the  science  of  the  production  and 
distribution  of  Wealth,  relieves  the  political  philosopher  of  a 
considerable  part  of  his  load.  The  legislation  regarding  Pro- 
perty in  Land,  Trade,  Manufactures,  Currency,  Taxation,  &c., 
is  guided  by  the  enquiries  of  Political  Ecomony.  Within  its 
own  sphere,  this  science  has  the  same  logical  character  as  the 
mother  science.  It  has  its  definitions,  its  principles  or  laws, 
partly  inductive  and  deductive,  and  its  methods,  which  are 
the  ordinary  logical  methods. 

(4)  Statistics  is  a  branch  of  the  Science  of  Society,  admit- 
ting of  being  cultivated  separately.  It  furnishes  the  facts.and 
data  of  political  reasoning  in  the  most  complete  and  authentic 
form. 

4,  The  subjects  remaining  to  Political  Science,  are  (1) 
the  Form  of  Government,  and  (2)  Legislation  on  all  topics 
not  otherwise  embraced. 

The  difierent  Forms  of  Government,  their  precise  defini- 
tion, and  their  several  tendencies,  constitute  the  foremost 
problem  of  the  political  science.     The  discussion  of  Monarchy, 


\ 


\ 


:  a 


650 


LOGIC  OF  POLITICS. 


THE  POLITICAL  STKUCTURE. 


551 


Aristocracy,   Democracy,   enters   into  every   treatise   called 
political. 

In  immediate  connexion  with  this  subject,  if  not  a  part  of 
it,  is  the  distribution  of  the  functions  of  government,  into 
Legislative,  Administrative  and  Judicial ;  the  delegation  of 
the  powers  of  government  to  subordinate  authorities,  as  in 
provincial,  local,  or  municipal  government. 

These  subjects  are  sometimes  considered  as  exhausting  the 
sphere  of  Politico;  but  in  a  very  narrow,  although  distinct 
signification  of  that  sphere.  Thus,  Mr  Mill  remarks, — *  To 
attempt  to  investigate  what  kind  of  government  is  suited  to 
every  known  state  of  society,  would  be  to  compose  a  treatise 
on  political  science  at  large.* 

It  must,  however,  be  matter  of  enquiry  how  a  government, 
when  constituted,  is  to  discharge  its  functions.  This  supposes 
that  the  functions  aro  classitiod  and  defined;  an  operation 
involving  one  very  important  enquiry  in  Politics,  namely,  the 
proper  Province  of  Government 

There  are  certain  things  that  Government  must  undertake, 
in  order  to  fulfil  its  primary  ends ;  such  are  Defence,  and 
the  Preservation  of  Life  and  Property. 

There  are  other  things  that  government  may  or  may  not 
undertake — as  the  Support  of  Religion,  Education,  Postal  com- 
munication, the  maintenance  of  Roads,  main  Drainage,  and 
other  works  of  general  utility. 

5.  The  curtailment  of  Individual  Liberty  is  a  necessary 
effect  of  government ;  and  the  degree  of  this  curtailment 
is  a  vital  consideration  in  Political  theory. 

In  order  that  men  may  act  together  in  society,  each  must 
in  part  subordinate  their  own  actions  and  wishes  to  the 
general  scheme.  Obviously,  however,  individual  liberty, 
which  is  in  itself  a  chief  element  of  well-being,  should  be 
restricted  in  the  least  possible  degree  ;  and  the  burden  of 
proof  must  always  lie  upon  the  proposer  of  restraint. 

The  StriLcture  of  Political  Society, 

6.  The  preliminary  branch  of  the  Social  Science,  con- 
tains the  Definition  of  Political  Society,  and  of  all  the 
Eelationships  and  Institutions  implied  therein. 

This  is  the  part  of  the  subject  entitled  by  Sir  G.  C.  Lewis 
Positive  or  Descriptive  Politics.  It  teaches  what  is  essentially 
involved  in  the  idea  of  political  government.     It  explains  the 


necessaiy  instruments  of  government ;  as  a  law,  rights  and 
obligations,  sanctions,  executive  commands,  and  the  like.     It 
neither  enquires  into  the  operation  and  tendency  of  institutions 
(which  is  Theoretical  Politics),  nor  urges  the  preference  of 
one  to  others  (Practical  Politics).     It  explains  the  meaning  of 
monarchy,  aristocracy,  democracy,  but  does  not  teach  which 
is  the  best  form.     It  shows  what  is  the  nature  of  punishment 
but  does  not  say  which  punishments  are  the  most  efficacious! 
It  expounds  the  relations  of  master  and  free  servant,  and  of 
master  and  slave,  but  does  not  trace  their  bearings  on  the 
welfare  of  the  parties  concerned.     It  explains  the  nature  of  a 
dependency,  without  arguing  the  question— Should  colonies 
have  a  separate  government.      It  shows  what  are  the  acts 
constituting  an  exchange,  and  the  difference  between  barter 
and  a  money  equivalent,  but  does  not  dwell  upon  the  advan- 
tages of  exchange  in  facilitating  trade.  (Methods  of  Reasoning 
in  Politics,  vol.  I.,  p.  54j. 

The  fundamental  notions  of  Political  Society— Sovereignty, 
Law,  Command,  Duty,  Sanction,  Obligation—are  treated  of 
by  John  Austin  as  a  part  of  the  special  science  of  Jurispru- 
dence, That  these  notions  are  at  the  basis  of  Jurisprudence 
is  beyond  doubt.  Still,  in  a  completely  formed  Political 
Science,  they  would  be  given  once  for  all  at  the  outset,  under 
the  head  of  the  Structure  of  Political  Society,  and  would  need 
only  to  be  referred  to  by  the  Jurist. 

7.  The  very  fact  of  Political  Society  involves  a  series  of 
primary  notions,  forming  a  mutually  implicated,  or  corre- 
lative group. 

Government— ThiB  is  the  essential  fact  of  political  society ; 
to  define  it,  or  any  one  of  its  numerous  synonyms— Sovereio-ntv 
Authority,  Ruler,  Political  Superior— is  to  define  polTtical 
society.  The  definition  must  be  gathered  from  the  Particulars 
common  to  Political  Societies.  It  is  given  by  Sir  G.  C.  Lewis 
as  follows  :— *»  When  a  body  of  persons,  yielding  obedience  U> 
no  superior,  issue  their  commands  to  certain  other  persons  to 
do  or  to  forbear  doing  certain  acts,  and  threaten  to  punish  the 
disobedience  of  their  commands  by  the  infliction  of  pain,  they 
are  said  to  establish  political  or  civil  government:' 

Closely  examined,  this  definition  contains  the  very  terms  to 
be  defined— for  example,  superior  and  command— so  that  it  is 
not  a  definition  suited  to  inform  the  ignorant.  It  is  rather  of 
the  nature  of  the  first  definitions  of  geometry  (Line,  Angle, 
&c.)  which  do  not  communicate  notions,  but  employ  terms  to 


i 


552 


LOGIC  OF  POLITICS. 


THE  POLITICAL   STRUCTURE 


653 


fix  with  more  precision  the  boundaries  of  notions  already 
gained  from  experience.  We  should  require,  in  the  first 
place,  to  know  political  societies,  in  concrete  instances ;  and 
the  definition  would  teach  us  the  corresponding  abstraction  or 
generality. 

Austin  (Province  of  Jurisprudence  Examined)  endeavours 
to  build  up  the  definition  from  its  simplest  assignable  elements. 
Starting  with  Command,  he  defines  this  as  *  the  expression  or 
intimation  of  a  wish,  to  be  followed  with  some  evil,  if  not 
complied  with.'  This  involves  only  such  facts  of  human  nature 
as  wish,  expression,  non-compliance,  infliction  of  evil.  In  the 
notion  of  Command,  as  thus  defined  we  have  nearly  all  that 
is  signified  by  Government,  Sovereign,  Superior,  Authority. 
We  have  only  to  specify  the  persons  intimating  the  wish  (to 
some  other  persons)  and  following  up  the  non-compliance  with 
the  infliction  of  pain. 

The  supposed  command  is  a  Law.  The  evil  to  be  inflicted 
is  a  Sanction,  Penalty,  or  Punishment.  The  persons  addressed 
are  Subjects,  Inferiors ;  they  are  placed  under  Obedience,  Dtity^ 
Obligation.  The  aggregate  of  persons  comprised  within  the 
scope  of  the  same  commands,  is  a  Political  Society,  a  Community, 
a  People.  They  are  in  the  Social  state,  as  opposed  to  the  state 
of  nature. 

Moral  Right  and  Wrong  must  be  referred  to  the  same  com- 
plex fact. 

8.  Government  is  usually  said  to  have  three  distinct 
functions — Legislative,  Executive,  and  Judicial ;  each  one 
giving  birth  to  a  numerous  class  of  notions. 

Legislature. — The  power  of  making  general  commands  uni- 
versally applicable,  under  given  circumstances,  is  called 
Legislation  ;  it  is  the  most  extensive  and  characteristic  func- 
tion of  government.  The  process  is  very  difierent  under 
different  forms  of  government.  In  every  shape,  there  are 
implied  as  subsidiary  notions — statute,  and  its  synonyms,  pub- 
lication or  proclamation,  enactment  and  repeal,  <fea.  *"^ 

Executive,  Administration. — Implies  performance  of  the  speci- 
fic acts  occurring  from  day  to  day,  in  the  exigencies  of  society 
— organizing  and  directing  the  military  force,  negotiating  with 
foreign  governments,  appointing  the  officials  of  government, 
erecting  public  works,  &c.  In  this  function,  the  government 
is  said  to  use  ministers,  to  issue  orders,  to  receive  and  issue 
despatches,  reports,  to  superintend  all  functionaries. 

Judicial, — A  distinct  function  of  government,  usually  en- 


trusted to  a  separate  class  of  persons.  It  supposes  impedi- 
ments to  the  commands  and  operations  of  government,  either 
m  the  way  of  misunderstanding,  or  of  disobedience.  These 
are  removed  by  Judicial  Institutions,  called  Courts  of  Law 
presided  over  by  Judges,  said  to  administer  Justice,  according 
to  a  definite  Procedure,  and  rules  of  Evidence.  The  ramified 
arrangements  belonging  to  these  several  heads  are  detailed  and 
defined  by  the  special  science  of  Jurisprudence. 

With  all  varieties  of  government  there  must  exist  these 
three  functions ;  m  rude  governments,  they  are  exercised  by 
the  same  persons  ;  in  civilized  governments,  they  are  more 
or  less  divided  between  different  persons. 

9.  Under  '  Form  of  Government,'  there  is  a  number  of 
structural  modes,  for  which  there  are  specific  designations. 

The  Form  of  Government  brings  out  the  designations 
Monarchy,  Aristocracy,  Democracy,  Republic,  Mixed  Govern- 
ment, Balance  of  Power,  Constitution. 

The  logical  division  of  Forms  of  Government  is  into  the 
government  of  one  person  (Absolute  Monarchy)  and  the  govern- 
ment of  more  than  one  [Republic  or  Commonwealth).  If,  in 
the  second  alternative,  the  governing  body  is  small,  the 
government  is  an  Aristocracy ;  if  the  power  is  lodged  in  the 
majority  of  adult  citizens,  the  government  is  a  Democracy. 
buch  names  as  Limited  Monarchy,  Constitutional  Monarchy, 
mean  either  Aristocracy  or  Democracy;    they   indicate  the 

?^™j°5r"^^°^^^^^'  ^*^^  *^®  ^^^-^  of  another  power.  A 
Mixed  Government  is  a  mere  semblance  ;  some  one  of  the  con- 
stituents is  in  point  of  fact  the  sovereign. 

Aristocracy,  where  it  prevails,  makes  a  division  of  the 
people  mto  Nobility  and  Commonality.  Often  the  governincr 
body  is  a  hereditary  nobility.  * 

^  Representative  Government,  the  growth  of  modern  Democracy, 
IS  a  leading  notion  of  Political  Science.  The  meaning  is  that 
the  whole  people,  or  a  large  portion,  exercise  the  ultimate 
controlling  power,  through  the  deputies  periodically  elected  by 
themselves.  In  the  ancient  republics,  the  corporate  or  col- 
legiate action  lay  with  an  assembly  of  all  the  citizens,  or  of  as 
many  as  could  be  got  together. 

The  operations  of  corporate  government  give  birth  to  the 
political  elements  expressed  by  assembly,  deliberation  and 
debate,  decision  by  a  majoHiy,  chairman,  election,  suffrage. 

10.  The  Functions  or  Business  of  government  introduce 
many  structural  elements. 


t 


554 


LOGIC  OF  POLITICS. 


ORDER  AND   PROGRESS. 


555 


The  first  function  of  a  political  society  being  defence^  there 
is  a  large  institution  corresponding,  called  the  War  Organiza- 
tion— Army  and  Navy. 

The  protection  of  the  members  of  the  society  from  one 
another  is  either  by  an  application  of  the  War  force,  that 
is  the  soldiery,  or  by  a  separate  force  called  Police. 

These  two  leading  institutions  involve  many  others.  An 
official  machinery,  or  bureaucracy^  is  interposed  between  the 
sovereign  power  and  the  actual  instruments.  For  paying  the 
cost,  there  must  bo  a  levy  of  Taxes,  with  a  bureaucracy 
corresponding. 

If  the  government  undertakes  public  works — roads,  bridges, 
public  buildings,  means  of  communication — it  becomes  a  sort  of 
industrial  management  on  the  large  scale. 

The  coining  of  money  is  a  proper  function  of  government. 

The  regulation  of  bargains  and  contracts  of  every  description, 
as  well  as  the  enforcing  of  them,  is  a  matter  for  the  state.  The 
marriage  contract,  in  particular,  the  relations  and  rights  of  the 
different  members  of  the  family,  are  under  state  control. 

A  Church  Establishment,  whether  incorporated  with  the 
civil  government,  as  is  most  usual,  or  existing  apart,  is  a  vast 
social  machinery  with  elements  and  terms  corresponding,  all 
admitting  of  definition. 

11.  In  a  society  spread  over  a  wide  territory,  there  must 
be  a  division  into  local  governments,  duly  subordinated 
to  the  chief  or  Central  Authority. 

This  originate3  the  terms  Central,  Centralization^  and  Local, 
Provincial^  or  Municipal  government  and  institutions.  A  small 
locality  may  represent  in  miniature  nearly  all  tbe  features  of 
the  entire  society.  The  delegation  of  power  to  tbe  locality 
may  be  small  or  may  be  great.  Moreover,  the  Form  of 
Government  of  the  entire  cociety  repeatsitself  in  the  localities. 
If  the  sovereign  is  an  absolute  monarch,  the  local  authority  is 
absolute  ii}  the  local  sphere ;  such  is  the  oriental  satrap,  and 
the  viceroy  of  the  absolute  European  monarch. 

12.  The  Province  of  Government  marks  the  line  between 
Public  and  Private  management. 

The  habitual  industry  or  every  day  avocations  of  the  mass 
of  the  people  must  be  left  to  themselves.  Their  manner  of 
subsistence,  their  recreations  and  amusements,  are  also  their 
own  choice  ;  although  governments  have  often  interposed  to 
regulate  all  such  matters. 


13.  The  mutual  bearings  of  Public  and  Private  Institu- 
tions are  so  numerous,  that  a  statement  of  the  Political 
structure  is  incomplete  without  the  Private  Institutions. 

The  Industry  of  the  People  is  an  important  element  of  the 
state  politically.  So  are  their  Recreations,  Tastes,  Opinions, 
Literature,  and  Science.  However  much  the  government  ab- 
stains from  control  in  these  matters,  its  operations  in  its  proper 
sphere  are  influenced  by  every  one  of  them.  An  agricultural 
community  gives  a  peculiar  character  to  the  entire  action  of 
its  government.  A  community  largely  occupied  in  foreign 
trade  involves  the  government  in  relations  with  foreign  coun- 
tries. 

14  The  ffood  or  ill  working?  of  the  Political  svstem 
leads  to  a  variety  of  situations,  requiring  the  consideration 
of  the  political  reasoner. 

When  the  government  fails  to  accomplish  its  main  functions 
—defence,  protection,  justice,  &c.- — it  receives  the  designations, 
*  bad  government,'  *  mis-government.'  Its  badness  may  con- 
sist in  partiality  to  individuals,  which  is  injustice ;  in  not 
adhering  to  its  own  published  regulations ;  in  the  capricious 
introduction  of  changes  ;  in  preying  upon  the  community  by 
exactions,  or  by  affronts. 

When  the  government  is  excessive  in  its  restraints  on  indi- 
vidual movements,  it  is  called  despoticaly  tyrannical,  oppressive ; 
and  the  re-action  or  revolt  is  Political  Liberty.  When  it 
meddles  with  what  might  be  left  to  private  management,  it  is 
BSiidto  over- govern  ;  the  euphuistic  phrase  is  a  pa/erwai  govern- 
ment. 

The  emphatic  expression  Social  Order  means,  in  the  first 
place,  that  the  government,  whether  good  or  bad,  is  obeyed ; 
the  opposite  state  is  Anarchy,  Revolt. 

Order  is  also  contrasted  with  Progress,  Improvement,  or 
Civilization.  Those  things  that  maintain  the  existing  structure 
in  its  integrity  are  said  to  minister  to  Order  ;  while  the  agen- 
cies that  raise  the  society  to  a  higher  pitch  of  improvement, 
are  said  to  minister  to  Progress.  In  point  of  fact,  the  opposi- 
tion between  the  two  is  very  slight ;  what  is  good  for  one  is, 
with  very  trifling  allowances,  good  for  the  other  (Mill's  Bid- 
presentative  Government,  chap.  II). 


I 


I 


556 


LOGIC  OF  POLITICS. 


POLITICAL  ETHOLOGY. 


557 


THEORETICAL   POLITICS. 

15.  The  Laws,  Principles,  or  Propositions,  of  political 
society,  together  with  the  Methods  of  Investigation,  consti- 
tute Theoretical  Politics. 

The  foregoing  head,  including  the  Analysis  of  the  Social 
Structure,  the  meaning  of  State  of  Society,  the  Notions  of 
Politics — is  preparatory  to  the  enunciation  of  the  Laws  of 
Society,  so  far  as  known.  These  Laws  are  best  discussed  in 
the  theoretical  form  ;  they  may  afterwards  be  changed  into 
the  practical  or  preceptive  form,  that  is,  into  maxims  of  the 
Political  Art 

16.  The  Laws  of  Society  may  be  either  Laws  of  Co- 
existence, or  Laws  of  Succession,  of  the  different  parts  of 
the  Social  Structure.  In  both  cases,  they  are  laws  of 
Cause  and  Effect. 

The  complex  structure  of  Political  Society  involves  many 
relationships  of  Co-existence  and  of  non-coexistence.  Some 
arrangements  always  carry  with  them  some  other  arrange- 
ments ;  some  things  are  repugnant  to  other  things.  The  re- 
mark was  made  by  Volney  that  the  *  plains  are  the  seat  of 
indolence  and  slavery,  the  mountains  of  energy  and  liberty.* 
But  whatever  co-existences  and  repugnances  can  be  predicated 
generally  are  dependent  on  causation. 

Again,  we  may  take  any  ooe  part  of  the  social  structure  as 
a  cause,  and  lay  down  the  laws  of  its  effects ;  as  when  we 
describe  the  consequences  arising  in  a  given  state  of  society, 
from  an  absolute  monarchy  or  from  a  state  church. 

We  may  even  take  up  an  entire  state  of  society,  with  all  its 
mutual  actions,  and  endeavour  to  trace  its  future  destiny. 
This  is  the  large  problem  of  the  Philosophy  of  History. 

But  for  devices  of  simplification,  such  problems  would  be 
wholly  unworkable  ;  the  complication  of  elements  could  not 
be  embraced  by  the  human  mind.  We  should  need  to  fasten 
upon  some  single  agency,  either  comprehending,  or  outweigh- 
ing the  others,  whose  solitary  operation  will  give  the  key  to 
the  entire  problem.  The  state  of  opinion  and  enlightenment 
of  a  community  is  an  example  of  those  over- mas  tiering  cip- 
cumstances. 

Human  Character  as  a  Political  Element. 

17.  As  the  subject-matter  of  Political  Science  is  human 


beings,  the  characteristics  of  humanity  must  enter  as  a 
primary  element. 

If  all  human  beings  were  alike,  either  wholly  or  in  those 
points  concerned  in  political  action,  the  construction  of  a 
political  society,  whether  easy  or  not,  would  be  but  one  pro- 
blem. But  there  are  wide  differences  as  regards  peculiarities 
of  character  essential  to  the  working  of  the  political  scheme. 
The  differences  between  an  American  Indian,  a  Hindoo,  a 
Chinaman,  a  Russian,  an  Englishman,  an  Irishman,  an  Italian, 
taken  on  the  average,  are  such  as  to  affect  seriously  the  struc- 
ture and  the  workings  of  political  institutions.  Given  a  certain 
Form  of  Government,  or  a  certain  constitution  of  Landed 
Property,  the  tendencies  would  alter  greatly  under  these 
various  types  of  character. 

The  theory  of  Society  consists  in  stating  how  human  beings 
will  act  under  a  given  social  arrangement;  it  is,  therefore, 
essentially  a  special  application  of  the  laws  of  mind  and  char- 
acter. Hence  a  thorough  knowledge  of  what-ever  Psychology 
can  teach  would  be  a  preparation  for  this  study. 

Yet,  all  parts  of  human  nature  are  not  equally  concerned  in 
political  action ;  the  ethical  qualities  of  Honesty,  Industry, 
Steadiness  of  Purpose,  are  more  vital  than  the  Artistic  sensi- 
bilities. 

Moreover,  Politics  is  concerned  only  with  the  characteristics 
that  appear  in  collective  bodies.  The  politician  leaves  out  of 
account  all  those  individualities  that  are  merged  when  men  act 
together  in  a  body ;  that  is,  the  qualities  occuring  merely 
in  scattered  individuals  and  in  minorities.  Whence,  national 
character  is  a  much  simpler  phenomenon  than  individual 
character ;  as  the  flow  of  a  river  in  mass  is  a  simpler  physical 
problem  than  the  molecular  adjustments  of  the  liquid  state. 

18.  A  Political  Ethology  would  be  a  modified  science  of 
character,  consisting  (1)  of  a  selection  of  the  qualities  that 
appear  in  national  character,  and  (2)  of  the  laws  of  their 
operation. 

(1)  Following  the  divisions  and  subdivisions  of  character, 
as  formerly  sketched  (p.  518),  we  should  have  to  bring  out  into 
prominence  all  that  arise  in  human  beings  when  working 
collectively. 

Thus,  to  commence  with  Action,  in  the  form  of  Spontaneous 
Energy.  Prior  to  an  account  of  the  various  motives  that 
induce  men  to  activity,  there  is  a  notable  peculiarity  of  cha- 


) 


558 


LOGIC  OF  POLITICS. 


CAUSE  AND  EFFECT. 


racter  in  the  degree  of  the  energetic  disposition  itself.  Now 
this  shows  itself,  as  high  or  as  low,  in  whole  nations,  and  is  of 
importance  as  respects  both  the  Form  of  Government  and 
many  other  political  arrangements.  The  inhabitants  of  tempe- 
rate climates  are  superior  in  natural  energy,  irrespective  of  all 
modes  of  stimulation,  to  the  dwellers  either  in  the  tropics  or 
in  the  arctic  circles.  The  English  and  Anglo-American 
peoples  are  probably  at  the  top  of  the  scale. 

Now  this  attribute  has  numerous  social  bearings.  It  favours 
private  industry  and  the  accumulation  of  wealth,  an  effect 
leading  to  many  other  effects.  It  is  both  directly  and  indirectly 
hostile  to  monarchical  or  despotical  rule,  and  is,  therefore,  the 
parent  and  the  guardian  of  liberty. 

In  like  manner,  we  might  survey  in  detail  the  Feelings, 
Sensibilities,  or  Emotions  of  the  mind,  and  mark  those  that 
have  social  significance,  and  those  that  appear  in  men  col- 
lectively. Thus,  the  Tender  Sentiments,  or  the  Sociability  of 
the  Mind,  when  strong,  draw  human  beings  together  in  society, 
and  favour  the  cohesion  of  states  as  well  as  of  families.  Again, 
the  strength  and  the  mode  of  the  Sentiment  of  Power  may  be 
a  collective  peculiarity,  with  national  consequences.  The 
conjunction  of  tender  feeling,  as  patriotism  within  our  own 
nation,  with  the  love  of  domination  beyond,  is  a  peculiarity 
often  repeated. 

The  Intellectual  qualities  that  stand  out  in  national  pro- 
minence are  too  numerous  to  be  touched  upon.  It  was  an 
intellectually  minded  people,  the  Greeks,  that  began  all  the 
civilization  flowing  from  science  or  philosophy.  There  is  a 
certain  depth  of  ignorance  and  incapacity  that  renders  the 
higher  modes  of  Political  society  impossible.  A  signal  failure 
in  either  of  the  intellectual  vii'tues — prudence  and  sympathy, 
is  incompatible  with  political  union. 

(2)  The  next  part  of  Political  Ethology  is  an  account  of  the 
tendencies  of  these  various  characteristics,  and  of  the  means 
whereby  they  themselves  are  modified.  The  general  science 
of  character  embraces  this  investigation  on  the  wide  scale,  and 
the  present  department  is  a  special  application  of  the  principles. 

Propositions  of  Theoretical  Politics. 

19.  The  Political  Structure,  or  Organism,  being  defined, 
the  Laws  of  Theoretical  Politics  are  the  laws  of  Cause  and 
Effect,  traceable  in  the  working  of  the  several  Institutions. 

What  are  the  consequences  of  Absolute  Monarchy,  or  of- 


559 


Democracy ;  of  Castes ;  of  Entails ;  of  Free  Trade ;  of  Poor 
Laws  ;  of  Indissoluble  Marriage  ;  of  State  Churches  ?  These 
are  a  few  of  the  enquiries  of  Political  Science ;  they  are  strictly 
enquiries  of  Cause  and  Effect.  Given  any  of  these  institutions 
as  causes,  the  effects  may  be  sought.  Again,  given  certain  effects 
as  the  repression  of  agrarian  crimes,  the  impartial  administra- 
tion of  justice,  the  encouragement  of  trade,— we  may  seek  for 
causes.  This  is  really  the  same  problem  in  a  different  form. 
To  all  intents  and  purposes,  the  one  enquiry  is— Given  a  cause* 
required  the  effect  ?  * 

It  is  not  uncommon  for  political  philosophers  to  entertain 
such  problems,  as  What  are  the  effects  of  Monarchy,  Aristoc- 
racy.  Democracy,  in  general ;  what  are  the  effects  of  Slavery 
m  general,  that  IS,  under  all  circumstances,  under  every  possible 
variety  of  human  character.     Now,  with  such  strongly-actinff 
causes  as  Absolute  Monarchy,  there  may  be  assigned  certain 
universal  tendencies  so  decided  as  to  be  seldom  wholly  defeated. 
Ihere  are  points  in  common  to  the  despotism  of  a  sinele  person 
m  all  countries  and  times.     The  possession  of  power,  whether 
on  the  great  scale  or  on  the  small,  operates  with  remarkable 
uniformity       This   is  a  psychological   tendency   whose   free 
course  is  best  seen  in  politics ;  where,  by  the  necessities  of 
the  case,  individuals  have  to  be  entrusted  with  power  in  a 
large  amount.     The  same  consideration  renders  the  workinffs 
ol  slavery  uniform  to  a  high  degree. 

20.  The  Propositions  of  Political  Science  range  between 
two  extremes ;  on  the  one  extreme  are  propositions  affir- 
ming universal  tendency,  and,  on  the  other,  propositions 
affirming  specific  effects  in  limited  cases. 

(^)  ,'^^®  propositions  affirming  a  universal  tendency  are 
exemplified  above.  Similar  propositions  may  be  found  respect- 
ing every  institution  of  human  society.  In  many  institutions 
however,  the  tendencies  are  difficult  to  find  out,  and  are  s<J 
liable  to  be  defeated  by  other  caoises,  that  their  enunciation 
has  scarcely  any  value.  For  example,  the  operation  of  guilds, 
or  privileged  corporations,  admits  of  no  definite  statement 
with  reference  to  all  possible  circumstances.  The  division  of 
and  into  large  or  small  properties  may  have  opposite  effects 
m  different  social  states. 

Nevertheless,  the  attempt  should  be  made  to  generalize  the 
tendencies  both  of  the  Forms  of  Government,  in  their  detaHed 
varieties,  and  of  all  the  leading  Institutions  growing  out  of 
legislative  action.     It  is  equally  indispensable  to  estimate  the 


I 


560 


LOGIC  OF  POLITICS. 


LIMITED  OR  PARTIAIi  THEORIES. 


561 


precise  worfcb  of  tbis  class  of  propositions,  to  be  aware  of  their 
infirmities,  and  of  the  cautions  needed  in  applying  them. 
There  are  prevailing  tendencies  of  every  important  Institution 
—of  the  Succession  of  Land,  of  Direct  or  Indirect  Taxation, 
of  Religious  Endowments,  and  the  rest.  The  affirmations  re- 
specting these  are  only  probable ;  they  afford  a  certain  pre. 
sumption  of  what  will  actually  happen  in  individual  cases. 
The  special  departments— Political  Economy  and  Jurispru- 
dence—share the  burden  of  these  difficult  problenis. 

(2)  Propositions  confined  in  their  range  to  limited  circum- 
Btances,  to  a  narrow  field  of  observation,  may  be  so  qualified 
as  to  state  the  causation  with  almost  perfect  exactness.  Thus 
if  we  confine  our  views  to  communities  in  similar  climates,  of 
the  same  race,  of  nearly  the  same  advancement  in  general 
intelligence,  we  can  formulate  with  comparative  precision  the 
tendencies  of  a  given  institution,  whether  the  Form  of  Govern- 
ment, or  any  of  the  other  leading  social  elements.  These 
Limited  or  Partial  Theories  are  the  really  valuable  parts  of 
Political  Science  ;  they  afford  the  guidance  in  the  art  or  prac- 
tice of  Politics.  . 

With  a  view  to  these  propositions,  there  must  be  a  division 
and  subdivisions  of  communities  into  classes.  An  example  of 
such  a  classification  is  given  by  Sir  G.  C.  Lewis,  as  follows:— 
*  One  large  classification  of  communities  for  the  purpose  of 
a  common  predication  is— 1,  those  communities  which  are  in 
a  wild  and  unsettled  state,  such  as  the  African  and  Indian 
savages,  the  Bedouin  Arabs,  the  Nomad  Tartars;  2,  those 
Oriental  communities  which  live  under  a  regular  political 
government,  but  whose  social  state  is  nevertheless  fixed  and 
nnprogressive,  such  as  the  Turks,  the  Persians,  the  Hindus, 
the  Chinese,  the  Japanese ;  3,  Christian  communities  partaking 
of  the  modem  European  civilization.' 

Setting  aside  the  first  class,  as  affording  too  limited  a  field 
for  political  data.  Sir  G.  C.  Lewis  institutes  a  comparison  and 
contrast  between  Oriental  and  European  communities,  showing 
the  numerous  important  peculiarities  that  may  be  affirmed  of 
each  of  the  two  classes  as  a  whole.  The  following  are  some 
leading  points  of  the  contrast. 

OiiiENTAL.  European. 

Government, 

Despotical  Free 

By  Delegation  Direct  from  the  centre 

International  Law, 

K,xi(ie  Intricate,  forming  a  bal- 

ance of  power 


Laws — Civil  and  Religious  codes. 
Interwoven  Distinct 

Marriage. 
Polygamy  Monogamy 

Women, 
Secluded  At  large 

Status  of  the  Labourer. 
Slavery  Civil  Freedom 

Punishments. 
Cruel  Mild 

Dress, 
Loose  Closely  fitting 

A  Iphabet. 
Intricate  Simple 

Form  of  Literature, 
Poetry  and  mystical  prose  Argumentative  prose. 
Numerous  propositions  of  Cause  and  Effect  could  be  laid 
down  respecting  these  peculiarities,  connecting  them  with 
one  another,  and  with  the  Climate  and  Physical  Situation,  the 
Physical  and  Mental  Constitution,  and  the  Historical  Ante- 
cedents of  the  oriental  races. 

Methods  of  Theoretical  Politics, 

21.  As  in  all  other  sciences,  there  must  be  Observation 
of  Facts. 

In  Political  Observation,  there  are  special  peculiarities 
amenable  to  logical  canons.  The  education  of  a  political 
observer  is  scarcely  in  any  degree,  as  in  the  physical  sciences, 
an  education  of  the  senses ;  it  consists  mainly  of  intellectual 
habits. 

22.  The  Facts  of  Politics  coincide  with  authentic  His- 
tory or  Narrative. 

The  individual  occurrences  that,  when  generalized,  make 
up  political  principles,  have  to  be  correctly  recorded,  with  all 
the  circumstances  essential  to  the  link  of  causation.  The 
sequence  of  events  in  a  revolution  must  be  stated  exactly  as 
they  occurred,  and  in  sufficient  fulness  to  give  the  conditions 
of  canoBe  and  effect. 

Th6  rules  of  historical  evidence  are  a  branch  of  Inductive 
Logic,  and  as  such  they  are  given  elsewhere  (Appendix,  I). 
They  have  in  view  principally  the  number  and  the  nature  of 
the  testimonies  needed  to  establish  the  truth  of  a  past  event. 


|i 


i  i] 


tisi 


662 


LOGIC   OF  POLITICS. 


POLITICAL  EXPERIMEXTS. 


563 


A  farther  exercise  of  discrimination  is  requisite  in  the  political 
historian,  namely,  to  include  all  the  circumstances  entering 
into  the  chain  of  causes,  and  to  separate  accompaniments 
that  have  only  a  poetic  interest.  To  do  this,  the  his- 
torian must  be  himself  a  political  philosopher ;  he  must 
know  that  the  dazzling  glitter  of  spears  in  the  sun  has  nothing 
to  do  with  the  fighting  strength  of  an  army,  that  the  stature, 
complexion,  voice,  or  dress  of  Charles  I.  had  no  bearing  upon 
his  quarrel  with  his  parliament.  In  short,  as  regards  the 
relevance  of  facts  and  circumstances,  the  narrator  must  under- 
stand what  it  is  to  trace  cause  and  effect  in  history.  *  In 
order  to  frame  a  coherent  narrative,  some  theory  of  causation 
is  necessary '  (Lewis). 

23.  In  Politics  was  first  developed  the  reducing  of 
observations  to  the  form  called  Statistics  ;  definable  as  the 
observation,  registration,  and  arrangement  of  such  facts  as 
can  be  given  in  numbers. 

The  cultivation  of  statistics  was  first  owing  to  the  impetus 
given  to  political  economy  by  the  French  economists  ;  it  being 
possible  to  state  in  numbers  the  most  material  facts  regarding 
trade,  currency,  taxation,  production,  population,  &c.  The 
subject  now  comprises  matters  relating  to  all  branches  of 
political  observation  ;  Population,  Births,  Marriages,  Deaths, 
Occupations,  Diseases,  Crimes,  Pauperism,  Education. 

Statistics  gives  an  entirely  new  precision  both  to  Theoretical 
or  Speculative  Politics,  and  to  the  operations  of  government. 
The  increase  or  diminution  of  pauperism  or  of  crime,  in  a  large 
country,  could  be  judged  only  in  the  vaguest  manner  without 
statistical  returns  from  the  officials  concerned.  The  govern- 
ment would  be  at  the  mercy  of  accidental  displays,  and  of 
circumstances  where  the  impressions  are  exaggerated.  A 
bread  riot  in  a  particular  locality,  an  outrage  of  appalling 
accompaniments,  would  distort  the  judgment  of  the  nation,  as 
to  the  general  state  of  destitution  or  of  crime. 

24  The  causes  of  erroneous  observation  in  Politics,  are 
partly  common  to  the  sciences  generally,  and  partly  special 
to  the  political  science. 

Indolence  and  inattention,  the  love  of  the  marvellous, 
BBsthetic  likings  and  dislikings,  the  support  of  a  favourite 
theory,  are  operative  in  politics  as  elsewhere.  The  more 
special  sources  of  bias  in  the  political  department  ai*e  admira« 
tion  of  individual  actors,  party  feeling,  and,  where  practice  is 


concerned,  direct  personal  interest.  As  a  matter  of  course, 
these  corrupting  motives  extend  their  influence  to  the  general- 
izing no  less  than  to  the  observing  of  facts. 

Politics  deals  with  human  beings,  whose  springs  of  action 
are  in  the  mind ;  while  observation  relates  only  to  outward 
appearances,  from  which  the  mental  states  are  obtained  by 
inference.  The  right  performance  of  this  process  of  inference 
is  an  operation  based  on  Psychology,  and  guided  by  the  rules 
of  Inductive  Logic.  That  Charles  I.  was  executed  is  a  fact ; 
the  motives  of  Cromwell  and  the  Puritans  in  executing  him 
are  a  matter  of  difficult  inference  ;  requiring  us  to  apply  laws 
of  human  nature  (veracity,  bias,  &c.),  to  what  the  actors  said 
and  did  in  connexion  with  the  fact.  The  secrecy  of  motives 
is  the  characteristic  of  many  ethical  maxims. 

Experiment  in  Politics. 

25.  Experiment,  in  the  strict  scientific  meaning,  is  usu- 
ally regarded  as  inadmissible  in  Politics.  The  su1)stitute3 
are  (1)  the  sudden  introduction  of  extraordinary  influences, 
and  (2)  the  practical  operations  of  government. 

It  is  not  possible  to  submit  a  society  to  the  process  em- 
ployed in  studying  a  metal,  or  in  detecting  the  laws  of  Heat 
or  Magnetism.  A  political  community  cannot  be  manipulated 
with  a  view  to  excluding  artificially  this  or  that  agency,  iso- 
lating it  from  all  but  known  circumstances. 

(1)  Some  of  the  advantages  of  experiment  are  derivable 
through  the  introduction  of  a  new  and  extraordinary  influence 
into  the  society — such  as  a  famine,  a  commercial  crisis,  an 
insurrection,  an  epidemic,  an  invasion,  a  new  invention,  as  the 
steam  engine,  a  religious  revolution.  The  Irish  potato  famine 
of  1845,  is  adduced  by  Lewis  as  a  case  in  point  The  influence 
of  this  terrible  calamity  laid  bare  the  evils  in  the  state  of  the 
Irish  poor,  and  disclosed  the  secret  springs  in  the  social 
economy  of  the  people,  as  effectually  as  could  have  been  done 
by  an  artificial  experiment  contrived  for  that  purpose. 

(2)  It  is  the  very  nature  of  government,  especially  an  im- 
proving government,  to  be  trying  experiments.  Every  new 
law  is  an  experiment.  There  being  an  object  to  be  achieved 
by  the  law,  the  public  is  supposed  to  be  interested  in  watching 
the  effects  of  the  measure.  A  Police  is  organized,  and  the 
effects  upon  crime  observed.  A  Poor  Law  is  introduced,  and 
the  consequences  traced.  So  every  great  innovation  is  a  new 
agent  in  society,  which  is  followed  by  definite  effecta     The 


564 


LOGIC  OF  POLITICS. 


DEFECTS   OF  THE  METHOD   OF  AGREEMENT. 


665 


experiments  are  not  always  free  from  ambiguity ;  there  may 
be  concurring  agencies  either  defeating  or  exaggerating  the 
results ;  hence  a  demand  for  the  precautions  of  the  various 
Inductive  Methods. 

Causatlun  in  Politics, 

26.  In  Political  Causation,  the  predominating  fact  is 
Collocation  ;  there  is  seldom,  yet  occasionally,  an  appeal 
to  Conservation. 

A  political  sequence  is  always  immersed  in  a  host  of  arrange- 
ments, positive  or  negative ;  and  although  impelling  forces 
must  always  be  present,  the  result  is  dependent  in  a  pre-emi- 
nent degree  upon  the  direction  given  to  these  forces.  Thus, 
a  political  rising  depends  less  upon  the  greatness  of  an  impel- 
ling force,  than  npon  the  direction  given  to  forces  always 
present.  The  demand  for  thirty  shillings  of  ship  money  from 
John  Hampden  was  the  turning  point  of  the  English  Revolu- 
tion. 

Yet  in  dealing  with  human  nature,  whether  as  individuals 
or  political  masses,  any  omission  to  allow  for  the  principle  of 
Conservation,  in  the  form  of  Limitation  of  Human  Energy, 
will  lead  to  mistakes.  Thus,  a  politician  that  would  expect 
an  Art-loving  people  like  the  Italians,  Germans,  or  French,  to 
tako  on  the  energy  of  the  English  in  business  and  in  politics, 
"without  becoming  less  artistic,  would  be  guilty  of  overlooking 
the  law  of  Limitation. 

27.  In  Political  Causation,  it  is  especially  necessary  to 
keep  in  view  the  entire  aggregate  of  conditions,  positive 
and  negative,  entering  into  the  cause. 

When  Luther  preached  against  Indulgences,  and  when 
Hampden  refused  to  pay  ship  money,  these  were  merely  a  single 
condition  out  of  a  large  assemblage  concerned  in  bringing 
abont  the  great  events  that  ensued.  Hence,  the  historian 
considers  it  requisite  to  describe  the  whole  of  the  surroundings 
in  the  state  of  society  at  the  time,  but  for  which  the  conse- 
quences would  not  have  arisen. 

To  seek  the  cause  of  a  political  event  in  a  single  cir- 
cumstance is  a  perversion  of  the  political  problem.  The 
most  enlightened  reasoners  and  historians  are  accustomed  to 
state  the  case  as  an  enquiry  into  the  causes  of  a  phenomenon. 
The  phrase  is  not  strictly  correct ;  the  entire  aggregate  of 
antecedents  is  properly  the  cause;  but  as  bringing  forward  the 


idea  oi plurality  of  circumstances,  conditions,  or  collocations, 
the  mistake  is  on  the  right  side.  The  causation  of  the  French 
Revolution  was  a  vast  aggregate  of  prior  arrangements  in  the 
state  of  the  French  nation,  together  with  numerous  circum- 
stances in  the  world  at  large. 

The  Method  of  Agreement  in  Politics. 

28.  The  Method  of  Agreement  enters  into  political 
investigation,  but  not  without  shortcomings. 

Like  every  other  inductive  enquirer,  the  political  reasoner 
first  collects  his  facts ;  then  compares  them  with  a  view  to 
attaining  laws  of  concomitance,  which  he  farther  verifies  by 
Agreement,  as  a  method  of  Elimination. 

This  has  always  seemed  the  obvious  course.  When  Aris- 
totle enquires  into  the  effects  of  Despotical  or  of  Democratical 
government,  he  collects  examples  of  each,  and  looks  out  for 
the  attendent  peculiarities.  By  an  inductive  determination, 
founded  on  Agreement,  we  are  accustomed  to  connect  diffeiv 
ent  forms  of  government  with  lower  or  with  higher  stages  of 
civilization. 

The  first  peculiarity  of  the  inductive  problem  of  society,  as 
affectmg  the  sufficiency  of  the  Method  of  Agreement,  is  the 
mere  number  of  concomitant  circumstances  in  a  state  of 
society.  The  cause  A,  say  Despotism,  works  in  conjunction 
with  such  a  large  variety  of  other  circumstances,— climate, 
race,  history,  institutions  in  detail— B  C  D  E  F,  &c.,— that 
we  can  hardly  find  in  the  whole  area  of  our  experience  a 
sufficiently  diversified  series  of  instances  to  eliminate  them  all, 
and  find  A  followed  in  every  instance  by  a. 

Worse  than  the  mere  number  of  accompaniments  is  plurality 
of  causes  with  intermixture  of  effects.      Whatever  results  might 
really  flow  from  Despotism— whether  discontent  and  insurrec- 
tions, or  the  repression  of  men's  energies  and  the  arrest  of 
prosperity  and  progress— could  flow  from  other  social  agencies; 
the  effect  a,  an  actual  effect  of  A,  might  also  be  an  effect  of 
C,  F,  H.    This  would  not  prevent  a  from  being  always  present 
with  A ;  it  would  rather  in  some  instances  make  it  supera- 
bundantly present ;  yet,  as  proving  too  much,  it  would  be  fatal 
to  the  evidence.  An  apparently  more  paralyzing  instance  would 
be,  when  the  effect  a,  properly  belonging  to  A,  is  neutralised 
by  some  accompanying  agent  D  ;  one  of  the  commonest  of  all 
occurrences  in  politics.  Hardly  any  effect  of  absolute  monarchy 
is  better  substantiated  than  the  discouragement  of  intellectual 


si 

I 

I  I 


566 


LOGIC  OF  POUTICS. 


DEDUCTION   IN  POLITICS. 


567 


activity  generally;  yet  this  did  not  follow  at  once  on  the 
imperial  despotism  of  the  Roman  Empire  ;  the  prior  impetus 
acquired  under  free  institutions  was  for  a  long  time  unspent. 
So,  a  law  designed  to  produce  a  certain  effect,  may  really  be 
acting  as  intended ;  but  the  effect  may  be  frustrated  by 
evasions,  or  by  passive  resistance  to  its  enactments.  Restric- 
tious  on  trade  are  adverse  to  commercial  prosperity  ;  yet  the 
effect  may  happen  to  be  counteracted  by  other  circumstances. 
The  United  States  of  America,  in  the  abundance  of  land  to  be 
occupied,  can  prosper  under  many  arrangements  that  would  be 
ruinous  to  Great  Britain. 

The  other  Experimental  Methods. 

29.  The  Method  of  Difference  may  be  exemplified  in 
Political  Cause  and  Effect. 

The  introduction  or  withdrawal  of  a  single  agent,  followed  at 
once  by  a  definite  change  in  other  respects,  is  our  most  cogent, 
as  well  as  our  shortest  proof  of  causation.  In  the  complications 
of  Political  Society,  we  cannot  always  be  sure  that  only  the 
one  innovating  circumstance  is  present ;  so  many  unseen 
operations  being  always  at  work.  This  source  of  ambiguity  is 
practically  overcome  when  an  agent  suddenly  introduced,  is 
almost  instantaneously  followed  by  some  other  change  ;  as  when 
the  announcement  of  a  diplomatic  rupture  between  two  nations 
is  followed  the  same  day  with  a  derangement  of  the  money 
market. 

According  as  the  supposed  change  is  more  gradual  in  its 
introduction,  and  the  consequences  slower  in  their  develop- 
ment, the  instance  is  less  and  less  a  decisive  example  of  differ- 
ence. The  deterioration  of  value  is  saved  only  when  we  are 
sure  that  every  other  thing  has  remained  the  same.  A  new 
religion  introduced  into  a  nation,  remarkably  stationary  in  its 
other  institutions,  would  be  held  as  the  cause  of  all  the  subse- 
quent changes. 

30.  Agreement  in  Absence  may  be  advantageously  re- 
sorted to  in  Politics. 

We  compare  the  cases  of  the  presence  of  Poor  Laws,  of 
Commercial  Restrictions,  of  a  Standing  Army,  of  Local  Self- 
Government, — with  the  cases  of  the  absence  of  these  institu- 
tions ;  and  if  any  circumstances  uniformly  present  in  the  one 
are  uniformly  absent  in  the  other,  the  force  of  proof  is  greatly 
augmented. 


30.  Concomitant   Variations    is    employed   in   tracin^y 
political  causation.  ° 

There  is  a  marked  concomitance,  in  the  History  of  England, 
between  the  growth  of  Free  Institutions,  and  the  progress  of 
the  nation,  both  materially  and  intellectually.  This  may  be 
compared  with  the  inverse  instances  of  Grreece  and  Rome, 
where,  by  a  gradual  process,  the  extinction  of  liberty  was 
ultimately  followed  by  intellectual  and  social  decay.  Even 
all  these  instances,  in  the  complications  of  Politics,  may  not 
be  final ;  yet  they  afford  a  very  high  presumption  of  cause  and 
effect 

The  Deductive  Method. 

31.  The  Deductive  Method,  in  conjunction  with  the 
Inductive  or  Experimental  Methods,  must  be  regarded  as 
the  mainstay  of  political  investigation. 

Neither  the  Deductive  Method  alone,  nor  the  Inductive 
Methods  alone,  can  be  trusted  in  the  complications  of  the 
social  science.  Their  mutual  consilience  or  confirmation,  ig 
requisite  in  order  yield  trustworthy  conclusions. 

Pure  Deduction  appears  to  most  advantage  in  following  out 
the  tendencies  of  separate  agents.  This  is  the  motive  for 
subdividing  the  Social  Science  into  branches,  as  Political 
Economy,  &c.  The  tendency  of  the  single  motive  of  the 
desire  of  wealth  can  be  studied  apart  from  other  tendencies. 

An  essential  part  of  political  deduction  consists  in  tracing 
the  wide  operation  of  the  Sentiment  of  Power,  in  the  various 
degrees  of  its  development  among  human  beings,  and  under 
all  circumstances.  The  deduction  should  comprise  a  wider 
area  than  mere  political  situations. 

The  Sociability  of  mankind,  their  Sympathies,  the  grades  of 
Intelligence,  have  consequences  traceable  by  a  purely  deduc- 
tive operation. 

We  might  even  venture  a  certain  way  in  the  second  deduc- 
tive process — Calculation  or  computation  of  concurring  agen- 
cies ;  as  Wealth,  Power,  Sociability,  Sympathy,  with  Habits, 
Customs,  &c.  Here,  however,  we  become  aware  of  the  help- 
lessness of  the  deductive  method  by  itself.  Having  no  correct 
quantitative  estimate  of  the  separate  agents,  our  attempt  to 
combine  them  in  a  quantitative  sum,  is  entirely  hopeless.  The 
errors  of  calculation  may  be  so  wide  as  radically  to  vitiate  the 
conclusions. 

It  is  the  third  step  of  Deduction — Verification— that  gives 
25 


568 


LOGIC  OF  POLITICS. 


the  method  all  its  weight,  by  joining  it  with  Inductions.  In 
point  of  fact,  politicians  in  applying  the  conjoint  methods 
usually  have  an  inductive  or  empirical  generality  presented  in 
the  first  instance  ;  which  induction  they  compare  with  the 
deduced  tendencies  of  the  agents  concerned.  Tims  the  work- 
ing of  despotism  is  first  given  as  an  empirical  generalization 
from  history  ;  we  then  compare  these  alleged  results  with  the 
deductive  consequences  of  the  love  of  power,  and  all  other 
human  motives,  both  of  the  ruler  and  the  ruled,  entering  into 
the  situation.  Such  maxims  as  the  following  require,  for 
their  verification,  the  consilience  of  induction  and  deduction. — 
*The  possessors  of  supreme  power,  whether  One,  Few,  or 
Many,  have  no  need  of  the  arms  of  reason  ;  they  can  make 
will  prevail.*  'The  governments  most  distinguished  for 
sustained  vigour  and  ability  have  generally  been  aristocracies.' 
The  deductive  reasons  in  favour  of  this  last  position  are 
founded  on  the  consequences  of  devoting  a  small  number  of 
men  exclusively  to  public  business. 

Thus,  the  usual  course  of  the  Deductive  Method  is  to  lay 
hold  of  a  number  of  empiricisms^  derived  from  history  and 
political  experience,  and  to  subject  them  to  the  test  of  deduction, 
thereby  converting  them  into  derivative  laws.  Considered  as 
inductive  generalities,  everything  should  be  done  for  them 
that  can  be  done  by  strict  compliance  with  the  Inductive 
Methods ;  after  which  they  are  to  come  into  comparison  with 
the  deductive  results  of  the  tendencies  concerned. 

•  Among  Empiricisms  demanding  to  be  confronted  with 
deductive  conclusions,  we  may  instance  thefoUowing — ^modern 
civilization  tends  to  collective  mediocrity,'  (J.^S.  Mill);  *  unity 
in  religion  is  unfavourable  to  civil  interests '  (Gr.  C.  Lewis) ; 

*  there°is  no  necessary  connexion  between  hereditary  royalty 
and  hereditary  nobility '  (ib)  ;  *  the  human  race  is  on  the 
whole  progressive  ' ;  *  there  is  a  constant  relation  between  the 
state  of  society  and  the  state  of  intellectual  speculation' — 

(Comte). 

Deductive  confirmation  is  especially  needed  in  assignmg  the 
causes  of  some  one  historical  event.  Unless  there  happen  to 
be  other  events  closely  analogous,  our  inductive  basis  is  of  the 
slenderest  kind  ;  succession  may  be  taken  for  causation  with- 
out any  check.  Thus,  the  account  of  the  rise  of  free  institu- 
tions, in  modern  Europe,  must  be  far  more  deductive  than 

inductive, 

'    The  introduction  of  Christianity  into  Europe  co-existed  with 

BO  many  other  changes,  that  its  consequences  cannot  easily  be. 


EMPIRICAL  AND   DERIVATIVE   LAWS. 


569 


eh'minated.  Our  only  means  of  varying  the  instances  is  to 
take  the  separate  nations  apart;  but  in  none  of  them  was  this 
one  cause  introduced  singly.  Hence  any  inference  as  to  the 
political  and  other  results  of  Christianity  would  want  much 
deductive  confirmation;  and  we  find  that  this  method  is 
largely  appealed  to.  The  tendencies  of  the  Christian  religion 
are  laid  out  deductively,  and  the  attempt  is  made  to  show  their 
coincidence  with  the  facts.  To  be  properly  checked,  a  similar 
deduction  should  be  made  of  all  other  tendencies— as  Greek  and 
Roman  influences,  and  the  mental  endowments  of  the  European 
races  ;  which  subtracted  from  the  total  would  give  a  case  of 
the  Method  of  Residues. 

In  the  foregoing  brief  allusion  to  the  Deductive  Method  is 
included  a  reference  both  to  Empirical  and  to  Derivative  Laws. 
The  subject  of  Politics  furnishes  pertinent  examples  of  the 
limitation  of  Empirical  Laws,  and  in  a  less  degree  of  Derivative 
Laws,  to  adjacent  cases.  There  is  safety  in  extending  an  em- 
pirical law  only  to  the  same  territory,  the  same  time,  and 
similar  circumstances.  When  a  ten  pound  suffrage  had  sub- 
sisted in  Britain  for  thirty  years,  with  good  effects,  it  was  a 
small  matter  to  risk  the  extension  to  a  seven  pound  or  a  six 
pound  franchise,  on  the  mere  faith  of  the  empirical  coincidence ; 
whereas,  the  sudden  transition  to  universal  suffrage,  could  not 
be  relied  on  from  the  same  empiricism.  The  consequences  of 
such  a  step,  if  computable  at  all,  could  be  computed  only  by 
the  aid  of  deductive  reasoning — by  the  establishment  of  a  dei-i- 
vative  law.  A  well-informed,  sagacious,  and  unbiassed  reasoner, 
might  be  trusted  to  predict,  within  certain  limits  of  error,  the 
probable  issue  of  such  an  extension  of  the  franchise  ;  but  only 
by  a  superior  handUng  of  the  deductive  method. 

The  Method  of  Residues  being  properly  a  Deductive  Method, 
is  occasionally  valuable.  It  takes  the  problem  on  a  varied 
aspect ;  as  in  the  case  of  Christianity  already  referred  to. 

In  applying  the  methods  of  Agreement  and  of  Difference,  to 
single  out  a  cause,  our  prior  knowledge  of  the  general  adequacy 
of  the  cause,  prepares  us  to  receive  the  inductive  evidence, 
without  the  misgivings  that  we  must  feel  when  we  know 
nothing  on  this  head. 

Hypotheses  in  Politics, 

32.  In  Politics,  we  are  seldom  under  the  necessity  of 
assuming  an  unknown  agency  ;  the  known  forces  of  human 
nature  are  the  sufficing  causes.      Our  assumptions  refer  to 


i>\ 


570 


LOGIC  OF  POUTICS. 


the  presence,  and  the  «raount,  of  the  supposed  agent ;  and 
these  may  be  proved  by  their  exactly  tallying  with  the 
facts. 

Assumptions  are  perpetually  made  regarding  the  conduct 
of  human  beings  under  all  circumstances.  The  passions  of 
Power,  Pride,  Fear,  the  Self-interestof  men,  their  Sympathies, 
are  all  real  or  genuine  causes.  There  may  be  doubts  which  of 
them  produced  a  certain  line  of  conduct ;  and  we  may  apply  the 
logical  conditions  of  hypotheses  to  solve  the  doubt.  If  any  one's 
actions  tally  precisely  with  the  consequences  of  Love  of  Power, 
we  receive  this  coincidence  as  so  far  a  proof  of  the  hypothesis. 
Bat  the  proof  is  completed  only  by  showing  that  the  action 
does  not  tally  with  any  other  motive;  a  thing  that  we  cannot 
always  be  certain  of.  The  execution  of  Charles  I.  might  have 
resulted  from  the  fears  of  the  Puritans,  from  their  revenge, 
from  their  ideas  of  justice,  from  their  interpretation  of  the 
designs  of  providence.  A  proof  from  hypothesis  would  have 
to  show  that  the  act  coincided  fully  with  the  tendencies  of  only 
one  of  all  the  supposable  motives. 

Simplification  of  the  Politiccd  Prohlem, 

33.  There  are  various  modes  of  reducing  the  complica- 
tions of  Politics.  Several  of  these  have  already  been 
glanced  at. 

(1)  By  studying  Institutions  separately,  due  regard  being 
had  to  their  mutual  action.  This  is  that  primary  Analysis  of 
Society  which  is  the  groundwork  of  scientific  method  through- 
out. There  may  be  difficulty  in  making  the  isolation,  and  yet 
allowing  for  mutual  influence ;  but  any  other  method  is 
hopeless. 

(2)  In  modern  political  theory,  much  stress  is  laid  upon 
the  distinction  between  Order  and  Progress;  and  we  are 
recommended  to  study  separately  the  influences  tending  to 
Order  or  Stability,  and  the  influences  tending  to  Pro<]^ress  or 
Improvement.  The  advantage  of  this  separation  is  chiefly  to 
divide  the  field  of  study,  for  the  ease  of  the  understanding. 
It  has  been  shown  by  Mr.  J.  S.  Mill  (Representative  Govern- 
ment, Chap.  II.)  that  the  two  interests  cannot  be  absolutely 
separated  ;  there  can  neither  be  Progress  without  Stability, 
nor  Stability  without  Progress  ;  yet  the  problem  of  Society  is 
greatly  simplified  by  first  studying  each  by  itself,  and  then 
paying  attention  to  their  reciprocal  action. 


SIMPLIFYING  OF  POLITICS. 


571 


^  Mr.  Mill  has  traced,  by  the  combined  Inductive  and  Deduc- 
tive Methods,  the  conditions  of  Stability  in  any  society,  and 
has  referred  them  to  the  following  heads  :— (1)  An  education  of 
the  citizens  calculated  to  impart  a  self-restraining  discipline  ; 
(2)  &  feeling  of  allegiance  or  loj^alty  to  something;  (3)  an 
element  of  cohesion  among  the  members  of  the  same  state.  It 
is  apparent  that  all  these  causes,  while  arising  from  the 
inductive  comparison  of  societies,  may  also  be  fairly  deduced 
from  general  principles  of  the  human  mind  ;  the  consilience  of 
the  two  results  being  essential  to  the  proof. 

(3)  In  the  variation  of  political  circumstances,  the  proposi- 
tions of  society  would  be  numerous  beyond  calculation,  but 
for  the  eminently   scientific    device  of  embodying  a  limited 
number  in  their  exact  circumstances  and  conditions,  so  that 
they  may  be  varied  at  pleasure.    It  may  be  a  question  whether 
certain   public   works  should   be   overtaken   by  the   central 
government  or  by  the  local  government ;    as  bridges,  roads, 
prisons,  &c.     Now  the  decision  of  this  question  in  any  one 
case,  if  accompanied  with  all  the  circumstantials  that  govern 
the  decision,  is  the  decision  for  innumerable  other  cases,  even 
although  diflering  considerably  from  one  another.     Thus,  if 
the  central  government  undertakes  the  work,  avowedly  and 
solely  because  the  locality  cannot  bear  the  expense,  this  decides 
also  the  opposite  case,  where  the  locality  can  bear  the  expense. 
It  is  thus  that  legal  judgments,  if  accompanied  with  a  full 
statement  of  reasons,  may  apply  to  a  wide  range  of  difi'erino- 
cases.     And  so  also  with  all  reasoned  conclusions  in  politics. 
The  very  same  proposition  that  declares  the  consequences  of  a 
despotism  in  given  circumstances,  implies  the  variation  of  the 
consequences  in  degree,  as  the  despotism  varies  in  degree; 
and  the  reversal  of  the  consequences  by  the  substitution  of 
freedom.     All  such  adaptations  and  principles  are  to  be  held 
as  of  the  nature  of  deductions,  for  which  inductive  verification 
is  desirable  according  to  the  extent  of  departure  from  the  case 
embodied. 

(4)  Attention  has  already  been  called  to  the  circumstance 
that  Politics  deals  with  men  collectively,  and  not  individually. 
In  the  view  of  the  politician,  a  million  of  human  beings  is  a 
less  complicated  thing  than  a  single  individual.  The  large 
scale  of  the  operation  reduces  its  complications.  The  maxims 
for  governing  a  nation  (in  a  certain  rude  way)  are  simpler 
than  the  maxims  for  managing  single  persons,  if  we  have  to 
consider  all  the  minute  peculiarities  of  each.  The  Foreign 
Minister,  who  has  to  transact  business  with  one  individual, 


0 


572 


LOGIC  OF  POLITICS. 


may  have  his  ingenuity  and  patience  more  severely  taxed  than 
the  Home  Minister,  who  deals  with  the  mass  of  a  nation. 
The  limits  of  the  proposition  are  contained  in  the  reasons  of  it 
(as  just  remarked)  ;  if  the  mass  of  the  community  breaks  up 
into  individualities,  by  social  discord,  there  is  an  end  to  the 
facility  arising  from  collectiveness  of  action. 

(5)  Not  the  least  important  simplification  of  the  Political 
Problem,  whether  for  theory  or  for  practice,  is  the  Limitation 
of  the  Province  of  Government — the  transferring  of  business 
from  Public  to  Private  management.  The  tendency  of  all 
societies  has  been  to  Over-government ;  and  the  relaxation  of 
this  is  one  of  the  favourable  symptoms  of  existing  societies. 
The  proper  province  of  government  is  a  question  to  be  solved 
according  to  the  circumstances  of  the  time.  A  state  religion 
may  be  suitable  under  one  state  of  things  and  unsuitable  in 
another  ;  so  great  are  the  advantages  of  disburdening  the  civil 
ruler  of  such  a  charge  that  a  case  must  always  be  made  for 


retaining  it. 


Fallacious  Methods  in  Politics, 


34.  These  are  for  the  most  part  implicated  in  the  state- 
ment of  the  sound  methods. 

(1)  The  exclusive  employment  of  the  Experimental  Methods  is 
shown  to  be  insufficient  in  the  complications  of  Politics.  How 
much  more  so  is  mere  Agreement  without  the  studied  variation 
of  circumstances  demanded  by  the  method ;  and  yet  such  is 
the  usual  procedure  of  untutored  minds.  Thus,  any  institution 
whatever  is  pronounced  beneficial,  because  the  country  has 
prospered  under  it.  This  is  the  grossest  form  of  empiricism. 
The  careful  emplojrment  of  the  Experimental  Methods  would 
avoid  such  errors ;  but  would  still  be  inadequate. 

(2)  A  purely  Deductive  Politics  is  equally  at  fault.  Even 
starting  from  the  best  Psychology,  and  the  best  Ethology  elabo- 
rated with  an  express  eye  to  Politics,  we  should  never  be  able 
to  infer  tendencies  with  perfect  precision,  still  less  to  compute 
the  sum  of  a  plurality  of  tendencies.  With  the  highest  skill 
in  psychology,  with  the  best  possible  appreciation  of  the  ave- 
rage development  of  the  great  leading  attributes  of  the  mind, 
in  a  given  race  of  men,  and  with  the  closest  attention  to 
physical  and  other  circumstances, — we  should  still  break  down 
in  the  attempt  to  say,  bow  a  community  formed  from  such  a 
race,  could  prosper  under  either  a  despotic  or  a  democratic 
government,  with  or  without  a  religious  belief. 


THE  POLITICAL  END. 


573 


Allusion  has  been  made  to  the  error  of  seeking  a  political 
cause  in  a  single  circumstance,  instead  of  an  aggregate  situa- 
tion,  or  group  of  circumstances. 

(3).  Sir  G.  C.  Lewis  has  fully  illustrated  the  assumption  of 
false  and  fictitious  causes  in  Politics.  Such  are  mythical  or 
legendary  causes ;  fictions  of  law  ;  and  the  supposed  social 
contract  suggested  by  Grotius,  and  formally  argued  by  Hobbes. 

PEACTICAL  POLITICS. 

35.  In  every  Practical  Science,  we  must  begin  by  setting 
forth  the  End.  In  Politics,  as  in  Ethics,  this  may  be 
variously  viewed. 

In  most  practical  sciences,  there  is  no  dispute  as  to  the  end. 
In  Ethics,  and  in  Politics,  the  case  is  different.  Even,  when 
parties  agree  to  call  the  end  *  human  happiness,'  they  differ  in 
the  meaning  attached  to  it. 

In  antiquity,  the  Athenian  and  the  Spartan  Ideals  of  So- 
ciety were  totally  different ;  so  much  so  that,  on  the  basis  of  the 
same  Theoretical  Principles  of  Society,  the  rules  of  Practice 
would  be  distinct.  The  end  in  the  Roman  Bepublic  was  the 
power  and  glorification  of  the  State.  A  leading  design  of  the 
Spanish  rule  of  America  was  the  conversion  of  the  nations  to 
Catholicism. 

According  to  some,  the  end  of  the  political  machine  is  good 
government,  or  the  best  mode  of  carrying  out  the  primary 
objects  of  Defence,  Security,  &c.,  on  whose  account  society 
exists.  If  a  despotism  accomplishes  this  best,  a  despotism  is 
the  best  government ;  if  not,  not. 

Others,  as  Mr.  Mill,  maintain  that  the  cultivating  of  the 
energies  of  the  people  is  an  end  independently  valuable.  When 
this  is  coupled  with  the  farther  assertion,  that  by  such  means 
alone  can  a  high  standard  of  government  be  maintained,  then 
both  parties  agree  as  to  the  end,  but  differ  as  to  the  means. 
It  is,  however,  possible  to  maintain  that  a  worse  government  by 
the  people  themselves,  is  preferable  to  a  better  that  excludes 
them. 

Another  way  of  expressing  the  same  antithesis  of  ends  is  to 
contrast  passive  enjoyment  with  free  action.  It  may  be  held, 
on  the  one  side,  that  what  gives  the  greatest  amount  of  sentient 
pleasure  with  the  least  pain,  is  the  highest  ideal  of  society ; 
and,  on  the  other,  that  what  allows  the  greatest  scope  to  liberty 
and  individuality,  with  or  without  mere  sentient  enjoyment,  is 
absolutely  the  best. 


U 


:'^ 


■ill 


574 


LOGIC  OF  POLITICa 


I:*' 


These  dilTerent  modes  of  conceiving  the  ends  of  society  have 
a  great  influence  on  actual  practice.  The  *  paternal  govern- 
ments '  will  not  conform  to  the  plan  of  leaving  to  the  individual 
the  utmost  liberty  compatible  with  the  liberty  of  others. 

36.  The  Political  end  being  stattijd,  the  principles  of 
Theoretical  Politics  are  all  convertible  into  maxims  of 
Practice. 

The  principles  of  Causation  in  society,  when  stated  as  laws 
of  the  order  or  succession  of  events,  are  theoretical  principles ; 
when  stated  as  rules  for  eifecting  a  given  object,  are  practical 
principles  or  maxims.  Discussing  theoretically  the  work- 
ings of  Democracy,  we  trace  certain  tendencies  of  the  predo- 
minance of  tho  numerical  majority,  and  the  tendencies  of 
certain  political  arrangements  to  counteract  these ;  whereupon, 
having  in  view  the  end  of  allowing  no  class  unlimited  ascend- 
ency, wo  lay  down  as  a  maxim  or  rule  the  providing  of  such 
checks. 

Theoretical  politics  enounces  the  proposition  that  certainty 
of  punishment  is  more  deterring  than  severity  ;  practical 
politics  converts  this  into  the  precept, — Make  punishments 
certain  rather  than  severe. 

The  requisites  of  Stability  above  laid  down  are  convertible 
into  maxims  for  attaining  stability.  So  with  the  theoretical 
conditions  of  Progress. 

Although  Practical  Politics  is  thus  Theoretical  Politics 
over  again,  with  tho  addition  of  well  defined  ends,  there  are 
great  advantages  in  laying  out  the  subject  in  both  forms,  we 
being  aware  that  tho  substance  is  the  same.  The  theoretical 
form  is  the  one  most  convenient  for  investigation  ;  while  the 
repetition  of  the  principles  in  the  preceptive  dress,  if  done  so 
as  not  to  confuse  the  mind,  is  both  suggestive  and  corrective. 
Moreover,  it  is  only  by  the  separate  treatment  of  the  two 
departments,  that  we  do  full  justice  to  the  special  point  raised 
in  the  practical  department  —  the  political  end.  The  full 
handling  of  the  various  modes  of  viewing  the  end  would 
justify  a  long  preliminary  chapter  of  Practical  Politics. 

It  has  been  well  pointed  out  by  Sir  G.  C.  Lewis  that  the 
propositions  of  politics  are  ordinarily  cast  at  random,  some- 
times in  the  theoretical,  sometimes  in  the  practical  mould. 
'The  more  haste,  the  worse  speed*  is  theoretical;  ^festina 
lentej*  is  practical. 

Much  of  Theoretical  Politics  may  be  unavailing  for  practice, 
at  least  the  limited  practice  of  a  given  country  and  time.     The 


PRACTICAL  DEVICES  IN   POLITICS. 


575 


tbeory  of  Politics,  in  its  most  imposing  pretensions,  compre- 
hends the  Philosophy  of  Universal  Plistory,  much  of  which  is 
of  limited  practical  application.  Hence  the  practical  branch 
is  content  with  selecting  a  portion  of  what  has  been  elaborated 
in  theory. 

Again,  the  practical  mode  of  selection  has  the  farther  pecu- 
liarity of  altering  the  arrangement  or  grouping  of  the  political 
dicta.  In  the  theoretical  investigation,  the  general  tendencies  of 
different  institutions  are  described  in  a  methodical  arrav — 
Forms  of  Government,  War  organization,  Police,  Justice, '&o. 
With  a  view  to  a  practical  end,  we  borrow  from  many  differ- 
ent parts  of  the  theoretical  exposition,  the  specific  links  of  cause 
and  effect  conjoined  in  a  peculiar  structure,  as  for  example,  the 
Poor  Law  of  a  given  country.  This  is  the  prevailing  form  of 
all  practical  departments  with  reference  to  the  allied  theoreti- 
cal sciences. 

Many  of  the  greatest  social  devices  have  originated  exclu- 
sively in  the  hands  of  men  of  practice,  and  have  been  stated 
first  in  the  practical  shape  ;  being  afterwards  enounced  in 
theoretical  propositions.  Such  are  the  English  Constitution, 
the  union  of  Local  Management  with  Central  control  and 
Inspection,  the  system  of  liastening  Responsibility  upon  the 
real  authors  of  political  acts.  Mr.  Mill  regards  as  one  of  the 
most  valuable  securities  yet  devised  for  good  government,  the 
device  that  grew  up  in  the  East  India  Company's  rule,  namely, 
to  associate  the  chief  administrator  with  a  Council  to  advise, 
but  not  to  compel;  thus  leaving  the  responsibility  upon  a 
definite  individual. 


I 


CHAPTER  IX. 


LOGIC  OF  MEDICINE. 

^  1.  llie  scope  of  the  Practical  Science  of  Medicine  is 
given  by  the  Definition  of  the  correlative  couple — Health 
and  Disease. 

The  phenomenon,  expressed  by  Health  on  one  side  and 
Disease  on  the  obverse,  is  indefinable  ;  it  is  an  ultimate  fact  of 
human  experience  like  Life  itself,  of  which  it  is  a  unique  mode 
or  manifestation.  The  attempt  to  convey  a  notion  of  Disease 
to  a  person  that  had  never  seen  or  experienced  any  examples 


576 


LOGIC   OF   MEDICINE. 


of  disease,  would  entirely  fail.  To  call  it  *  a  perverted  Life 
Process  '  is  to  give  an  analogical  phrase,  but  as  the  phenome- 
non is  unique,  analogy  gives  no  assistance. 

Thus,  although  Disease  is  a  highly  complex  fact,  yet  so 
novel  are  its  manifestations,  that  we  must  define  it  by  the 
methods  adopted  for  our  simplest  experiences,  as  resistance, 
motion,  colour,  line,  angle.  We  must  refer  to  a  number  of 
examples  in  the  concrete,  and  generalize  these  into  a  com- 
prehensive statement,  which  the  examples  make  intelligible. 
After  we  become  acquainted  with  a  certain  number  of  diseases, 
the  others  can  be  understood  by  description  alone. 

It  is  barely  possible  that  without  actual  experience  of  In- 
flammation, one  might  form  a  constructive  notion  of  it  from 
its  technical  characters — objective  and  subjective.  The  objec- 
tive characters — redness,  swelling,  heat — might  be  conceived ; 
the  pain  also,  if  otherwise  known  to  us,  could  be  called  to 
view,  and  united  with  the  other  symptoms ;  and  the  mind 
might  laboriously  fuse  the  whole  together.  This  is  only  not 
impossible.  But  the  greatest  powers  of  description  in  the 
expositor,  combined  with  the  highest  constructive  faculty  in 
the  learner,  would  break  down  in  the  endeavour  to  realize 
Fever.  The  subjective  experience,  being  one  unknown  to  a 
person  that  had  never  been  out  of  health,  would  be  unintelli- 
gible in  the  reference. 

A  few  experiences  of  Disease  give  a  meaning  to  the  corre- 
lative notion — Health ;  whence  we  can  define  disease  negatively, 
by  the  infringement  of  Health.  The  positive  definition,  would 
be  the  result  of  the  comparison  of  all  the  modes  of  derange- 
ment, the  generalization  of  diseases ;  but  writers  usually 
remain  content  at  the  outset  with  the  negative  statement ;  in 
other  words,  they  define  Health,  by  assuming  the  knowledge 
of  a  few  specimens  of  disease.  Health,  in  its  most  complete 
acceptation  up  to  this  time  is  the  absence  of  all  the  1146  dis- 
eases put  down  in  the  *  Nomenclature  of  Disease.' 

The  science  of  Medicine  is  an  adequate  description  of  all 
these  forms  of  derangement,  or  departure  from  Health,  with 
a  view  to  suggest  means  for  averting  or  removing  them.  This 
practical  end  implies  an  extensive  knowledge  of  causation  with 
reference  to  Disease. 

A.S  regards  the  large  number  of  Diseases,  the  complicacy  of 
their  characteristics,  and  the  existence  of  generic  and  specific 
agreements  and  differences  among  them,  impart  to  the  science 
of  Medicine  a  certain  community  with  the  Natural  History, 
or  classificatory  sciences — as  Mineralogy,  Botany  and  Zoology. 


BIOLOGY  iS  THE  BASIS  OF   MEDICINE. 


57-7 


The  analogy  to  the  two  last  is  still  closer  through  the  circum- 
Btance  of  evolution,  or  the  succession  of  stages,  in  most  dis- 
eases. 

Sciences  'preparatory  to  Medicine, 

2.  Disease  being  a  state  of  the  Human  system,  the  science 
of  medicine  rests  immediately  on  the  part  of  Biology,  called 
Human  Anatomy  and  Physiology. 

All  animals,  and  even  plants,  are  liable  to  abnormal  action, 
or  disease.  The  consideration  of  the  subject,  however,  reaches 
the  highest  development  in  connection  with  human  beings. 
Animals  share  in  many  of  the  human  diseases,  and  have  some 
special  to  themselves. 

When  we  name  Biology,  we  may  be  supposed  to  exhaust 
the  sciences  preparatory  to  medicine.  Strictly  speaking  this 
is  true  ;  inasmuch  as  all  other  knowledge  applicable  to  disease 
is  applicable  through  biological  science.  Yet  it  is  well  to  advert 
emphatically  to  the  inorganic  sciences — Natural  Philosophy 
and  Chemistry — which,  in  their  present  improved  condition, 
yield  many  suggestions  bearing  at  once  on  the  medical  art. 
Physics,  in  both  its  divisions — molar  and  molecular.  Chemistry 
— both  Inorganic  and  Organic,  are  full  of  applications  to 
medical  biology.  The  medical  man,  in  order  to  derive  the  full 
benefit  of  these  scienes,  needs  to  study  them  apart,  as  well  as 
in  their  applications  in  Human  Physiology. 

Intermediate  between  Human  Physiology  and  the  Practice 
of  Physic,  are  the  exhaustive  enquiries  into  special  organs, 
and  special  functions  ;  as  exemplified  in  the  work  of  Dr.  Parkes 
on  Urine,  and  in  the  researches  of  Dr.  Edward  Smith,  Prof. 
Haughton,  and  others,  as  to  Food,  Muscular  Power,  Respira- 
tion, and  other  applications  of  Physics  and  Chemistry,  with 
experimental  checks  and  verifications. 

Pathological,  hosed  on  Physiological ,  A  nalysis, 

3.  The  Analysis  of  the  Organism  for  Physiological 
purposes  is  likely  to  prove  a  basis  of  Pathological  analysis. 

It  being  found  that  the  greater  number  of  Diseases  are 
localized  in  separate  organs  or  tissues,  we  are  aided,  in  class- 
ing diseases,  by  a  full  enumeration  of  all  those  independently 
diseasable  parts.  Now,  Physiology  reckons  up  the  separate 
tissues  and  organs  of  the  body;  and  Pathology  enquires 
whether  these  are  all  separately  subject  to  disease.  The 
classification   of  diseases   (with  the   exception  of  what  are 


I 


.  i  fl 


^*  1 


fl 


■  ■'  n 


578 


LOGIC  OF  MEDICINE. 


termed  general  diseases)  is  made  to  follow  the  physiological 
division  of  tbe  organs — Brain  and  Nervous  System,  Senses, 
Circulation,  Absorbent  System,  Ductless  Glands,  Respiratory 
System,  Digestive  System,  Urinary  System,  Generative 
System,  Organs  of  Locomotion,  Cellular  Tissue,  Skin.  And 
inasmuch  as  most  of  these  systems  are  complicated  groups  of 
organs,  for  example,  the  Digestive  System,  a  farther  sub- 
division is  made  of  localities  of  disease — as  Teeth,  Gums, 
Tongue,  Salivai-y  Glands,  Stomach,  Intestines,  Liver,  &c. 

This  Anatomical  arrangement  of  the  seats  of  disease  would 
be  of  little  value,  did  not  diseases  confine  themselves  to 
separate  organs,  while  exercising  a  secondary  influence  on 
adjoining  and  connected  parts,  or  on  the  general  system. 
Thus,  a  disease  may  accomplish  its  entire  course  in  the 
bronchia,  the  stomach,  or  the  kidney,  with  no  farther  injury 
to  the  rest  of  the  system  than  arises  from  disturbing  the 
balance.  When  one  member  of  a  business  establishment  is 
incapacitated,  a  certain  deranging  efltct  is  felt  throughout  the 
whole ;  but  that  effect  is  a  different  thing  from  the  incapacity 
of  one  making  the  incapacity  of  another. 

The  point  for  the  pathologist  to  consider,  therefore,  is 
•what  parts  and  tissues  may  be  saparately  diseased.  This  is 
to  push  the  local  analysis  of  disease  to  the  very  utmost.  Each 
of  the  parts,  thus  distinguished,  must  be  supposed  to  have 
independent  vigour  or  weakness,  as  measured  by  the  energy 
of  function,  and  by  the  resistance  to  deranging  causes. 

Even  in  properly  local  diseases,  however,  there  must  be 
more  or  less  tendency  to  affect  adjoining  or  connected  organs  ; 
and  there  is  thus  a  scale  of  kindred  established  between  each 
organ  and  the  rest ;  disease  of  the  stomach  affects  the  intestines 
and  the  liver  before  the  lungs  or  the  kidney. 

It  must  be  admitted,  however,  that  the  alliance  of  local  con- 
nexion is  apt  to  be  overborne  by  the  distant  alliances  established 
through  the  two  carrying  organs — the  blood  and  the  nerves. 

4.  The  analysis  of  physiological  Functions  is  also  an  ana- 
lysis of  diseased  actions. 

Every  function  performed  by  an  organ  may  be  affected  in 
disease  ;  and,  in  some  casf^s,  one  function  may  fall  into  disorder 
independent  of  the  others.  Thus  the  liver  has  a  plurality  of 
functions ;  and  disease  may  consist  in  changing  one,  with  no 
more  than  an  indirect  result  upon  the  rest.  The  pathologist 
needs  to  avail  himself  of  this  analysis  likewise. 


GENERAL  PROCESSES  IN   DISEASE. 


579 


6  A  farther  analysis  must  be  made  of  morbid  Products, 
or  substances  generated  in  disease,  and  unknown  m  tbe 
same  localities  during  health. 

This  is  a  department  special  to  morbid  Anatomy,  or  Patho- 
logy ;  and  is  prosecuted  by  the  assistance  of  chemical  analysis, 
and  microscopical  examination.  All  such  products  are  to  be 
carefully  ascertained,  classified,  and  described.  After  an 
account  of  the  characters  of  each,  some  mention  might  be 
made  of  the  diseases  wherein  they  severally  manifest  them- 
selves. Finally,  their  causes,  known  or  supposed,  might  be 
given.  But  care  is  to  be  taken  not  to  jumble  up  all  these 
three  expositions  in  one.  ^ 

There  is  a  close  and  natural  connexion  between  the  account 
of  new  morbid  deposits  and  the  morbid  alterations  of  the 
several  tissues.  The  same  method  needs  to  be  followed  with 
these ;  each  morbidly  transformed  structure  being  described 
with  reference  to  all  its  appearances  and  re-actions,  ascertained 
by  chemical,  microscopical,  or  other  means  ;  the  description  to 
be  followed  as  before  by  mentioning  the  diseases  wherein  eacH 
occurs,  together  with  any  assignable  causes  of  the  change. 

Enumeration  of  Diseased  Processes— General  Pathology. 

6.  The  numerous  diseases  affecting  the  various  organs  of 
the  body,  as  well  as  those  attacking  the  whole,  consist  in 
the  repetition  of  a  small  number  oi  diseased  'processes.  Such 
are  Inflamation,  Congestion,  Hsemorrhage,  Degeneration, 

Tumours,  &c.  ^         ,  .  -j      j  i 

7.  The  process  called  '  Fever   is  considered  as  a  general 

disease. 

Upwards  of  twenty  forms  of  diseased  process  can  be  enume- 
rated •  Fever  and  Inflammation  taking  the  lead.  This  is  doubt- 
less  a' great  means  of  simpHfying  disease,  although,  in  the 
specific  varieties  of  the  different  processes,  there  is  a  consider- 
able burden  of  detail.  Inflammation  is  pretty  much  the  same 
in  all  organs ;  being  similarly  caused,  and  similarly  brought 

to  a  termination. 

It  is  proper  to  give  a  general  and  comparative  account  of 
every  one  of  these  processes,  adverting  to  their  modes  and 
varieties,  before  taking  up  the  special  diseases  where  they 
enter  Chapters  on  Fever  in  general,  and  on  Inflammationiu 
general,  are  usually  provided  in  advance  of  the  detailed  de- 
scription of  diseases. 


:  il 


580 


LOGIC   OF  MEDICINE 


General  Therapeutics, 

8.  The  generalizing  of  Diseases,  through  the  recurrence 
of  a  limited  number  of  diseased  process,  suggests  the 
generalizing  of  Remedial  agencies. 

By  way  of  anticipating  the  remedies  for  the  special  diseases, 
there  is  the  same  propriety  in  taking  a  general  view  of 
remedial  agencies,  as  in  taking  a  general  view  of  diseased 
processes ;  the  one  being  made  possible  by  the  other.  Very 
great  advantage  accrues  from  studying  each  remedial  agent, 
not  apart  from  all  particulars,  which  would  be  absurd,  if  it  were 
possible,  but  in  connexion  with  all  particulars. 

For  example,  that  remarkable  fact  called  by  the  various 
names — metastasis,  counter-irritation,  derivation,  revulsion — 
should  be  discussed  at  the  outset  on  a  comparative  survey  of 
its  characters  in  all  variety  of  circumstances.  This  is  the 
only  means  of  gaining  a  clear  and  steady  grasp  of  its  compass 
and  limitations,  or  of  the  causative  conditions  of  its  working. 

Again,  a  similar  generalized  view  should  be  taken  of  the 
process  called  Stimulation,  whereby,  through  a  variety  of 
means,  nervous  action  is  heightened,  with  an  increase  of  other 
dependent  functions. 

The  justification  of  a  General  Therapeutics,  to  assist  both 
in  investigating  disease,  and  in  treasuring  up  knowledge  for 
use,  is  apparent  in  the  great  number  of  diseases  that  have  no 
specific.  Take  Typhus,  for  example.  The  only  directions 
given  relate  to  the  employment  of  the  general  remedies 
adapted  to  the  symptoms  of  the  disease ;  cold  affusion  or 
cooling  drinks  for  the  main  fact — excessive  heat ;  stimulants 
to  resist  the  depression  of  the  powers ;  purgatives  when  the 
bowels  are  confined ;  sudorifics,  &c. 

Although  the  removal  of  the  came  of  a  disease,  with  the 
occasional  plying  of  the  opposite,  must  always  be  a  large  part 
of  Therapeutics,  it  does  not  make  the  whole.  When  the 
poison  of  typhus  has  once  entered  the  blood,  the  removal  of 
the  cause  is  irrelevant ;  the  eSects  are  already  produced,  and 
must  be  counteracted  by  new  agencies.  Hence,  we  have  first, 
General  Causes  of  Diseases,  with  Hygiene  (which  a  know- 
ledge of  causes  may  fairly  exhaust)  ;  secondly.  General  Thera- 
peutics, as  counterworking  the  derangement  actually  produced. 

General  Therapeutics  might  thus  conveniently  follow  the 
general  account  of  the  Causes  of  Disease.  The  two  branches  are 
closely  connected  without  being  identical.     The  general  causes 


DEFINITIONS   OP  MEDICINE. 


581- 


are  such  as — Hereditary  Constitution  ;  Atmospheric  causes 
(Miasmata,  Cold,  Heat,  Light,  Electricity,  moisture) ;  unsuit- 
able Food  and  Drink  ;  Over-exertion  or  Excesses ;  deficient 
Sleep  ;  insufficient  Exercise ;  Poisons,  &c.  &c.  In  the  account 
of  these  noxious  agents  is  implicated  the  branch  called  Hygiene, 
or  warding  off  diseases  by  avoiding  their  causes,  under  which 
are  indicated,  obversely,  the  causes  of  that  vigour  of  the  organs 
which  we  measure  by  the  distance  placed  between  us  and  dis- 
ease. 

The  Materia  Medica  usually  contains  a  Therapeutical  classi- 
fication of  Medicines ;  as  Tonics,  Exhilarants,  Narcotics, 
Emetics,  Purgatives,  Sudorifics,  Diuretics,  &c.  The  minute 
detail  of  properties  under  each  of  these  classes,  occurring  in 
the  larger  works  on  Materia  Medica,  is  to  a  great  extent  a 
repetition  of  general  Therapeutics. 

Notions  of  Medicine. — Definition  and  Classification  of 

Diseases, 

9.  Of  Disease  on  the  whole,  there  is  no  definition  that 
is  of  any  value  ;  defining  begins  with  the  special  appear- 
ances of  disease. 

The  very  best  generalization  that  can  be  given  of  Disease  on 
the  whole,  is  too  vague  to  furnish  any  useful  indications. 
When  we  begin  to  specify  morbid  appearances,  and,  under  the 
name  of  a  Disease,  to  group  those  that  are  connected  in  the 
same  outbreak,  we  are  enabled  to  construct  definitions,  often 
short  of  absolute  precision,  yet  faithful  to  the  great  mass  of 
actual  instances. 

The  Notions  of  disease  concern  (1)  diseased  processes,  and 
(2)  diseases.  The  diseased  processes  include  Fever,  Inflam- 
mation, Congestion,  Hasmorrhage,  Dropsy,  Atrophy,  Hyper- 
trophy, Degeneration,  Tumours,  Parasites,  Calculus,  Functional 
weakness,  &c.  Of  these  various  processes,  we  may  specify  as 
distinguished  for  their  prevalence  in  common  diseases — Fever, 
Inflammation,  Degeneration,  and  Functional  derangement. 

Fever, — Fever  is  a  general  state  entering  into  many  diseases, 
and  now  susceptible  of  being  characterized  in  its  generic  char- 
acter. Mainly  through  the  careful  observations  of  Dr.  Parkes, 
a  generalization  of  Fever  has  been  arrived  at,  such  as^o  con- 
ciliate all  the  appearances.  The  generalization  is  expressed 
by  the  simple  fact — *  Elevation  of  Temperature.'  A  rise  of 
temperature  in  the  body  generally,  to  the  extent  of  4°  of 
Fahrenheit,  is  a  state  of  Fever ;  while  the  increase  may  pro- 
ceed to  6%  8**,  or  even  12°  Fahrenheit. 


I 


m 


i 

*  h  tl 

m 


I 


:n 


I 


582 


LOGIC  OF  MEDICINE. 


As  there  is  no  circumstance  characteristic  of  Fever  in 
general,  but  this  one  fact,  and  its  implications  or  consequences, 
this  is  the  complete  definition  of  the  febrile  state.  Any  expla- 
nation or  illustration  of  it  should  consist  in  stating  a  variety 
of  instances  showing  the  elevated  temperature. 

The  following  definition  is  encumbered  with  statements  not 
belonging  to  the  definition — *  A  complex  morbid  state  accom- 
panying many  diseases  as  part  of  their  phenomena,  more  or 
less  constantly  and  regularly,  but  variously  modified  by  the 
specific   nature  of  the   diseases  which   it  accompanies.      It 

ESSENTIALLY  CONSISTS  IN  ELEVATION  OF  TEMPERATURE,  wllick  TtlUst 

arise  from,  a7i  increased  tissue  change,  and  have  its  immediate 
cause  in  alteration  of  the  nervous  system.*  The  first  sentence  is 
a  pure  superfluity.  The  setting  apart  of  Fever  for  separate 
consideration,  as  a  preliminary  to  the  discussion  of  particular 
febrile  diseases,  implies  what  is  therein  stated — that  fever  is  a 
morbid  state,  and  that  it  accompanies  many  diseases.  All 
Buch  wordiness  should  be  sedulously  avoided  in  definitions. 
A  difierent  criticism  applies  to  the  expressions  given  in  italics 
— *  arising  from  an  increased  tissue  change,'  *  having  its  imme- 
diate cause  in  alteration  of  the  nervous  system.'  These  are 
not  idle  phrases,  but  describe  circumstances  of  radical  import- 
ance. Why,  then  exclude  them  from  the  definition  ?  The 
reason  is  that  the  complications  of  disease  require  the  separate 
discussion  of  whatever  can  be  separately  discussed  with  ad- 
vantage ;  and,  almost  everywhere  in  medicine,  it  is  advan- 
tageous to  separate  the  description  of  the  fact,  from  the 
enquiry  into  the  causes  of  the  fact.  A  definition  should  give 
whatever  is  essential  to  the  determining  of  a  fact  or  pheno- 
menon. It  should  not  assign  the  causes,  nor  deduce  the 
consequences  of  the  phenomenon  ;  this  is  to  advance  beyond 
definition  to  predication,  and  should  be  a  distinct  expository 

statement. 

It  is  a  proper  appendage  to  the  definition,  to  enumerate  the 
ordinary  superficial  appearances  of  fever,  which  constituted 
its  definition  before  the  exact  generalization  was  arrived  at, 
*  hot  skin,  quick  pulse,  intense  thirst,  scanty  and  high-coloured 
nrine  ;*  at  the  same  time  subjecting  these  symptoms  to  a  critical 
examination,  so  as  to  point  out  their  shortcomings. 

The  fact  of  Elevated  Temperature  being  sufiiciently  shown 
by  an  appropriate  selection  of  particular  cases,  the  important 
predications  above  alluded  to  may  be  taken  up.  From  the 
Law  of  Conservation,  as  applied  to  the  animal  economy,  there 
must  be  an  increase  of  tissue  change  to  support  the  heat,  and 


DEFINITION  OF  FEVEB. 


583 


the  endeavour  should  be  made  to  assign  this  tissue  change  in 
its  exact  circumstances,  and  numerous  outlying  efiects.  The 
account  of  fever  is  not  complete  without  this  development. 
The  conclusions  of  Dr.  Parkes,  obtained  by  a  large  induction, 
and  corroborated  deductively  by  the  Law  of  Conservation,  are 
most  valuable.  *  The  increase  of  temperature  may  be  (or  is 
frequently)  attended  with  increased  elimination  ;  and  therefore 
presumably  with  increased  tissue  change.'  Again,  what  seems 
to  contradict  the  general  law  of  Conservation,—'  the  products 
of  metamorphosis,  as  judged  by  the  excreta,  maybe  diminished 
in  febrile  cases.'  The  contradiction,  however,  is  only  apparent 
for  there  is  good  evidence  in  such  cases,  of  an  undue  retention 
of  excreta,  which  makes  one  of  the  bad  accompaniments  of 
fever.  Careful  observations  prove  that  while  the  actual 
amount  of  excreta  is  small,  the  tissue-change  may  still  be  great. 

It  is  obvious  that  this  topic  involves  a  great  amount  of 
detail,  ascertainable  only  by  observation,  although  checked  by 
the  general  law  of  definite  changes  accompanying  definite 
results.  The  state  of  every  organ,  and  the  alterations  in  all 
the  excretions  —  pulmonary,  urinary,  cutaneous,  intestinal, 
&c. — need  to  be  exactly  gathered  from  the  facts,  and  made  a 
clue  to  the  windings  of  the  special  febrile  disease. 

The  second  predicate  given  with  the  foregoing  definition — 
I  the  alterations  in  the  nervous  system  ' — also  deserves  to  be 
illustrated,  proved  and  unfolded,  in  a  separate  section. 

Other  important  predications  extend  the  discussion  of  fever : 
such  are  the  procuring  cause,  and  the  course  or  evolution,  in 
so  far  as  belonging  to  fever  generally. 

The  foregoing  outline  represents  the  exhaustive  account  of 
Fever,  as  a  diseased  process.  We  began  with  the  intention  of 
illustrating  definition  in  Medicine ;  but,  it  was  advisable,  once 
for  all,  to  show  the  boundary  between  legitimate  definition  and 
predication,  which  is  habitually  disregarded  in  medical  sub- 
jects to  the  detriment  of  the  handling,  both  in  a  logical  point 
of  view,  and  as  regards  expository  clearness.  The  filling 
up  of  the  sketch  would  be  the  account  of  Fever,  coming  under 
a  previous  heading— *  Enumeration  of    Diseased   Processes* 

Inflammation,  The  complication  of  this  state  is  very  consider- 
able ;  but  the  method  is  plain.  We  must  separate  the 
definition  from  the  predications ;  and,  in  the  definition,  we 
may  separate  the  superficial  appearances  of  the  ordinary 
diagnosis,  from  the  essential  fact,  or  facts  of  the  state. 

First  as  to  the  definition.  The  traditional  characters  of  inflam- 


II 


t  i-  'I 


M 


* 


III 


"I 


584 


LOGIC   OF  MEDICINE. 


DEFINITION   OF  INFLAMMATION. 


matioii  are  the  four  facts — redness,  sweVing,  heat,  pain — which 
are  a  tolerably  close  approximation.  There  might  be  a  con- 
venience in  briefly  illustrating  these  points,  as  a  prelude  to  the 
improved  generalization  that  can  now  be  afforded. 

Even  then,  however,  the  only  correct  course  is  to  adhere 
in  the  first  instance  to  a  description  of  the  characters,  for  the 
pui'poses  of  identification  ;  refraining  from  all  remarks  bearing 
on  the  causes  or  explanation  of  the  several  symptoms.  The 
kind  of  rec?nes5,  its  various  hues,  the  more  or  less  extensive 
prevalence  of  the  mark, — are  the  points  proper  to  the  eluci- 
dation of  the  property  as  a  defining  and  diagnostic  circum- 
stance ;  the  same  rigid  plan  to  be  followed  with  the  three 
remaining  symptoms.  The  triumph  of  the  expositor's  art 
in  this  effort  would  be,  that  no  one  could  ever  mistake  the 
inflammatory  redness,  swelling,  or  the  rest. 

The  appearances  being  thus  expounded  with  all  the  neces- 
sary enforcement,  it  is  admissible  to  consider  how  far  they 
may  be  connected,  either  by  implication,  or  as  cause  and  effect, 
with  one  another,  or  with  circumstances  still  more  funda- 
mental. It  is  then  easy  to  point  out  that  the  fact  of  congestion 
is  a  very  important  addition  to  our  knowledge,  and,  if  imparted 
on  the  plan  now  stated,  re-acts  on  our  previously  obtained 
knowledge,  by  resuming  in  a  single  statement  all  the  four  facts, 
and  still  more,  by  accounting  for  the  failures  of  one  or  other 
of  these  in  particular  instances. 

The  faulty  mixing  up  of  description  with  causation  is  exempli- 
fied in  the  following  sentences  regarding  Inflammation  : — '  Very 
often  the  pain  is  a  "bulking"  or  throbbing  pain— every  beat  of 
the  heart  makes  itself  felt  in  the  tender  part.  The  pain  of  inflam- 
mation results  no  doubts  from  the  implication  of  the  nerves  in  the  dis* 
eased  processes.'  *  Speaking  generally,  therefore,  there  is  more  pain 
felt  in  external  inflammation,  because  there  are  more  nerves  of  com- 
mon sensation.' 

It  is  next  to  be  seen  what  better  account  can  be  given  of 
inflammation,  grounded  on  the  superior  physiology  and  ob- 
servations of  recent  times.     The  definition  of  Dr.  Aitken*  is 

•A  complex  morbid  process  characterized, — (1.)  By  a  suspension  of  the 
concurrent  exercise  of  function  among  the  minute  elements  of  the  tissue 
involved ;  (2.)  By  stagnation  of  the  blood  and  abnormnl  adhesiveness  of 
the  blood  discs  in  the  capillary  vessels  contiguous  to  the  tissue-elements 
whose  functions  are  suspended ;  (3.)  By  contraction  of  the  minute  arteries 
leading  to  the  capillaries  of  the  affected  part,  with  subsequent  dilatation 
and  panilysis  of  the  contractile  tissue  of  the  aflfected  blood-vessels.  The 
nutritive  changes  between  the  blood  and  the  minute  component  elements 
of  the  aflfected  tissue  become  visibly  altered,  and  although  an  appreciable 
exudation  does  not  necessarily  ioUow,  yet  a  constant  tendency  betrays 


585 


▼eiy  exhaustive,  but  might  be  disburdened  of  varioTis  points 
more  suitable  to  predication.  The  following  appear  to  be  the 
essentials  of  the  enumeration. 

(1)  Suspended  function  of  the  tissue  involved. — It  appears 
from  the  observations,  that  an  alteration  of  the  tissue — such 
as  to  impair  its  proper  functions,  that  is,  its  relations  to  the 
blood  in  the  way  of  absorbing  nourishment,  and  its  secreting 
or  other  functions — is  the  primary  fact,  the  starting  point  of 
the  subsequent  changes. 

(2).  Stagnation  of  the  blood. 

(Z).  Abnormal  adhesiveness  uf  the  blood  discs  in  the  capillaries 
adjoining. 

(4).  Contraction  of  the  minute  arteries  supplying  the  capillaries 
of  the  part,  follotued  by  dilatation  and  loss  of  contractile  power. 

(5).  A  tendency  to  exudatio7i,  varying  according  to  circum- 
stances. 

Not  until  each  of  these  constituent  facts  is  made  intelligible, 
and  verified  by  references  to  observation,  should  any  discussion 
be  commenced  as  to  their  causative  connexions  among  them- 
selves, or  with  other  facts.  The  description  being  first  ren- 
dered complete  and  intelligible,  there  is  the  greatest  interest  in 
trying  to  show,  for  example,  that  the  first  fact— suspended  func- 
tion of  tissue — leads  to  the  blood  derangements  afterwards 
enumerated ;  and  that  the  heat,  redness,  swelling,  and  pain,  in 
the  old  enumeration,  follow  as  effects  from  the  train  of  cir- 
cumstances, as  given  in  the  definition. 

^  The  new  growths  and  deposits  should  be  reserved  for  dis- 
tinct predication.  So  also  should  be  the  cause  or  event  of  the 
attack,  whether  favourable  or  unfavourable. 

The  extreme  variations  of  degree  in  morbid  states,  originate 
appearances  scarcely  short  of  differences  of  kind ;  and  these 
have  to  be  explicitly  enumerated,  as  specific  modes  of  the  main 
phenomenon.  A  distinct  consideration  should  be  given  to 
such  an  important  accompaniment  as  fever,  and  to  the  con- 

itself  to  the  occurrence  of  an  interstitial  exudation,  but  which,  under 
proper  regimen  and  proper  remedies,  is  often  abortive.  When  »n  exuda- 
tion follows  as  a  result  of  the  inflammatory  state,  it  is  apt  to  be  associated 
with  an  unhealthy  condition  of  the  blood,  and  of  the  blood  plasma,  and 

to  be  associated  with  varied  forms  of  new  growth,  according  to, (1.) 

The  elementary  structure  in  which  it  occurs ;  (2.)  The  special  zymotic, 
constitutional,  or  local  disease  with  which  this  complex  morbid  process 
may  co-exist ;  and  (3.)  According  to  the  progress  of  the  inflammation, 
the  amount  and  suddenness  of  the  effusion,  the  extent  of  tissue  involved, 
the  diminished  vascularity,  and  the  powers  of  absorption  of  the  surround- 
ing parts.' 


i  y 


ft 


586 


LOGIC   OF  MEDICINE. 


DEFINITION  OF  SPECIFIC   DISEASES. 


587 


ditions  of  it  (the  chief  being  probably  severity  of  the  local 
attack,  and  poisonous  virulencej. 

The  hypothetical  views  started,  in  the  absence  of  a  theory, 
to  connect  the  whole  cycle  of  circumstances  should  be  given 
last  of  all. 

To  frame  definitions  o£  Dcjeneratloa  and  Functional  Disease^ 
beyond  the  statement  of  the  palpable  appearances  so  named, 
would  involve  hypothetical  considerations,  such  as  require  to 
be  admitted  into  medicine,  with  due  regard  to  their  exact 
value. 

Correlative  with  the  definitions  of  Health  and  Disease 
generally,  are  those  of  the  important  words  Constitution,  Tern- 
peramentf  Diathesis,  indicating  a  hypothetical  permanent  con- 
dition of  the  system,  manifested  by  the  tendency  to  incur  or  to 
resist  diseases ;  and  more  especially  diseases  of  enfeeblement 
and  degeneration.  A  weak  chest,  a  strong  stomach,  suscep- 
tible nerves, — are  modes  of  stating  in  a  useful  form  such  actual 
occurrences,  as  that  certain  persons  are  easily  affected  with 
chest  disease,  or  resist  the  agencies  of  stomachic  disorder,  and 
so  on.  They  suggest  the  mode  of  life  best  fitted  in  each  case 
to  ward  off  attacks  of  disease. 

Definition  of  specific  Diseases. — The  very  general  states 
above  quoted  exemplify  definition  under  the  greatest  simplicity, 
as  respects  the  number  of  characters,  although  not  as  respects 
the  generalizing  and  seizing  of  the  true  characters.  When 
we  proceed  to  the  more  concrete  forms  of  disease,  Typhus, 
Gout,  Pleurisy,  Neuralgia,  Jaundice,  &c.,we  have  the  general 
processes.  Fever  and  the  rest,  with  many  various  accessories, 
constituting  the  specific  characters  of  the  individual  affections. 
Consequently,  the  definitions  are  apt  to  be  voluminous  in  their 
statement ;  and  there  is  still  more  need  of  method. 

Examples  have  now  been  given  of  the  two  difierent  modes  of 
medical  definition  ;  the  one  corresponding  to  Diagnosis,  and 
framed  with  a  view  to  identify  a  disease  by  such  signs  as  are 
best  accessible  ;  the  other,  the  most  complete  generalization  of 
the  essential  fact  or  facts  of  the  disease,  which  facts  may  or 
may  not  lie  upon  the  surface.  The  first  is  requisite  for 
distinguishing  diseases  ;  the  second,  for  understanding  them. 

Let  us  take  an  example.  Gout  is  defined  by  Dr.  Garrod — 
*  A  specific  form  of  articular  inflammation,  invariably  accom- 
panied with  uric  acid  in  the  blood,  and  the  deposition  of 
urate  of  soda  in  the  afiected  tissues.'  The  positions  given  to 
the  words  *  specific'  and  *  accompanied '  suggest  what  was 
probably  not  in  the  author's  mind.     Strictly  interpreted,  the 


language  means — Gout  is  articular  inflammation  of  a  speclfio 
character  (not  described) ;  it  has,  for  concomitants,  uric  acid 
in  the  blood,  and  deposits  of  urate  of  soda.  The  real  mean- 
ing must  be  presumed  to  be — Gout  is  articular  inflammation, 
Bpecifically  marked  by  uric  acid,  &c. 

This  definition  is  one  of  those  advanced  generalizations, 
attained  in  some  diseases,  which  penetrate  to  the  essential 
features  of  the  disease,  without  fully  expressing  the  symptoms. 
A  detailed  account  of  the  symptoms  is  therefore  added,  first 
under  the  title  *  Description  of  an  attack  of  Gout,  and  of  the 
progress  of  the  disease '  (a  sort  of  popular  history  of  a  case), 
and  secondly,  under  *  Phenomena  occurring  during  an  acute 
Gouty  Attack,*  where  there  is  a  more  rigid  and  systematic 
analysis  into  (1)  Febrile  Disturbance,  and  (2)  Local  Appear- 
ances. 

Again,  Small-Pox  is  thus  defined  (Dr.  Aitken).  *  The  pro- 
duct of  a  specific  and  palpable  morbid  poison,  which  is 
reproduced  and  multiplied  during  the  course  of  the  malady. 
(1).  After  a  definite  period  of  incubation  a  remittent  fever  is 
established  and  followed  by  an  eruption  on  the  skin,  and 
sometimes  on  the  mucous  surfaces,  with  other  concomitant 
and  occasionally  succeeding  afiections  (2).  The  eruption  on  the 
skin  passes  through  the  stages  of  pimple,  vesicle,  pustule,  scab  ; 
and  leaves  marks  or  cicatrices  on  its  site  (3).  The  disease 
runs  a  definite  course,  and,  as  a  rule,  exhausts  the  suscepti- 
bility of  the  constitution  to  another  attack  (4).' 

Here  we  have,  in  sentences  (2)  and  (B),  the  leading  symp- 
toms of  the  disease,  which,  when  elucidated  at  full,  make  up, 
as  far  as  book  description  can  go,  the  characters  whereby  the 
disease  is  known  and  discriminated.  Sentence  (1)  does  not 
properly  belong  to  the  definition,  but  to  the  predication  ;  the 
cause  of  a  disease  must  always  be  accounted  a  predicate. 
Sentence  (4)  contains  two  statements,  first,  '  the  disease  runs 
a  definite  course,'  which  surely  is  true  of  many  other  diseases, 
if  not  of  nearly  all ;  second,  '  it  exhausts  the  susceptibility  of 
the  constitution  to  another  attack,'  a  most  pertinent  circum- 
stance, but  still  better  reserved  for  a  predicate  or  concomitant, 
than  mixed  up  with  the  defining  marks. 

Influenza  is  thus  defined  by  Dr.  Parkes  : — *  An  epidemic 
specific  fever,  with  special  and  early  implication  of  the  naso- 
laryngo-bronchial  mucous  membrane  ;  duration  definite  of 
from  four  to  eight  days  ;  one  attack  not  preservative  in  future 
epidemics.*  The  transposition  of  the  epithet  *  specific  '  is 
desirable  : — '  An    epidemic  fever,   specially  characterized  by 


f   I] 


I 


i 


588 


LOGIC  OF  MEDICINE. 


early  implication,  &c.'  This  definition  also  is  a  summary  of 
symptoms,  and  nothing  more.  The  author  proceeds,  under 
the  head  *  Symptoms  *  to  describe  the  general  course  of  the 
disease,  and  under  *  Consideration  of  the  Special  Symptoms ' 
to  analyze  them  in  the  detail ;  Temperature,  Condition  of  the 
Skin,  Nervous  and  Muscular  Symptoms,  Respiratory  System, 
Circulation,  Digestion,  &c. 

All  the  facts  stated  in  the  Definition  may  be  fairly  allowed 
as  defining  circumstances,  with  the  exception  perhaps  of  the 
last '  one  attack  not  preservative  in  fature  epidemics,'  which 
might  be  reserved  for  predication.  Doubtless,  if  we  had  a 
generalization  of  the  central  or  fundamental  fact  of  the 
disease,  this  would  take  place  among  deductive  consequences, 
or  propria.  But  we  do  not  need  it  in  a  definition  consisting 
of  a  summary  of  the  symptoms. 

The  following  sentence  commences  Dr.  Buzzard's  definition 
of  Scurvy  : — *  A  peculiar  state  of  mal-nutrition,  supervening 
gradually  upon  the  continued  use  of  a  dietary  deficient  in 
fresh  vegetable  material,  and  tending  to  death,  after  a  longer 
or  shorter  interval,  if  the  circumstances  under  which  it  arose 
remain  unaltered.'  Here  we  have  first  a  theory  or  hypothesis 
of  the  essence  of  the  disease  (a  state  of  mal-nutrition),  secondly, 
its  cause,  and  thirdly,  an  announcement  of  its  dangerous 
character.  All  this  is  extraneous  to  the  definition,  which  is 
given  unexceptionably  (as  a  summary  of  symptoms)  in  what 
succeeds  to  the  above  quotation. 

Propositions  of  Medicine, . 

10.  The  Real  Predications  of  Medicine,  as  contraclistin- 
guished  from  the  Essential  or  Defining  Propositions,  fall 
under  distinct  heads. 

The  coupling  of  the  Essential  characters,  even  although 
numerous,  is  Definition,  and  not  Real  Predication.  Nay 
farther ;  the  modified  characters  shown  in  different  constitu- 
tions and  different  circumstances,  should  be  held  as  a  part,  or 
as  an  appendage,  of  the  Definition.  Real  propositions  may 
arise  in  connexion  with  these  modifications  when  certain  cir- 
cumstances are  alleged  to  intensify  or  to  resist  the  diseased 
action. 

11.  The  first  class  of  Eeal  Predications  conipnses  In- 
ferences or  propria  from  the  Essential  characters  of  a  Dis- 
ease. 


PBOPOSITJONS  IN  MEDICINE. 


689 


Having  given  the  defining  marks,  in  their  ultimate  state- 
ment, together  with  the  important  modifications  and  varieties, 
we  can  by  the  help  of  general  principles— Physical,  Chemical, 
Biological,  or  Pathological — draw  many  conclusions  bearing 
on  the  treatment  of  the  disease.  It  would  be  easy,  for  ex- 
ample, to  unfold  a  great  many  facts  respecting  Fever,  from 
the  Law  of  Conservation,  the  laws  and  facts  of  Organic  Che- 
mistry, &c.  The  maintenance  of  an  excessive  temperature, 
with  less  than  the  ordinary  nourishment,  involves  waste  or 
inanition  of  the  organs,  and  the  formation  of  special  products 
of  wasted  tissue  ;  with  many  other  consequences  under  given 
situations.  This  deductive  process,  when  based  on  well 
ascertained  generalities,  affords  propositions  capable  of  great 
precision  and  certainty. 

12.  The  second  class  of  Real  Predications  consists  of 
the  Causes  of  Disease. 

A  Disease  is  one  thing,  its  cause  is  another  thing ;  proposi- 
tions of  Causation,  are,  therefore,  in  their  nature,  strictly  real. 
Their  importance  demands  a  distinct  and  separate  enunciation. 

Implicated  with  the  great  subject  of  Hygiene,  or  Health 
preservation,  there  is  a  body  of  information  respecting  the 
General  Causes  of  Disease.  It  is  all  one  thing  to  know  what 
are  the  means  to  keep  the  body  in  health,  and  what  will  cause 
loss  of  health. 

Many  forms  of  disease  are  due  at  once  to  the  disproportion 
between  the  expenditure  and  the  nutrition  of  the  system. 
The  diseases  of  exhausted  organs — functional  weakness  and 
degeneration  of  the  muscles,  the  brain,  the  stomach,  the  lungs, 
the  heart,  the  kidney — are  of  this  class. 

To  the  same  general  head  should  be  referred  nearly  every- 
thing meant  by  Predisposing  Causes  of  Disease.  There  are 
many  diseases  that  do  not  spring  up  unless  by  poison  or  infec- 
tion from  without ;  called  Zymotic  Diseases.  As  the  poison 
of  many  (but  not  of  all)  such  diseases  may  be  resisted  by  a 
healthy  system,  any  circumstances  that  destroy  general 
vigour,  or  weaken  particular  organs,  are  called  predisposing 
causes ;  as  when  cholera  attacks  constitutions  exhausted  by 
intemperance,  or  by  insufficient  food,  or  by  ill- ventilated 
dwellings. 

It  is  less  easy  to  generalize  the  various  influences  expressed 
as  Infection,  Epidemic  poison.  Miasmata,  &c.  This  is  one 
great  field  for  Representative  Hypotheses  in  Medicine. 

Under  each  separate  Disease,  an  account  is  given  of  the 


i  f 
■ft  ■■% 


t 


!  i 

i  .11 


:\i 


'  '> 


t    ■!• 


i 


t 


yi 


590 


LOGIC  OF  MEDICINE. 


!.■<: 


Cause,  as  far  as  known,  whether  general  or  special.  Where- 
ever  there  is  a  loss  of  power  from  the  predominance  of  waste 
over  supply,  Causation  in  Disease  appears  as  *  Conservation ; ' 
it,  however,  still  more  largely  implicates  Collocations. 

13.  There  may  be  a  distinct  class  of  Eeal  Propositions, 
expressing  the  effects  of  Disease. 

The  full  definition  of  each  disease  comprises  its  whole 
history  to  the  termination;  the  temporary  prostration  of 
Typhus  is  not  an  effect  of  the  disease,  it  is  the  disease  itself. 
When,  however,  a  disease,  besides  accomplishing  its  course, 
makes  permanent  changes  in  the  organs  or  constitution  of  the 
patient,  this  is  a  distinct  fact,  and  may  be  enrolled  under  the 
head  of  Causation.  Such  are  the  after  effects  of  Small  Pox, 
Measles,  Scarlet  Fever,  and  Syphilis.  While  a  few  diseases 
have  a  wholesome  efficacy,  the  greater  number  weaken  the 
system  at  some  point,  and  are  therefore  predisposing  causes  of 
future  disease. 

14.  The  Eemedies  of  Disease  constitute  Eeal  Propositions. 

All  the  previous  classes  of  assertions  prepare  the  way  for  the 
present.  The  remedy  of  a  disease  may  be  suggested  by  its 
Characters,  whether  primary  (Definition),  or  inferred  from  the 
primary  (Propria) ;  or  by  its  Causation,  on  the  principle  of 
'  remove  the  cause.'  Diseases  of  functional  degeneration,  or 
premature  decay  of  organs,  involve  in  their  cure  *  repaying 
the  debt  to  nature — the  restoration  of  the  balance  of  nourish- 
ment and  waste. 

In  many  instances,  the  remedy  consists  in  something  differ- 
ent from  either  treating  the  symptoms,  or  removing  the  cause. 
The  Specifics  that  have  been  discovered  for  particular  diseases, 
as  quinine,  colchicum,  lime  juice,  cod  liver  oil,  are  affirmed  as 
independent  facts,  resting  on  no  deductive  inferences  from 
Cause  and  Effect  in  Disease,  but  on  the  experience  of  their 
efficacy. 

The  Experimental  Methods  in  Medicine. 

15.  All  the  Experimental  Methods  are  applicable  to 
Medicine,  with  certain  cautions  and  qualifications. 

The  ultimate  problem  of  Medicine  is  to  find  a  remedy  for 
every  remediable  disease  ;  and  the  apparently  direct  solution 
is  to  try  various  remedies  upon  actual  cases.  If  by  Agreement, 
under  a  wide  variation  of  circumstances,  a  certain  remedy  ib 


THE  EXPERIMENTAL  METHODS. 


591 


found   to   succeed   uniformly,    or  in   a   great   proportion    of 
mstances,  there  is  proof  that  it  is  the  remedy. 

Still  we  cannot  but  remark  the  very  serious  difficulties  that 
feeset  all  the  Experimental  Methods  in  this  attempt.  PluraHty 
ot  Causes  and  Intermixture  of  Effects  occur  in  the  most  agc^ra- 
vated  shape.  Moreover,  drugs,  being  natural  Kinds,  have  so 
many  possible  ways  of  acting,  that  the  elimination  of  the 
precise  property  that  affects  the  system  is  all  but  hopeless. 

VVithout,  therefore,  abandoning  the  tentative  process,  as 
applied  to  actual  disease,  modern  medicine  has  advanta- 
geously approached  the  problem  in  circuitous  ways  ;  and  has 
instituted  researches  where  the  experimental  methods  are  less 
likely  to  be  defeated.  Thus— to  take  the  example  that  departs 
least  from  the  empirical  method— the  mode  of  action  of 
medicines  and  of  remedi.es  is  studied  by  experiments,  not  re- 
Btricted  to  special  diseases,  but  applied  to  the  system  in  health 
and  in  disease  alike,  under  every  variety  of  conditions.  This 
is  a  far  more  thorough  and  searching  procedure ;  and  the 
Method  of  Agreement  will,  of  itself,  give  trustworthy  results 
under  so  great  an  extension  of  instances  ;  while  by  superad- 
ding Difference,  Inverse  Agreement,  and  Variations,  there 
may  accrue  results  of  the  highest  certainty.  I  may  cite,  amono. 
this  class  of  Researches,  the  Report  of  Dr.  Bennet  on  the 
Action  of  Mercury  on  the  Biliary  Secretion,  and  Dr.  Harley*s 
work  on  the  Old  Neurotics.  By  such  researches  is  built  up 
that  part  of  Materia  Medica  relating  to  the  Therapeutic  action 
of  medicines. 

Again,  the  Pathology  of  Disease,  the  concurrence  and  se- 
quence of  symptoms,  studied,  in  the  first  instance,  apart  from 
modes  of  treatment,  is  open  to  experimental  enquiry,  and  may 
lead  to  results  having  all  the  precision  attainable  in  the 
science  of  Medicine.  For  such  enquiries,  the  Experimental 
Methods  are  suitable ;  the  endeavour  being  made'  to  bring 
each  one  of  them  into  play,  by  searching  for  the  approp- 
riate class  of  instances.  Mere  Agreement  is  usually  what 
suggests  itself  to  the  untutored  mind ;  the  force  of  Agreement 
m  Absence  and  of  Variations  is  apparent  only  to  such  minds  as 
have  reflected  largely  on  the  conduct  of  scientific  researches. 

The  influences  commonly  called  Hygienic,  and  the  simpler 
Therapeutic  agencies,  as  cold  and  heat,  change,  exercise  and 
rest,  stimulants,  &c.,  not  only  present  fewer  difficulties  to  ex- 
periment, but  are  also  within  the  scope  of  the  Deductive 
method.  In  like  manner,  the  proof  of  noxious  agencies— as 
impure  water,  and  the  effluvia  of  decay— is  easy  and  complete. 
26 


s( 


{ 


/ 


692 


LOGIC   OF  MEDECINB. 


hi 


16.  The  Elimination  of  Chance  is  of  great  value  in 
Medicine.     Its  groundwork  is  Medical  Statistics. 

Nowhere  more  than  in  Medicine  may  laws  of  Causation  be 
defeated  ;  there  is  rarely  such  a  thing  as  a  simple  cause  yieia- 
incr  a  simple  effect.  Hence,  the  necessity  of  ascertaming 
whether  a  coincidence  is  more  frequent  than  would  be  ac 
counted  for  by  chance.  The  cinchona  bark  sometimes  fails  to 
cure  ac^ue,  yet  its  general  efficacy  is  satisfactorily  established. 
To  prove  the  efficacy  of  medicines  as  a  whole,  m  opposition 
to  some  speculators  that  ascribe  all  cures  to  nature  (aided  by 
repose  and  regimen)  the  physicians  of  a  French  hospital 
made  the  experiment  of  withholding  drugs  from  all  the  patients 
for  a  certain  time.  The  conclusion  seemed  to  be  that  the 
mortality  was  not  increased,  but  the  recoveries  were  more 
protracted.     This  was  a  competent  inference  from  statistics. 

The  difficulties  in  obtaining  a  statistical  proof  of  the  action 
of  a  remedy  in  a  given  disease  are  exactly  those  already 
mentioned  respecting  the  use  of  Agreement  in  the  same 
determination.*  A  large  hospital  statistics  is  better  than  the 
inferences  of  a  single  physician  in  private  practice,  and  yet 
may  come  short  of  the  proof  There  should  always  be  obtained, 
if  possible,  a  parallel  statistics— cases  with,  and  cases  without, 
the  treatment  in  question.  The  statistics  of  cholera  treatment 
may  be  alleged  in  favour  of  many  modes  ;  but  none  appear  to 
be  decisively  established. 

Statistics,  as  applied  to  Scarlet  Fever,  has  shown  that  a 
second  attack  is  extremely  rare ;  that  the  ages  of  two  and 
three  are  most  susceptible  to  the  disease  ;  and  that  the  maxi- 
mum of  prevalence  is  in  October,  November,  and  December, 
and  the  minimum  in  April,  May,  and  June. 

The  Deductive  Method, 
17    The  scope  of  the  Deductive  Method  in  Medicine  is 
co-exteusive  with  the  number  of  well-established  generali- 
ties than  can  be  appealed  to. 

The  sciences  applicable  to  Medicine— Physics,  Chemistry, 
and  Biology— yield  a  considerable  number  of  these  fertile 
ereneralities.  The  science  itself  contains  few  of  a  very  com- 
manding  character,  but  a  considerable  number  that  have  a 
sufficient  range  for  deductive  operation,  and  for  converting 
empirical  into  derivative  laws.  All  the  propositions  of  general 
♦  See  an  estimate  of  these  difficulties  in  Dr.  Barclay»8  work  on  Medical 
Errois,  p.  35. 


HYPOTHESES. 


593 


eansation  in  medicine,  the  laws  of  general  Therapeutics,  the 
laws  of  the  action  of  drugs  on  the  system  generally,  have 
sufficient  breadth  to  control  and  correct  empirical  practice ; 
and  the  mastery  of  these,  as  well  as  of  the  more  commanding 
principles  of  the  preparatory  sciences,  increases  the  power  of 
the  physician.  The  physiology  of  Food  as  regards  the  various 
forces  of  the  system,  muscular,  heat-giving,  nervous,  &c., 
and  the  products  of  elimination, — is  pregnant  with  deductive 
consequences,  both  in  warding  off  and  in  curing  disease. 

The  experimental  methods  are  greatly  at  fault  with  slow- 
acting  causes;  and  hence  deduction  is  pre-eminently  desirable 
in  such  points  as  the  influence  of  alterative  medicines,  stimu- 
lants, climatic  influences,  and  modes  of  life.  Only  a  thorough- 
going statistics,  or  a  deduction  from  general  principles,  caa 
dispose  of  the  doubts  that  arise  on  such  points. 

Hypotheses  in  Medicine. 

1 8.  Medical  Science  is  largely  dependent  on  Hypotheses. 

As  a  department  of  applied  Biology,  Medicine  needs  all  the 
aids  rendered  by  hypotheses  in  the  mother  science,  and  some 
special  to  itself.  The  great  biological  fact — Assimilation — 
takes  on  a  new  aspect  in  the  production  and  spread  of  Disease. 

The  first  and  simplest  case  of  Hypothesis,  the  assuming  of 
an  agent  known  to  exist,  but  not  known  as  present  in  ade- 
quate amount  in  the  given  case,  is  abundantly  exemplified. 
Thus,  the  origin  of  contagious  disease  is  ascribed  hypotheti- 
cally  to  various  real  agents,  and  among  others,  to  actual 
living  organisms.  The  effects  tally  in  a  general  way  with 
such  an  agency.  What  remains  is  to  find  whether  they  tally 
closely  at  all  points.  The  hypothesis,  however,  receives  a 
powerful  support  from  individual  cases  where  the  presence  of 
an  animalcule,  or  living  germ,  appears  to  be  actually  estab- 
lished. The  alternative,  and  older,  hypothesis  is  that  organic 
particles,  in  a  state  of  change  or  activity,  are  thrown  off  from 
one  living  body  and  infect  another,  such  particles  not  being 
complete  organisms  or  the  germs  of  organisms.  This  hypo- 
thesis may  seem  to  assume  less  than  the  other,  but  in  reality 
it  assumes  a  class  of  particles  not  distinctly  proved  to  exist. 
A  strong  analogy  may  be  pleaded  for  them,  in  the  supposed 
communication  of  morbid  action  within  the  system;  the  action 
of  the  poison  of  small  pox  must  be  the  same  on  the  blood 
of  the  innoculated  patient  as  on  the  original  patient.  Yet  the 
aerial    effluvia   of  typhus   may   consist   of    something   more 


I  II 

11 
"I 


-  I 


rx 


594 


LOGIC  OF  MEDICINE. 


definitely  organized  than  tbe  supposed  active  particles.     Fer- 
mentation by  yeast  is  found  to  be  due  to  an  animalcule. 

The  Representative  Fiction  is  indispensable  in    Medicine, 
and  its  rules  and  properties  need  to  be  well  understood. 

Diseased  appearances,  like  all  manifestations  of  living  bodies, 
are  the  superficial  outcome  of  a  vast  concatenation  of  hidden 
chano-es.  These  intermediate  links  are  in  great  part  unknow- 
able f  yet,  by  following  the  clue  of  what  we  know,  we  may  so 
conceive  or  imagine  them,  as  thereby  to  unite  the  appearances 
in  a  consistent  whole.  When  an  organ  is  liable  to  derange- 
ment from  slight  causes,  we  prononnce  it  weaJc,  which  is  merely 
to  express  the  fact  in  another  word  ;  when,  however,  we  assign 
such  circumstances  as  that  its  tissue  has  degenerated  or 
changed,  that  it  has  very  little  tendency  to  assimilate  nutri- 
ment from  the  blood,  or  that  the  superior  exercise  of  all  the 
other  organs  of  the  body  withholds  from  it  the  fair  amount  of 
blood  and  nerve  force, — we  employ  convenient  hypotheses, 
which  are  more  or  less  in  keeping  with  the  facts. 

As  regards  the  two  leading  diseased  processes — Fever,  and 
Inflammation— probably  no  hypothesis  yet  framed  adds  any- 
thing to  the  facility  of  conceiving  or  of  generalizing  the  facts. 
Supposing  the  difierent  fevers  generated  each  by  a  specific 
virus,  or  animated  body,  we  cannot  even  in  imagination  sup- 
pose a  connexion  between  the  structure  of  the  infecting 
element,  and  the  specific  characteristics  of  the  fever ;  as  in  the 
difierence  between  typhus,  scarlet  fever,  or  intermittent  fever. 
Indeed,  we  cannot  form  a  plausible  supposition  as  to  the 
intermediate  link  that  connects  a  certain  infecting  substance 
with  the  febrile  state  generally.  The  difficulty  here  is  exactly 
the  difficulty  in  representing  the  facts  of  living  action.^ 

Hypothesis  appears  to  more  advantage  in  connexion  with 
what  is  termed  Functional  Degeneration,  Functional  weakness, 
strength  and  weakness  of  parts.  Great  convenience  attaches 
to  the  use  of  such  phrases  as  healthiness,  robustness,  vigour, 
constitutional  force— which  are  modes  of  stating  the  absence 
of  disease  under  circumstances  that  u^sually  provoke  it.  We 
may  increase  the  value  of  this  class  of  terms,  by  hypothetical 
interpolations,  to  the  following  effect : — 

Assuming  an  average  healthy  system  to  begin  with,  we 
know  by  reasonable  inferences,  (1)  that  every  one  of  the  organs 
needs  an  equable  supply  of  blood,  with  more  or  less  aid  from 
the  nervous  centres,  and  (2)  that  each  organ  is  capable  of  a  cer- 
tain amount  of  exertion.  Suppose  now,  that  by  any  cause, 
either  the  nutrition  is  below  the  mark,  or  the  exertion  above 


HYPOTHESIS  OF  DEGENERATION. 


595 


it,  or  both.  It  is  the  nature  of  the  system  not  to  show  im- 
mediately the  effects  of  such  a  mal -proportion,  yet  there  must 
be  an  immediate  effect ;  the  overwork,  or  the  defective  nutri- 
tion, of  a  single  day  does  not  leave  the  organ  exactly  as  it  was ; 
we  are  entitled  to  assume  that  there  is  superinduced  a  minute 
structural  change,  or  degeneration,  perceptible  only  after  many 
repetitious,  but  actually  realized.  Suppose  the  disproportion 
of  expendituie  and  supply  to  continue  for  a  length  of  time; 
the  first  outward  symptoms  will  probably  be,  that  the  organ  is 
enfeebled  in  some  duty  that  is  required  of  it,  and  becomes 
positively  disordered  under  influences  that,  in  its  regular  con- 
dition, it  would  have  successfully  resisted.  At  this  point, 
degeneration  or  structural  change  has  made  a  decided  ad- 
vance ;  another  equal  advance  would  bring  down  the  organ  to 
the  bare  performance  of  its  functions ;  a  third  would  be  utter 
suspension  and  death.  Now,  we  have  here  scope  for  a 
great  variety  of  suppositions,  as  to  the  relative  condition 
of  all  the  organs  in  the  body.  We  can  represent  the  constitu- 
tional peculiarities  at  birth,  by  the  proportionate  dispositions 
of  the  several  organs — nerves,  muscles,  lungs,  digestion — to 
appropriate  nutriment,  and  to  become  vigorous  or  the  oppo- 
site ;  we  can  state  to  ourselves  the  practical  mode  of  redressing 
the  inequality,  namely,  by  restraining  the  vigorous  organs  from 
their  tendency  to  impoverish  the  rest,  and  by  giving  greater 
opportunity  to  the  nourishment  of  the  weak.  We  can  also  state 
the  rationale  of  the  constitutional  treatment  of  diseases,  viz., 
the  placing  of  the  weakened  organs  in  such  a  position  as  to 
increase  their  nutriment  and  abate  their  over-exertion.  We 
can  give  a  hypothetical  account  of  the  degeneration  of  or- 
gans such  as  the  heart  and  kidney,  which  often  show  no 
signs  until  the  structure  has  reached  a  mortal  disease.  We 
should,  moreover,  feel  no  surprise  at  the  sudden  breaking  down 
of  constitutions  reputed  strong  ;  the  popular  eye  sees  only  the 
prosperity  of  those  organs  that  cast  a  dash  and  a  glare — the 
muscles,  the  stomach,  and  the  brain.  The  deeper  glance  dis- 
closes the  degeneracy  of  the  heart,  the  lungs,  the  kidney, 
following  on  the  very  strength  of  these  ostentatious  members 
of  the  system. 

Classification  of  Diseases. 

19.  There  being  upwards  of  one  thousand  recognized 
Diseases,  they  may,  like  other  great  aggregates,  come 
under  a  regular  Classification. 


ml 


•It 


i  * 
t 


t  I 


596 


LOGIC   OF   MEDICINB. 


Disenses  may  fall  under  a  classified  arrangement,  like 
Minerals,  Plants,  or  Animals,  attention  being  given  to  the 
peculiarities  of  the  department. 

I.  Order  of  Charaders.—ln  Mineralopry,  and  in  Botany,  a 
strict  order  of  characters  is  observed.  This  is  disregarded  in 
Zoology,  and  also  in  Medicine,  from  difficulties  that  can  be 
readily  assigned.  There  is  every  likelihood,  however,  that 
both  sciences  would  gain  by  a  systematic  arrangement  of  char- 
acters, avoiding  the  sacrifice  of  the  spirit  to  the  letter. 

In  a  work  to  be  afterwards  referred  to  (p.  597),  the  remark 
is  made  *  that  the  labour  of  analyzing  and  comparing  clinical 
observations  would  be  greatly  lightened,  and  the  precision  of 
the  observations  themselves  increased,  if  the  records  of  these 
were  in  every  instance  arranged  on  an  uniform  plan.' 

One  obvious  precaution  is  to  make  the  outward  symptoms 
precede  the  subjective.  Thus,  of  the  usual  marks  of  inflam- 
mation, the  pain  should  come  last.  In  nervous  diseases,  the 
physical  symptoms  should  be  fully  enumerated  before  entering 
upon  the  mental  symptoms  ;  the  two  classes  are  then  viewed  in 
such  a  way  as  to  check  and  confirm  each  other. 

II.  Maximum  of  Affinities.  —  The  propriety  of  classing 
Diseases  by  their  closest  resemblances  is  sufficiently  allowed 
in  the  abstract ;  the  difficulties  in  execution  are  not  logical, 
but  pathological. 

III.  Arrangement  hy  Grades. — The  formality  of  Grades  is 
observed  in  the  classification  of  Diseases,  but  without  the  full 
carrying  out  of  what  it  involves.  There  is  something  of  lax- 
ness  attending  the  use  of  the  method  even  in  Chemistry,  the 
statement  of  the  points  of  community  of  the  higher  grades 
beinf*"  sometimes  given,  and  sometimes  not,  without  any- 
apparent  reason. 

Occasionally  there  is  vacillation  as  to  whether  diseases  are 
different  in  species,  or  mere  varieties.  Little  importance 
attaches  to  the  question  ;  and  the  workable  criterion  is  the 
comparative  number  and  persistence  of  the  distinctive  marks. 

IV.  Statement  hy  Agreement  and  Difference. — Everything 
already  said  on  this  head  applies  to  the  exposition  of  Diseases. 
The  systematic  and  orderly  stating  of  Agreements,  and  the 
pointed  contrast  in  Difference,  have  the  same  efficacy  here  as 
elsewhere.  Under  the  heading  'Diagnosis,'  it  is  usual  to 
mention  the  closely  resembling  diseases,  and  to  indicate  the 
diagnostic  marks.  For  example.  Roseola  is  distinguished 
from  Scarlet  Fever,  thus  : — the  eruption  in  Roseola  is  gene- 
rally confined  to  the  chest.     When  the  diagnostic  points  are 


INDEX  CLASSIFICATION. 


597 


two  or  more,  they  might  be  set  forth  in  the  formal  manner 
already  exemplified. 

20.  V.  Index  Classification. — For  ]^Iedicine,  an  Index 
Classification  might  be  provided  on  the  tabular  plan. 

This  aid  to  the  discrimination  of  Disease  is  still  wanting. 
Probably,  it  would  be  best  attempted,  in  the  first  instance,  on 
the  tabular  plan.  A  basis  is  afforded  in  a  small  work,  pub- 
lished by  the  Medical  Society  of  Observation,  with  the  title 
*  What  to  Observe  in  Medical  Cases.' 

The  work  professes  to  lay  out  in  order  an  exhaustive  state- 
ment of  all  the  appearances  connected  with  each  bodily  organ, 
besides  adverting  to  the  external  circumstances  of  the  patient. 
The  enumeration  commences  with  the  Skin,  which  is  followed 
by  the  organs  of  Locomotion,  Digestion,  Respiration,  Circula- 
tion, Lymphatics,  Urinary  Organs,  Organs  of  Generation,  Brain 
and  Nerves,  Vascular  Glands. 

As  an  example,  I  quote  the  varieties  of  the  Pulse : — '  Radial 
Pulse: — number; — size  and  force;  large,  small,  thready,  equal, 
unequal,  strong,  feeble ; — resistance ;  soft,  compressible,  hard, 
incompressible  ; — rhythm  ;  regular,  irregular,  intermittent ; — 
time  as  compared  with  that  of  heart's  impulse ; — artery  tortuous, 
rigid. — Special  characters  of  pulse ;  jerking,  bounding,  undula- 
tory,  continuous  (one  pulse  appearing  to  run  into  the  following), 
vibrating,  quick,  tardy,  vermicular,  tremulous,  reduplicate. — 
Effects  of  posture  on  pulse  (its  number  and  other  characters). — 
Phenomena  of  pulse  in  one  arm  as  compared  with  the  other.* 

The  authors  have  evidently  studied  exhaustiveness  to 
begin  with.  It  is  possible,  however,  to  be  too  minute ; 
distinctions  that  are  not  marks  of  anything  else  are  worthless 
and  may  be  an  encumbrance.  The  next  step,  therefore, 
should  be  to  abridge  and  group  the  symptoms  with  a  view  to 
the  maximum  of  significance. 

There  being  obtained  a  methodical  array  of  symptoms 
under  each  organ,  the  mode  of  proceeding  with  a  view  to  an 
Index  is  to  append  to  each  symptom  a  list  of  the  diseases 
where  it  occurs.  Should  a  symptom  appear  in  only  one 
disease  (as  urate  of  soda  in  gout)  the  occurrence  of  the  symp- 
tom would  decide  the  disease  at  once.  Should  a  symptom 
appear  in  three  diseases,  its  occurrence  points  to  one  of  those 
three  diseases. 

By  appending,  to  every  symptom  of  value  in  diagnosis,  a 
complete  list  of  diseases,  there  is  provided  a  means  of  deter- 
mining every  disease  according  to  the  knowledge  of  the  time. 
One  symptom  refers  ns  to  one  list,  containing  two,  three,  or 


i  < 


i* 


t 


;  i 


M 


l;I? 


\t 


698 


LOGIC   OF  MEDICINE. 


four  diseases  ;  a  second  symptom  leads  to  another  list.  If  on 
comparison,  there  is  found  only  one  disease  common  to  the 
two  lists,  the  diagnosis  is  complete.  If  there  are  two  or  three 
common  to  both  lists,  a  third  symptom  must  be  sought  out 
with  its  corresponding  entries,  by  which  the  alternations  are 
again  reduced  ;  and  so  on,  till  the  concurrence  of  symptoms 
points  to  a  single  disease.  ^ 

Suppose,  for  illustration,  that  *  Irregularity  of  the  Pulse 
appears  as  symptom.     According  to  Dr.  Watson,  this  may 
attend  (1)  disease  within  the  head  ;  (2)  organic  disease  of  the 
heart ;   (3)  simple  disorder  of  the  stomach  ;  (4)  debility,  and 
a  prelude  to  stoppage  of  the  heart's  action  from  asthenia. 

Now  supposing  the  tabulation  of  symptoms  and  of  diseases 
complete  upon  this  plan,  and  supposing  a  second  symptom  in 
the  case  under  enquiry  had  opposite  to  it  a  list,  agreeing  with 
the  first  only  in  the  entry  *  simple  disorder  of  the  stomach/ 
ibhe  diagnosis  is  made  out  by  two  easy  references. 

Owing  to  obvious  causes — the  great  number  of  diseases 
accompanying  particular  symptoms,  the  occasional  ambiguity 
of  actual  diseases  by  the  failure  of  some  of  their  usual  symp- 
toms, and  the  imperfection  of  the  terminology  of  symptoms, — 
the  best  scheme  that  could  be  given  would  be  imperfect. 
This  would  not,  however,  prevent  it  from  being  a  boon  to  the 
student,  and  an  occasional  aid  to  the  experienced  practitioner. 
It  does  not  supersede,  but  indicates,  the  reference  to  the 
systematic  works  on  Medicine  and  Pathology,  which  are  the 
authorities  in  the  last  resoi't 


BOOK  YL 

FALLACIES- 


CHAPTER  L 

MILL'S  CLASSIFICATION  OF  FALLACIES. 

Mr.  Mill  regards  all  fallacies  as  divisible  into  two  great 
heads— Fallacies  of  Simple  Inspection,  and  Fallacies  of  Infer- 
ence By  the  first  class  he  understands  those  cases  where  a 
presumption  is  created  in  favour  of  a  fact  or  doctrme,  on  the 
mere  inspection  of  it,  and  without  any  search  for  evidence ; 
natural  prejudices  are  comprised  under  that  head.  By  the 
second  class  he  understands  erroneous  conclusions  from  sup- 
posed evidence.  This  class  is  subdivided  according  to  the 
nature  of  the  evidence  simulated  ;  which  may  be  deductive, 
inductive,  &c.  A  special  division  is  indicated  under  the  title 
« Fallacies  of  Confusion,*  where  the  error  arises,  not  in  the 
link  between  premises  and  conclusion,  but  in  the  incorrect 
handling  of  the  premises  themselves. 

There  are  thus  five  distinguishable  classes  of  Fallacy,  as  set 

forth  in  the  table  : — 

,o£  Simple  Inspection  -        •       -       1.  FaUacies  a  pnori. 

flndnctive  (2.  Fallacies  of  Observation 
'^^tincti°^!;^^^'®^  h-  Fallacies  of  GenemlizaUon 
conceived  "SDeductive  j  ^  Fallacies  of  RaUocination 


I  Fallacies    i 


from  evidence  (^ 
indistinctly  / 
conceived     J 


^ 5.  Fallacies  of  Confusion 

.of  Inference^ 
L  F<^llacie8  of  Simple  Inspeciion,  or  a  priori  Fallacies. — Re- 
fraining from  the  discussion  of  the  question,  which  this  desig- 
nation might  raise,  what  are  the  ultimate  facts  or  premises  at 


i  I 


I"  f ' 


II' 
If  I 


it 

i  I 

ll 


m 


i 


Hi 


tl" 


600 


MILUS  CLASSIFICATION   OF  FALLACIKa 


the  foundation  of  all  reasonings,  Mr.  Mill  adduces  first  the 
tacit  assumption  that  the  same  order  obtains  among  the  objects 
of  nature  as  among  our  ideas  of  them — that  if  we  always  think 
of  two  things  together,  the  two  things  must  exist  together. 
He  illustrates  this  tendency  by  numerous  popular  superstitions, 
talk  of  the  devil  and  he  will  appear,'  &c.     He  also  cites- 


as 


the  philosophy  of  Descartes,  which,  from  the  mere  conceptions 
of  the  mind,  inferred  the  existence  of  corresponding  realities  ; 
the  doctrines  that  *  whatever  is  inconceivable  is  false,*  *  that 
a  thing  cannot  act  where  it  is  not '  (applied  by  Newton  to 
show  the  necessity  of  a  gravitating  medium),  that  *  matter 
cannot  think,*  that  *  space  is  infinite,*  that  *  nothing  can  be 
made  out  of  nothing,'  that  *  nature  always  acts  by  the  simplest 
means.'  An  allied  Fallacy,  or  prejudice,  is  the  tendency  to 
presume  a  correspondence  between  the  laws  of  the  mind  and 
the  laws  of  external  things,  of  which  one  form  is  expressed 
thus  : — *  whatever  can  be  thought  of  apart  exists  apart.' 
From  this  springs  the  personifying  or  re-ifying  of  Abstractions, 
as  in  the  doctrine  of  idealism,  and  in  mystical  theories  gene- 
rally, whether  it  be  the  mysticism  of  the  Vedas,  or  the  mysti- 
cism of  Hegel ;  all  which  proceeds  on  ascribing  objective 
existence  to  subjective  creations—  feelings,  or  ideas. 

Another  kindred  fallacy  consists  in  representing  nature  as 
under  the  same  incapacity  with  our  powers  of  thought  ;  the 
great  example  being  the  celebrated  Principle  of  Sufl&cient 
Reason,  adduced  in  explanation  of  many  first  truths,  such  as 
the  laws  of  motion. 

*  That  the  differences  in  nature  correspond  to  the  received 
distinctions  of  language,*  is  another  wide  spread  and  baneful 
prejudice,  which  particularly  weighed  upon  Greek  philosophy, 
being  prominent  in  the  reasonings  of  Aristotle,  and  from  which 
Bacon  was  unable  to  set  himself  free,  as  is  shown  by  his  futile 
attempts  to  find  a  common  cause  for  everything  that  goes 
nnder  a  common  name,  as  heat,  cold,  &c. 

Lastly,  there  has  existed  the  prejudice  that  *  the  conditions 
of  a  phenomenon  will  resemble  the  phenomenon  * — like  pro- 
ducing like :  as  that  motion  must  necessarily  arise  from  the 
impact  of  a  moving  body  ;  that  a  sharp  taste  must  be  brought 
about  by  sharp  particles  ;  that  our  sensations  must  be  copies 
of  external  things ;  that  the  law  of  causality  can  hold  only 
between  what  is  homogeneous,  whence  there  can  be  no  causa- 
tion between  mind  and  matter ;  that  the  Deity  must  have  the 
exact  perfections  discoverable  in  nature. 

II.  Fallacies  of  Observation. — These  do  not  apply  to  the 


GENERALIZATION. — RATIOCINATION. 


601 


Operation  of  observing,  for  which  there  is  no  logic  strictly  so 
called,  but  to  the  omissions  and  partialities  in  collecting  facts 
with  a  view  to  the  generalizing  process.  There  may  be  Non- 
observation,  or  Mal-observation  ;  the  one  leaves  out  pertinent 
instances,  the  other  distorts  or  misrepresents  what  is  observed. 
Non-observation  explains  the  credit  given  to  fortune-tellers, 
to  quacks,  and  to  false  maxims ;  the  cases  favourable  being 
noted,  and  the  other  forgotten.  The  motive  in  this  class  of 
fallacies  is  a  strong  pre-conceived  opinion  or  wish  to  find  the 
dictum  true.  Farther,  the  Non-observation  may  be,  not  of 
instances,  but  of  material  circumstances,  as  when  it  is  stated 
that  lavish  expenditure  alone  encourages  industry,  the  circum- 
stances being  overlooked  that  savings  are  capital  for  the 
employment  of  labour. 

Under  Mal-observation  may  be  placed  the  chief  mistake 
connected  with  the  proper  act  of  observing,  namely,  the  con- 
founding of  a  perception  with  a  rapid  inference,  or  the  mingling 
up  of  inferences  with  facts.  This  is  the  common  infirmity  of 
uneducated  witnesses  and  narrators  of  events. 

III.  Fallacies  of  Generalization, — These  are  errors  in  the 
employment  of  the  Inductive  process.  The  chief  instances 
adduced  are  these : — All  inferences  extended  to  remote  parts 
of  the  universe,  where  no  observation  or  verification  can  be 
carried ;  all  universal  negatives  and  propositions  asserting 
impossibility  (not  being  contradictions  in  terras)  ;  the  theories 
professing  to  resolve  all  things  into  some  one  element,  of  which 
the  most  notable  instance  is  the  attempt  to  resolve  states  of 
consciousness  into  states  of  the  nervous  system ;  the  placing 
of  empirical  laws,  arrived  at  per  enumerationem  simpUcem,  upon 
the  footing  of  laws  of  causation,  largely  exemplified  in  reason- 
ings upon  society ;  the  vulgar  form  of  the  same  fallacy,  desig- 
nated post  Jioc,  ergo  propter  hoc  ;  and  the  fertile  class  of  False 
Analogies.  Under  the  same  head  are  specified  Bad  Classifica- 
tions, or  the  asserting  under  one  term,  things  that  have  little 
or  no  community ;  of  which  the  Greeks  gave  examples  in  such 
terms  as  Motion,  Generation  and  Corruption. 

IV.  Fallacies  of  Ratiocination,  These  comprise  the  errors 
against  the  laws  of  the  Syllogism.  Mr.  Mill,  however,  properly 
includes  under  them  the  fallacies  connected  with  the  Conver- 
sion and  Equipollency  of  Propositions ;  remarking  that  the 
simple  conversion  of  the  universal  affirmative,  and  the  errone- 
ous conversion  of  Hypotheticals  are  among  the  most  frequent 
sources  of  error.  Of  this  last  class,  is  the  maintenance  of  some 
favourite  doctrine,  on  the  ground  that  the  inferences  from  it 


tt 


i  k 


I  I 


■1 


M 


602 


mill's  classification  of  fallacies 


11 


m.  - 


are  true.  Connected  with  the  Opposition  of  Propositions  is 
the  confounding  of  the  contrary  with  the  contradictory  of  a 
statement.  Vicious  syllogisms,  whether  from  undistributed 
middle^  or  from  illicit  process,  are  the  more  noted  instances  of 
this  class  of  fallacies.  There  may  be  also  included  the  fallacy 
of  changing  the  'premises,  occurring  frequently  in  the  argument- 
ative discourses  of  unprecise  thinkers  (the  schoolmen's  a  dicto 
secundum  quid  ad  dictum  simpliciter)  ;  exemplified  in  the  once 
favourite  theory  that  *  whatever  brings  in  money  enriches.* 
Under  the  same  head  might  be  placed  the  misapplication  of 
gen^eral  truths,  or  the  supposition  that  a  principle  true  in  the 
abstract  must  hold  under  all  sets  of  circumstances. 

V.  Fallacies  of  Confusion.  The  first  class  under  this  desig- 
nation is  Ambiguity  of  Terms,  As  there  is  no  limit  to  that 
form  of  confusion,  a  logician  can  only  select  a  few  random 
instances  ;  those  chosen  by  Mr.  Mill  are  *  scarcity  of  money,* 
'influence  of  property,'  *  theory,'  *the  church,*  the  laudable* 
in  a  Stoical  argument  in  Cicero's  De  Finibus,  *  I  *  in  Descartes' 
argument  for  the  being  of  God,  *  necessity,'  *  same,'  *  force,' 

*  infinite,'  *  right  ;*  to  which  he  adds  examples  of  the  fallacy 
of  Composition  and  Division,  as  stric.tly  belonging  to  the  same 
class. 

The  second   division    is  Petitio  Principii,  otherwise  called 

*  arguing  in  a  circle,'  of  which  there  are  abundant  examples. 
A  certain  species  of  terms  received  from  Beniham  the  desig- 
nation *  question-begging  appellatives,'  because  they  begged  a 
question  under  the  guise  of  stating  it ;  such  is  the  word  '  Inno- 
vation.* Plato,  in  the  Sophistes,  has  an  argument  to  prove 
that  things  may  exist  that  are  incorporeal,  because  justice 
and  wisdom  are  incorporeal,  and  they  must  be  something : 
thereby  begging  the  question  that  justice  and  wisdom  are 
things  existing  apart  or  in  themselves.  One  of  the  most  re- 
markable examples  of  fallacy  is  furnished  by  the  political 
theory  of  Hobbes  and  Rousseau,  known  as  the  theory  of  the 

*  social  compact.*  We  are  supposed  bound  by  the  promise 
entered  into  by  our  ancestors  before  society  was  called  into 
existence  ;  but  there  is  no  such  thing  as  an  obligatory  promise 
until  society  has  first  been  formed. 

The  third  class  of  Fallacies  of  Confusion  is  the  Ignoratio 
JElenchi.  It  is  exemplified  in  most  of  the  replies  to  the  popu- 
lation doctrines  of  Malthus.  A  still  more  signal  instance  is 
the  stock  argument  against  Berkeley's  doctrine  of  the  non- 
existence of  matter  ;  Johnson's  kicking  the  stone  was  not  the 
point  denied  in  the  ideal  theory. 


CHAPTER  XL 


y 

li 


THE  POSITION  OF  FALLACIES. 

The  setting  apart  of  a  distiucfc  chapter  to  the  consideration 
of  the  errors  against  the  laws  of  reasoning  and  evidence  seems 
at  first  sight  an  incongruous  proceeding.  We  cannot  separate 
a  law  from  its  violations  ;  the  one  implicates  the  other.  When 
good  reasoning  is  exhibited,  there  must  be  exhibited  at  the 
same  time  the  coresponding  bad  reasoning.  If  the  rule  be 
given  that  the  middle  term  of  a  syllogism  must  be  distributed 
once,  whoever  understands  the  rule  must  conceive,  at  the 
same  time,  cases  of  its  fulfilment  and  cases  of  its  non-fulfil- 
ment. If  the  method  of  Difference  requires  that  the  instances 
compared  shall  coincide  in  every  particular  save  one,  we  are 
instructed  by  it  that  the  method  fails  if  any  two  instances  do 
not  coincide  to  this  extent.  If  a  good  classification  involves 
identity  on  one  or  more  points  of  importance,  there  is  implied 
in  the  same  statement  that  a  grouping  under  one  name,  with- 
out any  important  community,  is  a  bad  classification,  a 
*  fallacy  *  of  classification. 

Any  one  would  recognize  the  absurdity  of  a  grammar  that 
would  reserve  for  a  chapter  at  the  end  all  the  examples  of 
grammatical  errors.  Yet  such  is  apparently  the  plan  pursued 
in  Logic.  The  grammarian,  indeed,  frequently  provides  a 
separate  collection  of  errors  by  way  of  practice  to  the  pupil, 
but  these  are  additional  to  what  necessarily  and  properly 
occur  under  the  rules  that  they  severally  violate ;  this,  how- 
ever, is  not  avowed  by  the  logician  as  the  nature  of  his 
chapter  on  Fallacies. 

Without  entirely  exonerating  works  on  Logic  from  the 
inconsistency  of  distributing  between  two  departments  of  the 
subject  the  fulfilment  and  the  violation  of  the  same  rules,  we 
can  assign  certain  circumstances  that  account  for  the  prevail- 
ing usage.  The  main  circumstance  is  the  narrowness  of  the 
field  of  logical  precepts,  from  Aristotle  down  to  the  present 
generation.  The  part  of  reasoning  reduced  to  rules  was 
almost  exclusively  restricted  to  the  syllogistic  or  deductive 
departments ;  hence,  in  the  exemplification  of  those  rules,  no 
errors  could  come  to  light  except  such  as  violated  the  forma 


! 


604: 


THE  POSITION   OF  FALLACIES. 


h'i 


of  syllogism.  But  the  Greeks  had  surveyed  human  knowledge 
wide  enough  to  bo  aware  tliat  many  errors  passed  current 
that  could  not  be  reduced  to  errors  of  syllogism.  The  logician, 
therefore,  was  driven  to  one  of  two  alternatives — to  make  no 
allusion  to  some  of  the  most  notorious  failings  and  mistakes  of 
the  human  understanding,  or  to  provide  a  chapter  for  enumer- 
ating such  mistakes  entirely  apart  from  the  body  of  logical 
theory.  It  was  characteristic  of  Aristotle  to  choose  the  second 
alternative — to  be  inconsistent  rather  than  to  be  incomplete. 
His  treatise  on  Fallacies  comprises  errors  against  the  Syllo- 
gism, which  he  could  not  omit  noticing  under  the  Syllogism 
(Undistributed  Middle,  Illicit  Process)  ;  but  these  are  a  small 
part  of  the  mass  of  Fallacies ;  and  the  vest  he  had  not 
any  theory  for.  He  had  no  Inductive  Logic  (or  only  mere 
traces  which  his  followers  wiped  away),  and  therefore  he  had 
no  place  for  the  exhibition  of  the  rules  sitmcd  against  by  post 
hoCj  ergo  propter  hoc.  For  want  of  a  thoro'.igh-going  discussion 
of  the  department  of  Classification  and  Definition,  he  could 
not  exhibit  the  errors  connected  with  general  language  under 
precepts  for  the  classifying  of  thiii^^s  and  the  deiiuing  of 
terms. 

It  has  been  seen,  however,  that  even  the  thorough-going 
Logic  of  Mr.  Mill  does  not  dispense  with  a  '  Book'  on  Fallacies. 
This  is  explained  in  part,  but  only  in  part,  by  the  author's 
adhering  to  the  usage  of  all  former  logicians,  while  using  his 
own  extended  system  to  re-arran^^e  the  recognized  examples, 
and  to  introduce  new  ones.  Yet  all  the  fallacies  in  the 
second,  third,  and  fourth  classes  (Observation,  Generalization, 
Ratiocination)  might  with  the  utmost  propriety  be  absorbed 
into  the  body  of  the  work.  The  account  of  the  inductive  and 
deductive  processes  unavoidably  quotes  derelictions  from  the 
sound  performance  of  these  processes,  which  derelictions  are 
identical  with  the  fallacies  treated  of  under  the  heads  just 

named. 

The  case  is  different  with  Mr.  Mill's  first  and  last  classes 
(Simple  Inspection  and  Confusion),  The  chapters  on  these 
heads  contain  matter  that  would  not  reidily  find  a  place  in 
the  systematic  exposition  of  the  logical  methods.  T«)  take  the 
first  class.  Fallacies  of  Simple  Inspection,  or  a  priori.  Under 
these,  the  author  dilates  on  certain  fallacious  tendencies  of 
the  mind,  the  generating  causes  of  errors.  Now,  the  logician 
might  say  that  his  business  is  to  show  how  errors  are  to  be 
checked  and  corrected,  not  how  they  arise  ifi  the  imperfections 
of  the  human  constitution.     If  he  is  to  handle  this  subjectj  he 


NATURAL  COKRUPTION   OF  THE  INTELLECT. 


605 


could  not  with  propriety  take  it  up  in  the  detail  of  the 
Deductive  and  Inductive  Methods;  he  would  need  to  be 
allowed  a  corner  apart.  The  demand  is  irresistible.  It  would 
be  most  inexpedient  to  agitate,  under  the  Syllogism,  or  under 
the  Experimental  Methods,  enquiries  as  to  the  fallacious  ten- 
dencies of  the  natural  mind.  Granting  that  all  the  deductive 
and  inductive  fallacies,  and  the  mistakes  of  classification  and 
definition,  were  taken  up  into  the  main  body  of  the  work,  the 
fallacies  a  priori,  if  included  at  all,  must  receive  a  separate 
handling.  Some  doubts  might  be  raised  as  to  the  logician's 
title  or  obligation  to  enter  upon  the  subject,  but  there  could 
be  none  as  to  his  allocating  a  distinct  chapter  to  the  considera- 
tion of  it. 

Socrates  was  the  first  person  to  urge  strongly  the  natural 
corruption  of  the  human  intellect,  and  the  need  of  a  very 
severe  remedial  discipline,  which,  in  the  shape  of  personal 
cross-examination,  he  was  wont  to  apply  to  his  fellow  Athen- 
ians. The  theme  was  not  again  taken  up  in  a  vigorous 
manner,  until  Bacon  composed  the  first  book  of  the  Novum 
Organum.  The  elucidation  of  the  inevitable  miscarriages  of 
the  untutored  understanding,  inteUectiis  sibi  permissus,  and  the 
classification  of  idola — false  lures,  in  that  renowned  work, 
instead  of  being  laid  to  heart  and  followed  up  by  fresh  ex- 
amples, became  a  matter  of  mere  parrot  repetition.  The  next 
person  to  treat  the  subject  independently,  and  to  go  systemati- 
cally over  the  ground,  was  Mr.  Mill,  in  his  chapter  entitled 
*  Fallacies  a  priori.*  So  important  is  the  subject,  and  yet  so 
far  is  it  distinct  from  the  proper  field  of  Logic,  that  it  might 
be  embodied  in  separate  treatises.  It  is  a  kind  of  homily  or 
preaching,  a  rousing  address  on  human  frailty  ;  and  although 
the  logician  is  the  person  most  likely  to  be  impressed  with  the 
evil  consequences,  he  is  not  the  only  person  qualified  to  illus- 
trate them  ;  while  the  points  to  be  adduced  in  the  exposition 
are  not  precisely  such  as  fjall  under  either  the  deductive  or  the 
inductive  logic. 

Mill's  concluding  head  *  Fallacies  of  Confusion,'  still  remains 
extra-logical.  The  extension  of  the  field  of  logic  does  not  enable 
this  class  to  be  absorbed.  They  cannot  be  adduced  as  violating 
inductive,  any  more  than  deductive  precepts.  In  reality,  they 
are  owing  to  the  defective  acquaintance  with  the  subject  matter 
of  the  reasonings,  and  to  a  low  order  of  intellectual  cultivation 
generally,  rather  than  to  misapprehending  logical  method.  A 
considerable  stretch  of  the  logician's*  province  is  implied  in 
the  taking  up  of  this  class  of  errors.     The  ground  that  they 


m 

I 


«i  1 1 


606 


FALLACIOUS  TENDENCIES   OF  THE  MIND. 


if 


cover  is  boundless  and  indefinable ;  no  man  can  foreshadow 
the  intricacies,  the  incoherences,  the  perplexities,  the  entangle- 
ments, possible  to  the  human  understanding.  The  only 
circumstance  that  justifies  the  attempt  to  handle  them  syste- 
matically is  the  great  frequency  of  a  few  leading  forms ;  in 
consequence  of  which  they  can  be,  to  some  extent,  treated 
comprehensively.  Mr.  Mill's  three  classes  of  examples — 
Ambiguous  Terras,  Petitio  Principii,  Ignoratio  Elenchi — have 
this  character  of  extensive  recurrence.  Moreover,  in  the 
elucidation  of  such  classes,  there  come  to  view  many  prominent 
and  practical  errors,  thus  opportunely  laid  bare. 

From  these  considerations,  it  follows  that  the  most  defensible 
course  to  be  pursued  in  regard  to  Fallacies  is  to  absorb  into 
the  main  work  all  those  that  are  the  direct  violation  of  logical 
precepts  ;  and  to  handle,  in  the  chapters  apart,  the  Fallacious 
tendencies  of  the  human  mind,  and  the  Fallacies  of  Confusion. 
This  is  not  to  debar  the  assembling  of  additional  examples  in 
a  supplement  or  appendix  ;  it  being  understood  that  these  are 
merely  in  continuation  of  the  examples  already  furnished  ia 
the  regular  coarse. 


CHAPTER  m. 
FALLACIOUS  TENDENCIES  OF  THE  MIND. 


The  Fallacious  tendencies  of  the  mind  may  be  traced  through 
an  enumeration  of  the  sources  of  Belief 

The  state  of  Belief  is  a  form  or  manifestation  of  our  activity. 
The  import  and  measure  of  Belief  is  the  readiness  to  act  in  the 
direction  indicated  by  the  thing  believed.  A  man's  belief  in 
the  wholesomeness  of  a  regimen  is  shown  by  his  energy  and 
persistence  in  adhering  to  it. 

There  are  three  distinct  sources  of  belief.  L  The  inherent 
Activity  of  the  System — the  disposition  to  act  through  mere 
spontaneous  vigour.  II.  The  influence  of  the  Feelings, 
Emotions,  or  Passions.  III.  The  Intellectual  Associations,  or 
acquired  trains  of  thought.  Excepting  under  the  last  head, 
there  is  nothing  to  guarantee  sowwdwess  of  belief,  or  the  accord- 
ance of  the  thing  believed  with  the  reality. 


r  \ 


OUR  EARLY  BEUEFS   OVER-VAULTING. 


607 


L  Inherent  Activity  of  the  Si/stem. 

From  the  spontaneous  and  inherent  vigour  of  the  system,  we 
are  induced  to  act  somehow,  to  change  out  of  the  passive  into 
the  active  condition,  and  to  continue  that  activity  while  the 
energies  are  unexhausted,  and  while  there  is  freedom  from  ob» 
struction.  There  is  no  enquiry  beforehand  as  to  the  proper 
course  or  direction  to  act  in ;  opposition  is  not  presumed  until 
actually  encountered.  A  way  now  open  is  supposed  to  be  al- 
ways open ;  the  mind  does  not  anticipate  any  future  termination 
or  obstacle.  Blind  confidence  is  the  primitive  attitude  of  our 
mind.  It  is  only  through  the  teaching  of  experience  that  we 
suppose  any  limit  to  our  career  of  action. 

This  state  of  mind  shows  itself  in  our  early  beliefs,  which 
may  be  described  generally  as  over-vaulting ;  as  presuming 
that  what  holds  now  and  here,  will  hold  then  and  there  and 
everywhere.     The  following  are  instances  : — 

We  are  disposed  to  assume  that,  as  we  feel  at  the  present 
moment,  we  shall  feel  always.  After  a  certain  number  of 
checks,  the  tendency  is  somewhat  restrained,  bat  it  continues 
very  strong  all  through  early  life,  and  is  seldom  entirely 
conquered  at  any  age. 

We  begin  life  by  reckoning  with  the  utmost  confidence  that 
other  persons  feel  exactly  as  we  do.  After  lengthened  experi- 
ence, this  primitive  tendency  is  greatly  subdued,  although 
perhaps  in  few  minds  is  it  fully  sobered  down  to  the  measure 
of  the  actual  facts.  The  consequences  are  shown  in  our  not 
allowing  for  differences  of  character,  in  our  inability  even  to 
conceive  of  types  departing  widely  from  ourselves.  Without 
being  the  sole  origin  of  intolerance,  this  tendency  greatly 
ministers  to  that  prevailing  vice  of  mankind.  We  can  with 
difficulty  avoid  judging  all  men,  in  all  circumstances,  by  the 
standard  suited  to  ourselves  and  our  own  circumstances. 

From  one  or  a  few  instances  we  are  ready  to  infer  a  law 
applicable  without  limit.  The  mere  infant  parodies  the  induc- 
tive process  ;  the  most  ignorant  of  human  beings  are  the 
most  unrestrained  generalizers.  From  an  acquaintance  with 
one  or  two  Frenchmen,  Italians,  or  Russians,  we  conclude  the 
characters  of  the  entire  nation.  We  feel  assured  that  a 
remedy  found  to  answer  in  a  particular  case  will  answer  uni- 
versally. Happening  to  visit  a  place  during  fine  weather,  we 
are  led  to  suppose  that  the  weather  there  is  always  fine.  The 
word  *  always  '  is  a  familiar  expletive  to  vent  our  generalizing 
temper. 


*    \l 


:  ^  f 


^  f! 


H 


u-^*   '-.ibiKirir. 


■■■"'   "'■"^"^■-  ■ 


608 


FALLA.CIOUS  TENDENCIKS   OF  THE   MIND. 


We  presume  that  tlie  state  of  things  familiar  to  us,  prevails 
everywhere.  Not  only  are  we  indisposed  of  ourselves  to 
anticipate  and  conceive  different  arrangements,  natural  and 
social,  but  we  hold  out  against  the  very  existence  of  such. 
The  king  of  Siam's  energetic  repudiation  of  ice  was  a  genuine 
display  of  the  natural  man. 

Without  making  formal  generalizations  upon  a  single  in- 
stance, we  are  disposed  to  outrun  our  facts,  to  extend  the 
present  into  the  distant  and  the  future.  It  is  always  more 
congenial  to  make  leaps  in  the  dark,  than  to  abide  strictly  by 
what  we  actually  know.  We  have  no  sympathy  with  any  one 
proposing  to  restrain  gravitation  to  the  solar  system,  where  it 
can  be  proved  to  operate ;  our  natural  desire  is  to  extend  it 
everywhere,  with  or  without  positive  evidence. 

To  identify,  to  assimilate,  to  generalize,  constitute  one  of 
the  two  great  functions  of  science.  Yet  there  is  often  a 
necessity  for  restraining  the  too  great  ardour  for  these  pro- 
cesses. We  identify  and  assimilate,  without  real  likeness, 
thus  giving  birth  to  bad  analogies,  and  irrelevant  comparisons ; 
we  over-assimilate  and  over-generalize.  We  rush  blindly  on 
the  search  after  Unity,  Simplicity,  Fraternity. 

It  is  a  result  of  the  primeval  tendency  to  follow  out  a  lead 
to  unbounded  lengths,  that  we  so  strongly  assert  the  Law  of 
Causation,  irrespective  of  the  facts  that  have  gradually  estab- 
lished its  certainty.  Wo  have  a  subjective  assurance  that  bears 
no  proportion  to  the  objective  proofs.  We  shall  never  be  in  a 
position  to  assert  the  law,  by  the  force  of  legitimate  evidence, 
with  the  confidence  that  we  ^eei  respecting  it. 

That  human  nature  is  the  same  in  all  ages  is  affirmed,  not 
from  a  careful  examination  of  the  records  of  the  human  race, 
but  because  the  aflarmer  has  not  laid  himself  in  the  way  of 
checks  to  the  natural  tendency  to  reason  from  the  near  to  the 
distant.  The  doctrine  is  more  behoven  to  ignorance  than  to 
knowledge. 

The  most  of  Mr.  Mill's  Fallacies  of  Simple  Inspection  are 
referable  to  the  tendency  now  discussed.  That  *  we  should 
make  our  thoughts  the  measure  of  things,'  which  is  done  in 
so  many  celebrated  speculations,  is  the  result  of  the  inherent 
pushing  activity  of  the  system,  the  determination  to  proceed 
in  a  course  once  entered  on,  until  a  check  is  met  with,  and 
even  in  spite  of  a  good  many  checks.  *  That  the  conceivable 
is  necessarily  true,*  and  *  the  inconceivable  necessarily  false  ' 
are  merely  various  expressions  of  the  same  fact. 

The  supposition  that  *  the  effect  resembles  the  cause,'  that 


PERVERSION   OF  THE   FEELINGS. 


609 


*  like  produces  like '  also  grows  out  of  the  mind's  incontinent 
tendency  to  assimilate,  or  identify,  the  repugnance  to  depart 
from  a  familiar  type  until  compelled  by  a  power  from  without. 
The  reasonings  of  ancient  philosophy  frequently  exhibit  this 
fallacy,  especially  in  the  subject  where  it  has  most  frequently 
operated,  the  relations  of  mind  and  body.  Thus  Aristotle 
reasons  that  Intellect,  as  well  as  Sense — must  be  corporeal, 
since  it  has  to  deal  with  corporeal  things ;  and  Like  can  be 
comprehended  only  by  Like. 

II.  Influence  of  the  Feelings. 

The  perverting  influence  of  the  Feelings,  in  matters  of  truth, 
has  been  more  generally  noticed,  than  the  perversions  due  to 
inherent  activity.  That  men  have  in  all  ages  been  biassed  by 
their  interests,  their  fears,  their  antipathies,  their  likings,  their 
poetic  ideals,  their  religious  sentiments, — is  one  of  the  most 
widely-received  and  least  contested  doctrines  of  human  nature. 
Many  of  Biicon's  Idola  are  prejudices  of  the  feelings ;  the 
idola  theatn  relate  to  the  poetic,  artistic,  or  ideal  cravings  of 
the  mind  ;  the  idola  tribus  (which  would  properly  include  the 
other)  comprise  all  the  fallacious  tendencies  common  to  men 
generally,  in  opposition  to  individual  peculiarities  (^'rfoZa^^ecws); 
they  therefore  necessarily  include  the  feelings.  Mr,  Mill  gives 
fewer  illustrations  of  the  influence  of  feeling,  than  of  the  influ- 
ence of  activity  as  above  explained. 

The  operation  of  the  feelings  is  partly  through  the  will,  and 
partly  on  the  intellect.  What  gives  us  pleasure  urges  the  will 
forits  pursuit;  and  our  activity,  in  whatever  way  prompted, 
carries  belief  with  it.  We  believe  that  the  things  that  we  like 
are  free  from  harm,  if  not  beneficial — our  favourite  dishes, 
stimulants,  amusements.  The  effect  of  liking  is  to  induce  action 
in  a  given  course,  which  is  a  power  for  belief,  able  to  surmount 
a  certain  degree  of  hostile  evidence. 

The  obverse  is  also  implied.  What  offends,  annoys,  or  dis- 
pleases us  is  avoided  ;  the  will  is  against  it ;  and  we  have  a 
corresponding  difficulty  in  believing  it  to  be  a  proper  object  of 
pursuit,  or  in  any  way  commendable. 

The  other  mode  of  working  on  the  feelings  is  through  the 
Intellect.  A  strong  feeling,  whether  pleasurable  or  painful, 
occupies  and  detains  the  thoughts,  and  excludes  for  the  time 
all  other  subjects.  If  it  be  pleasurable,  the  detention  is  at  the 
maximum ;  but  even  pain  has  power  to  engross  us.  Hence, 
nnder  great  excitement,  thoughts  alien  to  the  state  of  feeling 
of  the  time,  are  not  allowed  to  rise  to   the  view  ;  we  judge 


4 


I 


610 


FALLACIOUS  TENDENCIES   OF  THE  MliTD 


if- 


t 


^ 


I 


r 
II 


upon  one-sided  facts  and  views.  Anorgie  of  pleasure  renders 
us  unable  to  entertain  disagreeable  facts  ;  a  fright  allows  us  to 
see  nothing  but  danger. 

The  present  purpose  will  be  served  by  the  following  enume- 
ration of  perverting  states  of  feeling:  (1)  Self-interest  gene- 
rally; (2)  Sympathy;  (3)  Special  Emofcions.  Such  is  the 
order  found  convenient  for  illustrating  the  Oratory  of  the 
Feelings  (English  Composition  and  Rhetoric,  p.  2l)l). 

Self' Interest. — This  comprises  our  pains  and  pleasures  gene- 
rally (to  the  exclusion  of  our  Sympathies),  whether  from  sense, 
from  emotion,  or  from  the  associated  and  comprehensive  ends, 
as  Wealth  and  Power.  That  men  believe  according  to  their 
self-interest  hardly  needs  illustration.  Not  only  does  each 
man  endeavour  to  deceive  others,  he  generally  succeeds  in 
deceiving  himself  when  his  interests  are  at  stake.  We  have 
all  great  difficulty  in  seeing  the  faults  of  an  institution  that 
we  profit  by ;  the  arguments  of  a  highly  paid  priest  for  his 
own  form  of  religion,  or  of  a  lawyer  for  lucrative  forms  of 
procedure,  are  regarded  with  suspicion.  Th«»  crrossest  forms 
of  error,  the  most  noxious  practices  will  be  vindicated  by  per- 
sons whose  worldy  position  depends  upon  t  hem. 

Among  the  particular  pleasures  and  pains  making  up  the 
great  aggregate  of  self-interest,  we  may  signalize  some  as 
especially  unfavourable  to  truth.  Indolence,  or  the  aversion  to 
labour,  the  source  of  so  many  moral  obliquities,  is  the  parent  of 
intellectual  error.  The  ascertainment  of  truth  demands  a  kind 
of  labour  that  the  average  human  beiiig  dreads  and  abhors  \ 
hence  the  acquiesence  in  such  views  as  come  easiest  to  hand. 
That  unqualified  extension  of  the  present  to  the  distant,  the 
past,  and  the  future,  which  we  have  seen  to  grow  out  of  the 
inherent  activity  of  the  system,  is  still  farther  recommended 
by  the  saving  of  toil.  Excessive  identification,  generalization, 
and  simplication  are  other  expressions  for  the  same  tendency  ; 
while  complication,  and  incoherent  details,  are  preferred  to  a 
simplifying  generalization  that  would  cost  great  labour. 

One  form  of  self-denial  requisite  for  getting  at  truth  is  to 
withstand  the  influence  of  the  present,  and  the  palpable.  A 
present  impression  has  a  commanding  potency.  The  inherent 
tendency  to  assume  that  what  is  will  be,  is  aggravated  by  any 
unusual  impressiveness  of  the  present  fact.  The  first  victory 
of  a  campaign  elates  the  conquering  array  with  confidence  in 
the  future. 

The  Sympathies, — The  sympathetic  tendency  of  our  nature 
while  antagonizing  self-interes^and  the  errors  thereby  induced, 


1  if 


EXCESSIVE   SYMPATHIES. 


611 


ig  a  source  of  errors  peculiar  to  itself.  In  making  us  chime 
in  with  the  feelings  and  views  of  those  about  us,  it  perpetuates 
opinions  that  have  once  got  a  footing ;  so  that  the  world  is 
sometimes  dependent  for  a  move  in  advance,  on  the  revolt  of 
an  excessive  egotist. 

The  disposition  to  see  as  much  good  as  possible  in  our 
fellow-beings  has  nursed  various  fallacious  judgments.  Thus 
it  is  said  of  errors,  that  they  are  almost  always  partial  or  half 
truths ;  which  may  be  the  case  with  certain  errors,  but  cer- 
tainly not  with  all,  probably  not  with  the  majority.  An  error 
has  usually  some  show  of  fact  to  rest  upon ;  but  we  cannot 
say  that  the  ante-copemican  doctrines  of  Astronomy  were 
half  truths ;  that  the  sun  and  stars  move  round  the  earth, 
was  a  total  mistake.  That  despotic  government  favours  the 
happiness  and  the  improvement  of  mankind  does  not  deserve 
to  be  called  a  half  truth.  It  is  the  conversion  of  a  few  ex- 
ceptional instances  into  a  general  canon. 

Another  fallacy  of  excessive  sympathies  is  that  what  has 
been  in  the  past  has  always  been  more  or  less  suitable  to  the 
time  and  circumstances.  Thus,  slavery,  it  is  said,  however 
disapproved  of  now,  was  once  necessary  and  suitable.  Perse- 
cution for  opinions  was  the  fitting  accompaniment  of  an  early 
state  of  civilization.  Feudality  and  hereditary  monarchy  may 
now  cease  to  be  essential,  but  were  so  in  former  times.  Such 
encomiums  on  the  past  need  to  be  received  with  great  mis- 
givings. To  justify  them  fully,  we  must  maintain,  first,  that 
the  good  of  mankind  has  been  the  chief  motive  of  the  founders 
and  supporters  of  the  actual  institutions  of  every  age  ;  and, 
secondly,  that  men's  ingenuity  of  contrivance  has  been  always 
on  a  level  with  their  necessities.  We  cannot  say  that  it  was 
essential  to  human  society  that  the  Greeks  of  the  time  of 
Pericles  or  of  Xenophon  should  be  sold  as  slaves,  when  they 
happened  to  be  taken  in  war ;  such  men  could  hava  been 
induced  to  work  by  the  motive  of  pay. 

The  Special  Emotions. — The  consideration  in  detail  of  a  few 
of  the  leading  emotions  will  bring  to  view  the  more  specific 
sources  of  fallacy  arising  from  the  feelings.  Their  operation 
is  still  mainly  due  to  their  being  pleasures  or  pains  ;  although 
there  is  in  emotion  also  the  influence  of  mere  excitement, 
irrespective  of  pleasure,  in  occupying  the  mind  and  directing 

the  trains  of  thought. 

We  may  remark  first  on  the  Emotional  Temperament 
generally,  or,  as  it  is  also  called,  the  Sanguine  Temperament^ 
the  effect  of  which  is  to  dwell  upon  the  good  side  of  every- 


i\ 


ill 

I: 


f 


>''iLiL^^ 


612 


FALLACIOUS  TENDENCIES   OF  THE  MIND. 


thing.  Men  endowed  with  this  peculiarity  over-estimate  all 
that  is  good  in  their  prospects,  and  in  the  prospects  of  the 
world  generally.  They  are  optimists  as  regards  both  the 
present  and  the  past.  They  fall  into  the  last  named  error — 
that  whatever  was,  was  rijii^ht.  Mere  sympathy,  without 
the  sanguine  temperament,  might  not  so  readily  fall  into  that 
mistake.  The  opposite  temperament  works  in  the  opposite 
direction;  it  is  the  source  of  disheartening  views  of  things, 
and  forebodinjrs  of  disaster.  The  fluctuations  of  the  mental 
tone  in  each  individual  have  temporarily  a  like  influence  on 
the  beliefs. 

The  emotional  ferapemment  indulges  in  delightful  ideal  con- 
ceptions, from  which  are  excluded  the  stern  features  of  the 
reality.  HeDce  the  fallacious  picture  of  a  beneficent  despot— 
the  blessings  of  absolute  authority  in  good  hands — which 
occupies  the  minds  of  sentimentalists,  and  plays  into  the 
hands  of  real  oppressors. 

The  emotions  of  Novelty  and  Wonder  have  been  often 
descanted  on  as  sources  of  corruption.  They  disincline  men 
to  any  facts,  views,  or  theories,  that  have  not  in  them  a  dash 
of  the  marvellous.  It  is  difficult  to  get  good  observations  on 
the  mental  faculties  of  the  lower  animals,  from  the  wish  to 
invest  everything  about  them  with  mystery  and  wonder.  The 
same  cause  preverts  the  records  of  travellers  in  foreign 
countries.  Even  physical  phenomena  that  have  any  thin  o^ 
marvellous  about  them  are  difficult  to  observe  with  precision  ; 
and  the  statements  of  unscientific  persons  are  generally 
untrustworthy.  The  fondness  of  the  human  mind  for  exag- 
geration and  hyperbole  renders  a  great  part  of  human  speech 
untrue  to  fact. 

The  Emotion  of  Fear,  superadded  to  mere  aversion  or  dis- 
liking, unhinges  and  debilitates  the  mind,  disposing  men  to 
dark  and  dismal  views  of  things,  and  fitting  them  to  be  the 
slaves  of  whoever  has  the  power  to  terrify.  Under  the  shape 
of  Superstition,  the  susceptibility  to  fear  has  held  mankind  in 
captivity  to  innumerable  delusions,  especially  in  all  that  per- 
tains to  the  supernatural.  As  the  enemy  of  science,  supersti- 
tion is  dwelt  upon  by  Bacon  with  peculiar  emphasis. 

The  feelings  of  Love,  tenderness,  affection,  amiability,  which 
are  distinct  from  sympathy  propei*,  although  always  in  some 
degree  fused  with  it,  are  corrupters  of  the  intellect,  by  creating 
a  disposition  favourable  to  whoever  is  loved;  hence  the  parti- 
alities of  affection  and  friendship,  the  incapability  of  seeing 
anything   wrong  in   one's   country,  sect,  or  party.      In  the 


SELF.— PERSONAL  DIGNITY. — .ESTHETIC  FEELINGS.    613 

*  higher  compounds,  termed  Admiration  and  Reverence,  there  is 
a  still  greater  power  to  sway  the  judgment  of  the  individual. 
Deference  to  great  authorities,  and  to  the  prevailing  views  of 
society,  and  the  readiness  to  admit  compromises,  maybe  traced 
to  the  loving  and  sociable  dispositions.  The  same  dispositions 
are  easily  led  into  the  worship  of  antiquity,  which  is  the  senti- 
mental stronghold  of  blind  conservatism. 

The  emotions  of  Self -- the  special  circle  of  Vanity,  Con- 
ceit, Pride,  Feeling  of  Dignity — in  proportion  to  their  power, 
disturb  the  judgment  of  what  is  true.  The  respect  for  our 
own  opinions,  because  they  are  ours,  the  plans,  devices, 
theories  of  our  own  concocting,  the  value  set  upon  everything 
that  touches  ourselves, — are  snares  in  the  way  to  truth.  Our 
egotism  even  comprehends  family,  friends,  party,  and  nation ; 
to  all  of  whom,  as  being  related  to  ourselves,  we  attribute  a 
superior  wisdom.  National  prejudice  is  one  of  the  great  ob- 
structives of  political  progress. 

The  sense  of  Personal  Dignity  operates  to  pervert  our  views 
in  a  remarkable  degree.  Many  prevalent  doctrines  are  recom- 
mended by  their  supposed  contribution  to  the  dignity  of  human 
nature.  A  leading  argument  in  favour  of  the  Immateriality  of 
the  Mind  or  Soul  is  expressly  grounded  in  the  greater  dignity 
of  the  immaterial  essence.  The  doctrine  of  Free-will  is  sup- 
posed to  elevate  human  nature  by  the  ennobling  function  of 
autonomy,  self-government,  or  jud'cial  arbitration.  The 
modern  hypothesis  of  Development  is  objected  to  as  offending 
our  ancestral  pride.  The  exceeding  sinfulness  attributed  to 
human  nature"  by  the  Calvinist  would  bo  highly  unpalatable, 
but  for  the  tribute  indirectly  paid  to  our  self-importance. 

Our  emotions  oi  Anger,  like  Fear,  are  manifestations  superin- 
duced upon  mere  pain.  Revenge,  antipathy,  hatred,  party 
spirit,  are  forms  of  the  irascible  feeling,  and  are  antagonistic, 
in  a  conspicuous  degree,  to  the  ascertaining  of  truth.  Calumny, 
the  expression  of  anger,  connotes  falsehood. 

We  may  conveniently  group  under  the  Esthetic  Feelings,  a 
variety  of  emotional  states,  of  which  the  central  and  special 
mode  is  Artistic  Harmony,  but  which  involve  also  many  of  the 
other  emotions — as  Novelty,  Wonder,  Love.  They  are  the 
emotions  aimed  at  in  poetry  and  in  works  of  Art,  and  contain 
a  large  mass  of  powerful  feeling.  Many  false  systems  of 
philosophy,  and  numerous  petty  errors  and  perversions,  are 
to  be  ascribed  to  this  department  of  our  emotional  suscepti- 
bilities. Thus  in  the  ancient  world,  the  minds  of  philosophers 
were  dominated  by  the  idea  of  symmetry,  proportion,  order, 


* 


614: 


FALLACIOUS  TENDENICIES   OF  THE  MIND 


,.h; 


', 


and  harmony.  Pythagoras  was  entranced  by  the  mystery  of ' 
number ;  Plato  followed  him ;  ami  Aristotle  was  not  exempt 
from  the  spell.  But  the  predominant  source  of  fallacy  quotable 
under  the  present  head  was  the  supposed  Perfection,  Dignity, 
and  Becomingness  of  certain  arrangements  iu  nature,  which 
included  numerical  considerations  among  others.  The  superior 
worthiness  of  fire  was  declared  in  the  Pythagorean  philosophy ; 
and  even  in  the  later  Copernican  controversy  an  argument  was 
founded  on  the  circumstance  that  the  new  system  placed  fire, 
the  noblest  element,  in  the  centre  of  the  universe.  So  only 
Mind,  according  to  Plato,  in  Piiilebus,  is  sufiiciently  dignified 
to  create  the  world.  In  the  recital  by  Socrates,  in  Phaedon, 
of  the  phases  of  his  intellectual  history,  on  the  subject  of  Cause, 
the  doctrines  of  Thales  and  Auaxagoras  are  set  aside  because 
thev  do  not  recognise  the  becoming  as  a  power  in  the  world. 
The  adherence  to  the  circular  form  of  the  planetary  orbits, 
because  of  its  perfection,  was  inveterate  in  the  cool  mind  of 
Aristotle.  The  planets  could  be  only  six,  because  that  was  a 
perfect  number. 

The  dictation  of  a  plan  to  Nature  on  a  supposed  propriety 
has  run  through  all  times.  Even  in  hard  business  afiairs  of 
trade,  Aristotle  held  it  was  against  nature  that  money  should 
breed  money,  that  is,  pay  interest  on  loans.  Lamarck  argues 
that  a  Polype  cannot  have  Sensibility,  because  it  would  be 
contrary  to  the  plan  that  Nature  is  obliged  to  follow  in  all  her 
works  (Lewes's  Aristotle,  p.  97). 

The  fiction  of  Unity,  which  carried  away  the  early  Greek 
philosophers,  partly  proceeds  from  over-fissimilation,  and  partly 
ministers  to  artistic  emotion.  The  absolute  unity  of  mind 
is  still  worshipped  by  Grerraan  philosophers.  Herbart  and 
others,  rather  than  admit  the  radically  distinct  nature  of  Feel- 
ing, Will,  and  Intellect,  insist  upon  regarding  Intellect  or 
Cognition  as  the  basis  of  the  two  others. 

The  artistic  sublime  dictates  such  exaggerations  as  *  Let 
justice  be  done,  though  the  world  collapse  ; '  *  Truth  is  great 
and  all-prevailing.  *  Only  a  mind  driven  off  its  calm  centre 
by  the  sublime  of  Force  can  exclaim  *  Might  is  Right.*  The 
fallacy  that  makes  Artistic  Harmony  the  test  of  truth,  almost 
inevitable  in  poetry,  is  deliberately  maintained  in  Wordsworth's 
Essay  on  Epitaphs,  and  in  his  prose  criticisms. 

The  allegation  is  often  made,  on  instances  garbled  to  chime 
in  with  an  amiable  sentiment,  that  great  men  derive  their 
mental  power  chiefly  from  their  mothers. 

The  influence  of  ©sthetic  qualities — beauty,  sublimity,  har- 


.|^ 


INTELLECTUAL  ASSOCIATIONS. 


615 


? 

i   SI 


mony,  propriety— is  constantly  operating  to  twist  the  nnder- 
Btanding.  The  architecture,  music,  and  colouring  employed 
in  religion,  indispose  the  worshipper  to  canvass  the  validity  of 
the  doctrines.  The  art  of  the  orator  involves  the  tickling  of 
the  sense,  and  the  charms  of  style.  Such  subjects  as  History, 
Criticism,  Morality,  the  Human  Mind,  where  literary  polish  is 
more  or  less  attended  to,  are  liable  to  distortion  through  that 
circumstance.  Of  Rhetorical  devices,  only  a  few  are  subser- 
vient to  truth  ;  while  a  great  many  are  hostile. 

The  interests  of  Morality  and  Religion,  have,  in  almost 
every  age  and  country,  been  thought  to  require  a  habitual 
exaggeration  of  the  pleasures  of  virtue  and  the  miseries  of  vice. 
Plato  was  the  first  openly  to  recommend  the  pious  fraud  of 
preaching  doctrines,  in  themselves  false,  as  being  favourable 
to  morals  and  social  order.  And  although  only  one  society  in 
modern  times—the  Jesuits— has  formally  avowed  the  same 
principle,  there  has  been  a  wide-spread  disposition  to  put  it  in 
practice.  Various  apologists  for  Christianity  have  contended 
that,  even  supposing  it  untrue,  it  ought  to  be  propagated  on 
account  of  its  beneficial  consequences. 

III.  Influence  of  Asscciations, 
Belief  is  not  founded  in  the  intellect ;  yet  the  intellectual 
associations  confirm  tendencies  pre-existing,  and  contribute  to 
belief  both  in  the  true  and  in  the  false.  When  two  things  have 
been  often  associated  together  in  the  mind,  the  impetus  thus 
acquired,  in  passing  from  the  one  to  the  other,  counts  as  a 
force  of  belief.  We  are  disposed,  by  our  inborn  activity,  to 
proceed  upon  whatever  we  are  told,  there  being  no  counter- 
acting tendency  present ;  the  frequent  repetition  of  the  same 
declaration  enhances  our  disposition  to  believe  it.  The  force 
of  iteration  is  one  of  the  leading  causes  of  men's  beliefs.  What 
has  often  been  said,  and  seldom  or  never  contradicted,  is  all- 
powerful  with  the  mass  of  mankind. 

Thus,  one  part  of  the  influence  of  education,  and  of  prevail- 
ing opinions,  is  due  to  an  intellectual  link,  whose  growth  could 
be  arrested  by  mere  counter  iteration.  The  same  influence  is 
at  work  confirming  our  modes  of  looking  at  things.  There 
may  be  no  reason,  beyond  the  adhesion  generated  by  length 
of  time,  why  a  man  is  reluctant  to  entertain  a  new  opinion, 
and  yet  this  may  be  enough  to  render  his  conversion  impracti- 
cable. It  was  remarked  that  Harvey's  doctrine  of  the  circu- 
lation was  admitted  by  no  physician  past  forty.  Among  our 
habits,  we  are  to  reckon  beliefs.  The  invet,eracy  of  preconceived 
opinions  is  in  great  part  due  to  their  being  long  cherished, 
27 


It  ■ 


CHAPTER  IV, 

FALLACIES  OF  CONFUSION. 

These  fallacies  cannot  usually  be  produced  as  direct  contra- 
ventions of  logical  method.  Many  of  them  depend  on  imper- 
fect acquaintance  with  the  subjects  under  discussion.  A 
certain  number  may  be  regarded  as  snares  of  language 
(Baxjon's  idola  fori).  A  logical  discipline  is  good  as  against 
manv;  and  their  detailed  exposure  may  have  a  shghtly  torti- 
fvini  influence.  As  already  remarked,  an  exhaustive  treat- 
ment  is  not  possible ;  but  certain  genera  may  be  selected  as 
being  both  prevalent  and  deleterious. 

Fallacies  of  Language. 

AmliguouB  and  ill-defined  tenns.^The  Fallacies  of  Eqnwoca. 
tion  of  the  scholastic  logic  are  fallacies  of  ambiguous  langn- 
age;  for  which  the  remedy  is  an  exact  definition  of  ^l 
leading  terms,  and  an  adherence  to  the  meaning  so  settled. 

It  k  one  criterion  of  an  advanced  science  to  have  its  terms 
defined  In  subjects  not  raised  to  scientific  precision  we  may 
expLt^V^^^^^^  in  the  use  of  language.  The  Mathematical 
and  the  Physical  Sciences  were  the  first  to  make  progress  in 
2t  direction;  only  in  recent  times  has  the  prog^^^^^^^^ 
extended  to  the  Moral  Sciences-Psychology,  Ethics,  Politics, 

Law,  Political  Economy.  „r,lpflQ 

The  exemplification  of  ambiguous  words  has  no  limit,  unless 
we  adopt  some  principle  of  selection.     For  a  work  on  Logic 
The  most  appropriate  examples  are  terms  of  leading  importance 
whose  ambiguity  is  still  a  cause  of  error  and  perversion. 

The  word  *  Nature'  is  full  of  ambiguity.  Butler  pointed 
out  three  meanings.  Sir  G.  C  Lewis,  after  a  lengthened 
examination  of  particular  uses  of  the  word,  found  that  they 
foirunder  two  classes :-(!)  A  positive  idea  as  expressing 
Ssencer^uality,  or  disposition;  (2)  An.,a.Veide^^^^^^^^^^ 
art,  or  human  regulation  and  contrivance.  This  last  meamng 
^curs  in  the  phrase  siate  of  nature,  used  to  designate  maai  8 
existence  before  the  introduction  of  law,  government  and  the 
trte  of  cStion.     As  human  interference  may  sometunes  be 


AMBIGUITY  OF  TERMS. 


617 


i! 


good  and  sometimes  bad,  the  meaning  of  nature  varies  accord- 
ingly. When  men's  *  natural  rights  '  are  spoken  of,  there  is 
great  doubt  as  to  what  is  intended.  *  Every  man  has  a  natural 
right  to  his  liberty  '—is  a  jumble  of  uncertain  sounds  ;  *  natural' 
being  probably  used  in  Lewis's  second  acceptation,  as  the 
antithesis  of  art,  regulation,  and  interference. 

Liberty  *  has  various  meanings.  It  is  not  merely  the  absence 
of  coercion  or  restraint,  as  being  at  large  instead  of  being  impri- 
Boned  ;  it  extends  also  to  the  possession  of  powers,  rights,  and 
status;  thus  in  a  community  where  there  are  slaves,  being  impri- 
soned ;  it  extends  also  to  the  possession  of  powers,  liberty  is  a 
distinction,  and  freemen  compose  a  privileged  order  of  the  state. 
The  ambiguities  of  *  Moral  '  have  been  previously  adverted 
to.  Even  in  the  one  specific  meaning  of  *  right  and  wrong/ 
it  has  a  fluctuating  signification,  and  has  given  occasion  to 
erroneous  views.  The  criterion  of  *  moral '  and  *  immoral,' 
in  the  accurate  meaning,  is  Law  ;  a  moral  act  is  imposed  by  a 
superior  ;  hence  a  supreme  power  cannot  do  an  immoral,  any 
more  than  an  illegal  act.     When  the  Deity  is  said  to  have  a 

*  moral '  nature,  the  word  must  be  supposed  to  mean  simply 

*  goodness,'  or  else  *  equity,'  both  which  qualities  may  attach 
to  a  supreme  legislator ;  the  sovereign  power  may  do  a  mis- 
chievous act,  and  may  be  guilty  of  partiality  or  unfairness  as 
between  one  man  and  another;  which,  however,  is  not  the 
connotation  of  immoral  or  illegal,  according  to  the  proper 
definition  of  the  terms.  The  sovereign  has  no  moral  duties  ; 
his  acts  create  these  for  his  inferiors. 

The  confusion  of  Law  in  the  juridical  sense,  with  Law  as  the 
nniformity  of  nature,  is  exemplified  in  Butler's  chapter  on  the 
Moral  Government  of  God.  Butler  calls  the  *  course  of  Na- 
ture '  a  government,  merely  on  the  ground  that  it  induces 
precautions  te  avoid  pain.  But  these  precautions  have  nothing 
moral  in  them ;  they  may  be  used  for  criminal  ends.  Guy 
Fawkes  most  faithfully  obeyed  the  laws  of  nature,  when  he 
placed  his  barrels  of  gunpowder  so  as  to  ensure  the  blowing 
up  of  Parliament,  while  he  arranged  for  firing  them  in  safety 
to  himself.  It  is  the  object  of  a  Law  proper  to  prevent  men 
from  injuring  one  another;  the  uniformity  of  nature  lends 
itself  equally  to  good  and  to  evil  conduct 

The  word  *  Utility '  has  a  narrow  sense  opposed  to  Art, 
elegance,  and  refinement ;  and  a  wider  sense  (as  in  the  Utility 
theory  of  Morals),  comprehending  (he  whole  circle  of  human 
gratifications  and  well-being. 

*  Self  has  several  meanings,  which  have  to  be  disentangled 
in  ethical  reasonin^rs. 


-1    : 


618 


FALLACIES   OF  CONFUSION. 


I  I 


The  words  *  same,*  *  identity,'  have  often  been  commented 
on.  Similarity  or  sameness  is  a  matter  of  decree,  and  in  this 
consideration  alone  lies  the  ambiguity.  A  human  being  is 
called  the  same  person  all  through  life,  although  in  many 
respects  changed. 

*  Probability  *  is  not  always  nsed  in  its  proper  meaning, 
namely,  the  expression  of  what  is  true,  not  in  every  case,  but  in 
most.     Not  nnfrequently,  the  two  sets  of  cases,  yro  and  cr;n, 
are   called  the  probabilities  for  and  against  a  thing.      The 
wind  blows  from  the  east,  say  three  days  in  seven,  and  from 
the  west  four  days  in  seven;  the  proper  expression  then  is, 
there  is  a  probability  of  four  to  three  in  favour  of  west  wind 
on  a  given  day.     To  say  that  the  probabilities  are  four  in 
favonr  of,  and  three  against,  a  west  wind  leads  to  a  confounding 
of  the  probable  with  the  improbable.    A  vacillation  between  the 
meanings  is  observable  in  Butler's  Introduction  to  his  Ana- 
logy.    He  correctly  expresses  the  nature  of  probability  when 
he  speaks  of  there  being  a  greater  presumption  upon  one  side 
of  a  question  than  upon  another,  and  remarks  that  if  there  be 
the    slightest   preponderance,   prudence   requires   us   to   act 
accordingly.     He  goes  on,  however,  to  say  that,  in  qnestions 
of  great  consequence,  we  have  to  be  content  with  probabilities 
even  lower ;  that  is,  where  there  is  an  equal  balance  on  both 
sides  ;  nay,  even  to  less  than  this  ;   in  other  words,  we  are  to 
act  with  the  majority  of  cases  against  ns,  which  is  to  believe 
in  iha  improhahle. 

The  play  of  ambiguity  is  seen  in  the  remark  of  Aristotle — 
*  That  which  is  naturally  good  is  good  and  pleasant  to  the  good 
man  :*  an  equivocation  too  closely  resembling  what  occurs  in 
Plato's  argument  to  show  that  the  wrong-doer,  if  unpunished, 
is  more  miserable,  than  if  he  were  pnnished.    *  The  wrong-doer 
says  Plato,  *  when  punished  suffers  what  is  just ;  but  all  jnsfc 
things  are  honourable ;  therefore  he  suffers  what  is  honourable. 
Now  all  honourable  things  are  so  called  because  they  are  either 
agreeable,  or  profitable,  or  both  together.     Punishment  is  not 
agreeable;  it  must  therefore  be  profitable  or  good.    Whence  the 
wrong-doer  when  pnnished  suffers  what  is  profitable  or  good,  &c.' 
Separate  meanings  ascribed  to  separate  words. — This  is  one  of 
the  greatest  snares  of  language.     There  is  a  strong  tendency 
in  the  mind  to  suppose  that  each  word  has  a  separate  meaning, 
and  to  be  misled  by  tautologies  and  alterations  of  phraseology. 
The  ramifications  of  this  tendency  are  numerous  and  subtle ; 
they  include  the  master  fallacy  of  Eealism,  or  the  conversion 
cf  Abstractions  into  Realities. 


DREAD  OF  CHANGES  IN  LANGUAGE. 


619 


The  strong  verbal  associations  formed  with  all  our  opinions 
and  views  make  us  alarmed  when  it  is  proposed  to  withdraw 
the  customary  phrases  in  favour  even  of  such  as  are  more 
suitable.     Stillingfleet  complained  that  Locke's  doctrine  con- 
cerning  Ideas    *  had  almost  discarded  Substance  out  of  the 
world.*     This  feeling  has  been  manifested  against  all  the  great 
innovations  of  philosophy.     Because  the  Cartesian  doctrine  of 
Mind  and  Matter,  as  two  distinct  things,  is  declared  to  be 
gratuitous  and  destitute  of  proof,  people  are  shocked  as  if 
Mind  were  done  away  with.     The  same  revulsion  is  experi- 
enced towards  Berkeley's  attempt  to  reconcile  the  coutradio- 
tion  of  the  prevailing  mode  of  regard  ing  Perception.    Whatelj 
disposes  of  Hume's  objection  to  miracles  *  as  contrary  to  the 
Course  of  Nature,'  by  the  retort  that,  according  to  him,  there 
is  no  such  thing  as  a  Course  of  Nature,  there  being  nothing 
but  ideas  or  impressions  on  the  mind  of  the  individual.     The 
nnproducible  entity  *  Substance '  is  upheld  in  man's  minds  by 
the  force  of  the  word. 

The  fallacy  of  the  Identical  Proposition  is  due  to  there  being 
two  different  names  for  the  same  thing  : — 

There's  ne'er  a  villain  dwelling  in  all  Denmark 
But  he's  an  arrant  knave. 
Ferrier  complains  of  the  phrase  •  Perception  of  Matter,'  as  a 
a  duplication  of  words  for  one  fact,  leading  people  to  suppose 
that  there  are  two  facts.  So,  between  antecedent  and  conse- 
quent, in  Causation,  there  is  interposed  the  name  'power,* 
.to  which  there  is  nothing  corresponding  ;  the  fact  belnff 
sufficiently  stated  by  the  uniform  sequence  of  the  antecedent 
and  its  consequences.  ' 

There  is  a  difficulty  in  satisfying  men's  minds  that  Resist- 
ance, Force,  Inertia,  Momentum,  Matter,  are  all  one  fact.  So 
with  the  terms  Motion,  Succession,  Direction,  Distance,  Situa- 
tion, Extension — which  are  modifications  of  one  fundamental 
fact— Movement  and  the  possibility  of  movement. 

The  giving  reality  to  Abstractions  is  the  error  of  Realism 
and  is  not  as  yet  fully  conquered.  Space  and  Time  are 
frequently  viewed  as  separated  from  all  the  concrete  experi- 
ences of  the  mind  instead  of  being  generalizations  of  these  in 
certain  aspects.  Certain  things  are  said  to  be  *  out  of  all  relation 
to  Time,'  which  should  mean  that  such  things  have  no  suc- 
cession and  no  endurance.  *  Time  as  the  innovator,*  is  either 
an  unapt  metaphor,  or  nonsense.  So,  '  Truth '  in  the  abstract 
is  a  fiction;  the  reality  is  a  number  of  true  propositions. 
*  Chance  *  lingers  in  men's  minds  as  an  independent  existence, 


!:' 


•J'^v^v,* 


G20 


FALLACIES  OF  CONFUSION. 


instead  of  an  assertion  of  identity  between  certain  concrete 

"  The^word  '  Existence  *  in  its  most  abstract  form  refers  to  ft 
snpposed  something  attaching  alike  to  the  Object  and  to  the 
Subiect,  over  and  above  Quantity,  Succession,  and  Co-existence 
which  are  attributes  common  to  both.  The  only  meaning  of 
the  word  is  the  Object  together  with  the  Subject ;  for  which 
addition  we  also  employ  the  synonymous  names,  Universe, 
Being:,  Absolute,  Totality  of  Things.  To  predicate  existence 
of  matter  or  mind  is  pure  tautology.  ^Existence  means 
matter  or  mind,  or  both,  as  the  ca^e  may  be  The  only  use  Ox 
the  word  is  to  express  Object  or  Subject  indiscriminately, 
there  being  occasions  when  we  do  not  need  to  specify  either. 

The  valuable  distinction,  struck  out  by  Aristotle,  of  Poten- 
tial  and  Actual,  is  made  the  occasion  of  giving  reality  to 
fictions.  The  potentiality  has  no  meaning  but  by  a  reference 
to  actuality;  the  power  of  moving  means  motion  m  given 
circumstances.  *  Educability  '  means  education  under  certain 
conditions.  Hamilton  has  created  a  fictitious  intellectual 
faculty  under  the  name  *  Conservative  faculty;  a  pure  re- 
duplication  of  his  *  Reproductive  Faculty.*  We  know  nothing 
of  the  conservation  of  thoughts,  except  that  under  certam 
circumstances  they  are  recalled  or  reproduced. 

Unsuitable  phraseology  and  unreal  questions. --M^ny  purely 
artificial  perplexities  have  arisen  from  applying  to  a  subject 
terms  incongruous  to  its  nature.     The  words  '  true    and    false 
are  properly  applicable  to  knowledge  or  aflirmations  respect-, 
ine  the  order  of  the  world  ;  they  cannot  be  applied  to  pleasures 
and  pains  except  by  mere  metaphor      A  *  ^ake  pleasure    is  an 
incongruous  jumble,  like  a  *  loud  circle  \or  a  *  bright  toothache. 
Aristotle  puts  the  question—*  Is  happiness  praiseworthy  r'  — 
to  which  there  is  no  proper  answer,  because  there  is  no  proper 

°^  The^fld  puzzle  respecting  Motion  is  due  to  the  improper  use 
of  language.  Motion  means  *  change  of  place.'  The  P^zz  e  is 
brought  about  by  insisting  that  the  phenomenon  shall  be 
expressed  as  in  a  place,  that  it  shall  be  either  in  one  place  or 
in  another.  If  we  give  way  to  this  arbitrary  restriction  of 
language,  we  must  allow,  with  Hamilton  and  many  others, 
that  Motion  can  be  shown  to  be  impossible. 

Allusion  has  already  been  made  (p.  364)  to  the  unsuitability 
of  the  word  *  hypothesis '  to  express  abstract  notions,  as  the 

definitions  of  Geometry.  ,  t       i  -d    -r^^ 

The  application  of  terms  of  Extension  and  Local  I'osition 


i 


FALLACIES   OF  SUPPRESSED  RELATIVE. 


621 


to  the  mind  has  been  the  source  of  factitious  puzzles  and  arti- 
ficial mysteries.  *  How  the  immaterial  can  be  united  with 
matter,  how  the  unextended  can  apprehend  extension,  how 
the  indivisible  can  measure  the  divided, — this  is  the  mystery 
of  mysteries  to  man'  (Hamilton's  Reid,  p.  886).  The  answer 
is,  no  attempt  should  be  made  to  express  the  union  of  mind 
and  matter  in  the  language  that  would  be  suitable  to  the 
union  of  one  extended  thing  with  another. 

The  most  conspicuous  example  of  an  artificial  difficulty 
created  by  incongruous  language  is  the  celebrated  Free-will 
theory.  The  sequences  of  the  Will  consist  of  feelings  followed 
by  actions  ;  they  exemplify  mental  causes  giving  birth  to 
activity,  and  are  broadly  contrasted  with  the  physical  prime 
movers— as  water  and  steam  -which  are  devoid  of  any  mental 
element.  There  is  no  mystery  in  these  peculiar  sequences 
except  the  mystery  of  the  union  of  mind  and  body,  formerly 
remarked  on  (p.  357).  The  introduction  of  the  idea  of  Free- 
dom or  Liberty  into  the  voluntary  operation  is  totally  without 
relevance;  and  the  consequence  has  been  a  seemingly  insoluble 
problem,  a  mesh  of  inextricable  contradictions. 

Fallacies  of  Belaiivity .—A  large  class  of  Fallacies  consist  in 
denying  or  suppressing  the  correlatives  of  an  admitted  fact. 
According  to  Relativity,  the  simplest  affirmation  has  two 
sides ;  while  complicated  operations  may  involve  unobvions 
correlates.  Thus  the  daily  rotation  of  the  starry  sphere  is 
either  a  real  motion  of  the  stars,  the  earth  being  at  rest,  or  an 
apparent  motion  caused  by  the  earth's  rotation.  Plato  seems 
to  have  fallen  into  the  confusion  of  supposing  that  both  stars 
and  earth  moved  concurrently,  which  would  have  the  effect 
of  making  the  stars  to  appearance  stationary. 

Every  mode  of  stating  the  doctrine  of  innate  ideas  commits, 
or  borders  upon,  a  Fallacy  of  Relativity,  provided  we  accept 
the  theory  of  Nominalism.  A  general  notion  is  the  affirma- 
tion of  likeness  among  particular  notions ;  it,  therefore,  subsists 
only  in  the  particulars.  It  cannot  precede  them  in  the  evolu- 
tion of  the  mind ;  it  cannot  arise  from  a  source  apart,  and 
then  come  into  their  embrace.  A  generality  not  embodied 
in  particulars  is  a  self-contradiction  unless  on  some  form  of 
Realism. 

Kant's  autonomy,  or  self-government  of  the  will,  is  a  fallacy 
of  suppressed  relative.  No  man  is  a  law  to  himself;  a  law 
co-implicates  a  superior  who  gives  the  law,  and  an  inferior 
who  obeys  it ;  but  the  same  person  cannot  be  both  ruler  and 
subject  in  the  same  department 


i 


I 


622 


FALLACIES   OF   CONFUSION. 


,fl  I 


In  Ethical  questions  there  are  examples  of  suppressed  rela^ 
tives.  Thus,  it  is  often  set  down  as  essential  to  the  highest 
moral  virtue,  that  law  and  obligation  should  embrace  every 
act  of  human  life,  that  the  hand  of  authority  should  never  be 
nnfelt.  Now,  authority  means  operating  by  penalties,  and 
appeals  exclusively  to  the  selfishness  of  men  s  nature.  Uni- 
versal obligation  is  universal  selfishness,  which  is  not  what  is 
intended  by  the  supporters  of  the  doctrine.  .  ^     .     . 

The  view  is  sometimes  expressed  that  the  civil  magistrate  is 
bound  to  support  (by  public  establishment)  the  true  religion  ; 
which,  however,  can  mean  only  what  he  thinks  the  true  reli- 
gion •  and  the  correlative  or  consequence  is  that  he  is  bo^nd 
to  establish  a  fahe  religion,  provided  he  believes  it  to  be  the 
truth.  This  is  an  ofi-shoot  of  the  fallacy  arising  from  the 
suppression  of  the  subject  mind  in  affirmations.  An  aflirma- 
tion  con-elates  with  an  affirmer  ;   a  truth  supposes  a  believer. 

(SeePartFirst,  p.  80).  ,     ,,     xr         •    ii. 

A  Fallacy  of  Relativity  is  pointed  out,  by  Mr.  Venn,  in  the 
doctrine  of  Fatalism ;  a  doctrine  implying  that  events,  depend- 
ing upon  human  agency,  will  yet  be  equally  brought  to  pass 
whether  men  try  to  oppose,  or  try  to  forward  them.     (Logic 

of  Chance,  p.  36G).  ^  „     •  ^  i. 

The  doctrine  of  Relativity  is  carried  to  a  fallacious  pitch, 
when  applied  to  prove  that  there  must  be  something  absolute, 
because  the  Relative  must  suppose  the  non- Relative.  It  there 
be  Relation,  it  is  said,  there  must  be  something  Un-related, 
or  above  all  relation.  But  Relation  cannot,  in  this  way,  be 
brought  round  on  itself,  except  by  a  verbal  juggle.  Relation 
means  that  every  conscious  state  has  a  correlative  state  ;  which 
brings  us  at  last  to  a  couple  (the  subject-mind,  and  the  object 
or  extended  world).  This  is  the  final  end  of  all  possible  cogni- 
tion. We  may  view  the  two  facts  separately  or  together; 
and  we  may  call  the  conjunct  view  an  Absolute  (as  Ferrier 
does),  but  this  adds  nothing  to  our  knowledge.  A  selt-con- 
traduction  is  committed  by  inferring  from  *  everything  is 
relative,*  that  *  something  is  non-relative.' 

Fallacies  of  Relativity  often  arise  in  the  hyperboles  of 
Ehetoric.  In  order  to  reconcile  to  their  lot  the  more  humble 
class  of  manual  labourers,  the  rhetorician  proclaims  the  dignity 
of  all  labour,  without  being  conscious  that  if  all  labour  is 
dignified,  none  is  ;  dignity  supposes  inferior  grades  ;  a  moun- 
tain  height  is  abolished  if  all  the  surrounding  plains  are  raised 
to  the  level  of  its  highest  peak.  So,  in  spurring  men  to 
industry  and  perseverance,  examples  of  distinguished  success 


BEGGING  THE   QUESTION. — SHIFTING  THE  GROUND.    623 

are  held  up  for  universal  imitation  ;   while,  in  fact,  these  cases 
owe  their  distinction  to  the  general  backwardness. 

Petitio  Principii, 

Petifio  Principii,  Petitio  Qucesitiy  arguing  in  a  circle^  begging 
the  question — are  names  for  a  fallacy  always  included  by 
logicians  in  the  List  of  Fallacies.  To  assume  somewhere  in 
the  premises  the  very  point  to  be  proved  is  frequent  in  dealing 
with  ultimate  truths.  The  attempts  to  prove  causation  or  the 
uniformity  of  nature  usually  take  it  for  granted  in  some  form 
or  other.  The  inductive  syllogism  is  a  petitio  principii.  As 
another  instance,  suppose,  on  the  one  hand,  the  continuity  of 
motion  were  given  as  the  proof  of  Persistence  of  Force,  and 
on  the  other  hand,  the  Persistence  of  Force  given  as  the  proof 
of  the  continuity  of  motion,  the  argument  would  revolve  in  a 
circle. 

A  chemical  writer  (Gmelin)  assigns  as  the  cause  of  chemical 
decomposition  by  superadded  bodies  leading  to  new  com- 
pounds, that  the  forces  tending  towards  the  new  compounds 
are  stronger  than  those  maintaining  the  old. 

Hamilton  remarks  that  Plato,  in  Phaedon,  demonstrates  the 
immortality  of  the  soul,  from  its  simplicity,  and  in  the  Re- 
public, demonstrates  the  simplicity  from  the  immortality. 

Ignoratio  Elenc?d. 

Ignoratio  Elenchi,  shifting  the  ground^  or  answering  to  the 
wrong  point,  is  committed  in  many  controversies.  An  example 
is  furnished  in  the  controversy  relating  to  a  Moral  Sense. 
The  opponents  of  the  doctrine  urge  as  an  argument  against 
a  primitive  or  intuitive  moral  standard,  that  different  nations 
differ  widely  in  their  notions  of  what  is  right  and  wrong. 
The  reply  is,  that  although  they  differ  in  the  substance  of  the 
moral  code,  they  agree  in  holding  some  things  to  be  right  and 
morally  obligatory.  This,  however,  is  shifting  the  ground. 
The  reason  for  appealing  to  an  implanted  sense  of  Right  was 
to  obtain  for  certain  moral  precepts  a  higher  authority  than 
human  convention  could  give.  It  was  not  to  prove  us  endowed 
with  a  sense  that  something  or  other  is  a  moral  obligation,  but 
to  establish  the  obligation  of  certain  assigned  rules  (the 
morality  of  our  own  time). 

In  books  on  Practical  Ethics,  there  is  usually  a  chapter  on 
*Our  duties  to  ourselves.'  Like  the  autonomy  of  the  Will,  this 
is  a  Fallacy  of  Relativity,  being  a  contradiction  of  the  very- 
idea  of  duty,  which  implies  a  superior  authority.     The  diffi- 


i  \ 


: 


'--j^^kii.k.. 


624 


LOGICAL  FALLACIES. 


I 


culty  is  met  by  shifting  the  ground ;  the  allegation  bein^ 
that  the  care  of  our  person  and  our  interests  is  a  duty  to 
Bociety  and  to  God. 

The  *  Fallacia  accidentis  *  and  the  *  a  dicto  secundum  quid 
ad  dictum  simpliciter  '  might  be  brought  under  *  shifting  the 
ground/  The  meaning  of  a  term  is  changed  in  its  application  ; 
•water  quenches  thirst,*  does  not  mean  *  boiling  water.*  So,  the 
pleasures  of  duty  are  not  pleasures  attaching  to  it  as  duty,  or 
as  self-sacrifice,  they  are  incidental  consequences  of  the  situsr- 
tion,  through  the  reciprocal  conduct  of  the  other  party. 

False  Analogies, 

The  irrelevant  comparison,  or  unsuitable  analogy,  is  a  usual 
form  of  confused  and  erroneous  thinking,  especially  in  the 
older  philosophy.  It  abounds  in  Plato  (see  especially  Timaaus) 
and  is  not  unfrequent  in  Aristotle;  it  is  also  prevalent  in 
Bacon's  attempts  at  scientific  investigation. 

A  familiar  but  highly  illustrative  example  is  the  comparison 
of  the  history  of  a  nation  to  the  life  of  man,  in  respect  of  birth, 
growth,  maturity,  and  inevitable  decay.  The  comparison  is 
in-elevant ;  the  likeness  palpably  fails  in  the  most  important 
points.  A  nation's  losses  are  repaired ;  the  physical  failure 
of  a  human  being  is  irreparable. 

The  reply  to  all  such  comparisons  is  to  indicate  the  failure 
of  identity.  They  are  false  minor  propositions  ;  and  the  false- 
hood is  exposed  by  pointing  out  the  dissimilarity  of  the  subject 
with  the  subject  of  the  major.  They  are  of  the  same  nature 
as  a  pleading  in  law  where  the  relevance  is  unsound.  The 
remedy  is  found  in  hostile  criticism. 


CHAPTER  V. 
LOGICAL  FALLACIES. 

There  may  be  advantage  in  providing  a  supplemental  colleo 
tion  of  examples  of  Logical  Fallacies  properly  so  called,  that  is, 
violations  of  the  prescribed  Logical  rules  and  methods ;  it  being 
fully  understood  that  the  exemplification  of  the  rules  them- 
selves, in  the  regular  exposition,  unavoidably  afibrds  instan- 
ces of  their  neglect  or  failure. 


EQUIVALENCE,   DEDUCTION,   AND   INDUCTION.  625 

The  proper  arrangement  of  such  an  additional  collection 
(unless  made  promiscuous  to  test  the  ingenuity  of  the  student) 
is  the  arrangement  of  the  general  subject.  Following  the 
order — Deduction,  Induction,  Definition — we  should  commence 
with  Deductive  or  Syllogistic  Fallacies. 

Since,  however,  a  separate  department,  preparatory  to  the 
Syllogism,  is  made  up  of  Equivalent  Forms,  called  also  Im- 
mediate Inference,  and  since  mistakes  may  be  committed  in 
this  department  (some  of  them  the  proper  sources  of  syllogistic 
fallacies),  the  first  clsss  of  Fallacies  should  be  Fallacies  of 
Equivalence,  or  of  Immediate  Inference.  The  chief  heads  where 
fallacies  occur  are  the  Opposition  of  Propositions,  and  Conversion, 

The  acutest  minds  have  been  snared  by  confounding  the 
Contrary  with  the  Contradictory,  of  Propositions.  '  The 
reverse  of  wrong  is  right '  should  be  *  The  reverse  of  wrong 
contains  something  that  is  either  right  or  indifferent.*  *  There 
are  objections  against  a  va>cuum ;  but  one  of  them  must  be 
true  :  *  the  guarded  statement  is,  *  if  there  be  not  a  universal 
plenum,  there  must  be  some  unoccupied  space,  or  vacuum.* 

The  chief  fallacy  of  Conversion  is  Simple  Conversion  of  A ;. 
*  all  the  geometrical  axioms  are  self-evident ;  all  self-evident 
truths  are  axioms.*  The  connection  of  this  mistake  with  the 
usual  fallacies  of  syllogism,  was  sufficiently  pointed  out. 

The  proper  Deductive  Fallacies  are  errors  against  the 
syllogistic  forms  and  canons.  They  are  mainly  resumed  in 
Undistributed  Middle  and  Illicit  Process,  which  again  usually 
involve  the  simple  conversion  of  A.  But  for  the  snare  of 
language  that  leads  to  this  inadvertence,  a  fallacy  of  syllogism 
would  be  comparatively  rare. 

The  Inductive  Fallacies  include  the  most  frequent  and  the 
gravest  of  logical  mistakes.  Their  exemplification  would 
naturally  follow  the  expository  order  of  the  subject  of  Induc- 
tion. We  might  commence  with  erroneous  views  of  the  nature 
of  Cause,  such  as  the  suppression  of  important  conditions  and 
collocations.  We  might  also  connect  with  this  part  of  the 
subject  the  error  of  assigning  more  causes  than  a  pheno- 
menon needs.  It  is  involved  in  the  very  idea  of  cause,  that 
the  effect  is  in  exact  accordance  with  the  cause;  hence, 
the  proof  that  more  causes  were  operative  than  the  effect 
needed,  defeats  itself.  If  we  have  an  adequate  cause  for 
slavery,  or  for  the  subjection  of  castes,  or  classes,  in  the  mere 
love  of  domination  on  the  part  of  the  stronger,  the  explanation 
that  the  state  of  society  demands  such  an  arrangement  ig  of 
no  value.     This  is  the  error  called  *  proving  too  much.' 


626 


LOGICAL  FALLACIEa 


Next  are  the  Fallacies  from  insufficient  employment  or 
neglect  of  the  Methods  of  Elimination.  Under  Agreement 
falls  the  mistake  (exemplified  in  Medicine)  of  confounding 
induction  with  multiplication  of  instances,  without  variation 
of  circumstances.  Mr.  Mill^s  Fallacies  of  non- observation 
likewise  sin  against  the  methods.  An  induction  is  not  com- 
plete  till  all  the  instances,  or  representatives  of  them  all,  have 
been  examined.  Paley,  in  affirming  *  that  happiness  is  equally 
distributed  through  all  classes  of  the  community,  must  have 
left  out  of  account  the  larger  part  of  the  facts.  ^ 

The  assertion   that  *  Species  are  never  transmuted,    even 
although  not  disproved  by  positive  instances  to  the  contrary* 
would°require  an  examination  of  facts  far  beyond  what  has 
ever  been  made.    Leibnitz  generalized  his  '  Law  of  Continuity 
from  a  few    unquestionable   instances,    without   verifying  it 

through  all  nature.  , 

The  fallacious  inferences  named  *  Non  causa  pro  causa, 
*  Post  hoc  ergo  propter  hoc,*  are  fallacies  of  the  inductive 
methods.  Some  circumstance  coupled  with  an  effect  is  held 
to  be  its  cause,  without  due  elimination.  Thus,  the  luxury  in 
the  Roman  empire  is  said  to  have  been  the  cause  of  its  down- 
fall ;  commercial  restrictions,  in  spite  of  which  trade  has 
prospered,  are  made  the  cause  of  prosperity. 

The  fallacy  of  not  recognizing  Plurality  of  Causes  will  be 
apparent  from  what  was  advanced  on  that  subject.  So,  the 
fallacy  of  trusting  to  the  Inductive  Methods  in  Intermixture 
of  Effects  was  necessarily  involved  in  the  reasons  given  for 
coupling  Deduction  with  Induction. 

Under  Secondary  Laws,  there  is  obviously  involved  the 
fallacy  of  applying  a  general  law  to  a  concrete  instance,  or  to 
an  intermediate  law,  without  the  due  modifications ;  as  if  we 
were  to  infer  from  the  Law  of  Gravity  that  all  the  planets  are 
falling  direct  to  the  sun. 

Fallacies  of  Explanation  were  expressly  exemplified.  A 
non-compliance  with  the  logical  conditions  of  Hypotheses 
would  yield  fallacies  on  that  subject. 

Fallacies  op  Definition  would,  in  the  first  place,  express 
the  use  of  ill-defined  terms.  Again,  the  failure  to  satisfy  the 
methods  and  rules  of  Classification  is  a  sin  against  Logic. 
We  need  but  instance  the  wide  prevalence  of  the  error  of 
Cross-divisions.  Bacon  is  prolific  of  divisions  and  sub-divisions, 
which  are  never  logical.  His  four  classes  of  Idola  are  not 
mutually  exclusive ;  his  Prerogative  Instances  will  be  after- 
wards remarked  on. 


ii 


APPENDIX. 

A.— CLASSIFICATION  OF  THE  SCIENCES. 

It  is  here  proposed  to  subjoin  a  short  account  of  the  different 
modes  of  classifying  Science  or  Knowledge.  The  subject  has 
various  logical  bearings.  The  concatenation  of  Knowledge  is 
in  itself  a  Logic. 

The  mode  of  partitioning  Knowledge  that  first  gained  atten- 
tion was  Bacon's  threefold  division  into  History,  Philosophy, 
and  Poetry  ;  in  correspondence  with  the  three  great  modes 
of  intellectual  production,  or  faculties — Memory,  Reason,  and 
Imagination.  History,  the  product  of  Memory,  deals  with  in- 
dividual things  ;  PHILOSOPHY,  the  product  of  Reason,  compares, 
classifies,  and  works  up  these  materials ;  Poetry,  the  product  of 
Imagination,  is  the  department  of  fiction,  fable,  or  creation,  as 
opposed  to  the  literal  rendering  of  things  in  History  and 
in  Philosophy. 

In  dividing  and  sub-dividing  these  leading  departments, 
Bacon  displays  his  usual  copiousness.  History  is  divided  into 
Natural  History  and  Civil  History.  Natural  History  is  the  col- 
lective matters  of  fact  of  the  world,  laid  out  under  Celestial 
Bodies,  Meteors,  the  Earth,  &c.  Civil  History  is  Ecclesiastical, 
Literary,  Political,  with  minor  sub-divisions. 

Philosophy  refers  to  God,  to  Nature,  and  to  Man.  The  first 
head  gives  Theology.  The  second  is  a  somewhat  crude  sylla- 
bus of  Mathematics,  Natural  Philosophy,  and  Metaphysics. 
The  Philosophy  of  Man  is  divided  and  sub-divided  in  much 
curious  detail,  but  with  no  logical  precision.  He  speaks  of 
man  in  a  three-fold  aspect — (1)  Man  in  general,  (2)  the  human 
body,  and  (3)  the  human  mind.  The  theoretical  and  the  prac- 
tical aspects  of  our  knowledge  respecting  humanity  are  indis- 
criminately mixed. 

As  a  first  attempt  at  partitioning  the  totality  of  Literature, 
the  scheme  of  Bacon  deserves  to  be  commended.  But  the 
lines  of  demarcation  are  for  the  most  part  vague  and  unsatis- 
factory. The  distinction  of  Individual  (as  History)  and  Gene- 
ral (as  Philosophy)  iL  wholly  unsuited  to  a  primary  division 


I 


628 


CLASSIFICATION   OF  THE   SCIENCES. 


of  knowledge ;  we  cannot    divorce  the   particulars  from  the 
generalities  in  the  same  subject  matter. 

The  main  outline,  as  regards  the  three-fold  Division,  was 
maintained  in  the  classification  of  D'Alembert,  intended  for  the 
plan  of  the  French  *Encylopedie';  but  with  great  improvements 
in  the  sub-divisions.  The  sub-division  of  Philosophy,  relating 
to  Nature,  is  a  methodical  arrangement  of  the  Mathematical, 
the  Physical,  and  the  Biological  Sciences,  together  with  the 
more  Scientific  Arts,  as  Medicine,  Agriculture,  and  Metallurgy. 

The  Natural  History  department  of  History  includes  Meteors, 
Geography,  Minerals,  Plants,  and  Animals,  very  much  on  the 
scheme  of  Bacon,  with  the  curious  detached  addition  (also 
after  Bacon)  of  a  division  for  Prodigies,  or  deviations  from  the 
usual  course  of  Nature. 

The  Science  of  Man  is  distributed  under  the  two  heads 
Logic  and  Morals.  Logic  comprises  the  arts  of  Thinking, 
Retention,  or  Memory,  and  Communication.  Morals  is  General, 
that  is,  regards  Virtue  at  large  (Ethics)  ;  or  Particular,— 
including  Law  or  Jurisprudence.  This  is  the  mode  of  ap- 
proaching the  science  of  mind  that  has  been  embodied  in  our 
Universities.  Excepting  in  recently  founded  schools,  there  is 
no  chair  for  Psychology  or  the  Theoretical  Science  of  Mind  ; 
the  subject  is  left  to  come  under  Logic  and  Moral  Philosophy  ; 
the  Intellectual  Powers  being  described  in  the  Logic  course, 
the  Active  Powers  in  Moral  Philosophy. 

Thus,  in  D'Alembert,  as  well  as  in  Bacon,  there  is  total 
confusion  of  the  Theoretical  and  the  Practical. 

The  plan  of  subjects  in  the  t  Encyclopedia  Metropolitana,' 
(begun  to  be  published  in  1815),  is  worthy  of  being  quoted. 
There  are  four  Divisions  in  the  work. 

The  First  Division  includes  PURE  SCIENCES,  divided 
into  Formal— -Grammar,  Logic,  Rhetoric,  Mathematics,  Meta- 
physics ;  and  Real,  Law,  Morals,  and  Theology. 

The  Second  Division  is  the  MIXED  SCIENCES,— Mechan- 
ics, Hydrostatics,  Pneumatics,  Optics,  Astronomy  [constitutmg 
the  larger  part  of  our  usual  course  of  Natural  Philosophy]. 

The  Third  Division  is  the  APPLIED  SCIENCES,  sub- 
divided into  ExperimentalPhilosophy— -Magnetism,  Electricity, 
Heat,  Light,  Chemistry,  Acoustics,  Meteorology,  Geodesy; 
Fine  Arts  ;  Useful  Arts  ;  Natural  History  (with  applications 

to  Medicine).  t         v  v 

These  are  the  proprrly  scientific  divisions  ;    the  other  sub- 


I 


NEIL  AKNOTT. — ^AUGUSTE  COMTE 


629 


jects  are  History,  Biography,  Geography,  Lexicography,  and 
Miscellaneous  information. 

The  designations  '  Pure,'  *  Mixed,*  and  *  Applied  *  Sciences 
have  characteristic  meanings,  although  not  precisely  carried 
out  in  the  above  scheme.  The  Pure  Sciences  are  the  more 
Abstract  and  Formal  Sciences,  not  involving  the  consideration 
of  objects  in  the  concrete  ;  the  two  leading  examples  are 
Mathematics  and  Formal  Logic.  The  Mixed  Sciences  consider 
the  applications  of  the  laws  of  the  Formal  Sciences  to  actual 
things.  The  Applied  Sciences,  in  so  far  as  distinct  from  the 
Mixed  Sciences,  should  be  equivalent  to  the  Practical  Sciences. 

Dr.  Neil  Arnott,  in  his  work  on  *  Physics,'  published  in 
1828,  gave  wide  publicity  to  a  division  more  in  harmony  with 
our  present  views.  He  distributed  the  leading  sciences  under 
four  heads,  representing  the  four  classes  of  general  Laws  of 
Nature — namely.  Physics^  Chemistry,  Life,  and  Miyid,  He 
viewed  Mathematics  as  preliminary  and  indispensable  to  these, 
being  the  Science  of  Quantity,  or  Measure,  but  not  a  depart- 
ment of  natural  operations,  in  the  same  acceptation  as  Physics 
or  Chemistry.     All  the  sciences  give  foundation  to  Arts. 

In  his  subsequent  treatise,  entitled  *  Survey  of  Human 
Progress,*  Dr.  Arnott  brought  out  more  decisively  the  distinc* 
tion  between  Sciences  and  Arts,  and  between  the  Concrete  and 
the  Abstract  Departments  of  Science.  Concrete  Science  he 
calls  the  knowledge  of  Things  ;  and  he  enumerates,  under  this 
head.  Astronomy,  Geography,  Mineralogy,  Geology,  Botany, 
Zoology,  the  History  of  Man.  Science,  or  Philosophy  (Ab- 
stract), is  the  knowledge  of  Phenomena,  and  comprises  the  four 
fundamental  departments — Physics,  Chemistry,  Biology,  Mental 
Science.  The  Arts  are  classified  as  Mechanical,  Chemical, 
Physiological,  and  Mental 

The  work  of  Auguste  Comte,  entitled  *  Cours  de  Philosophie 
Positive  '  (1830-42),  is  both  a  classification  of  the  sciences  as  a 
whole,  and  a  minute  sub-division  of  each,  according  to  certain 
fundamental  principles. 

He  first  draws  the  primary  distinction  between  the  Abstract 
and  the  Concrete  Sciences,  which  he  fully  illustrates.  The 
Abstract  Sciences,  being  the  fundamental  or  departmental 
branches  of  Knowledge,  are  susceptible  of  an  orderly  classifica- 
tion on  the  principles  of  Generality,  Simplicity,  and  Independ- 
ence. 

Accordingly,  he  commences  with  Mathematics,  whose  truths 


ii 


630 


CLASSIFICATION  OF  THE  SCIENCES. 


II 


I 


are  the  most  general  of  all,  and  wholly  independent  of  the 
truths  of  any  other  science,  while  all  other  sciences  depend 
upon  it.  Its  sub-divisions  are,  the  more  abstract  portion  called 
Number,  including  Arithmetic  and  Algebra,  and  the  applica- 
tions of  these  to  Space  (Geometry),  and  to  Motion  (Rational 
Mechanics). 

His  second  science  is  Astronomy,  which  is  the  embodiment 
of  the  Law  of  Gravitation.  It  receives  this  position  because 
the  carrying  out  of  gravity  requires  Mathematics  alone,  while 
the  phenomenon  of  gravity  is  a  prelude  to  Physics. 

Then  come,  in  order.  Physics,  Xhemistry,  Biology,  and 
Sociology,  whose  mutual  position  and  interior  arrangements 
are  governed  by  the  same  ideas  of  growing  dependence  and 
complexity,  and  decreasing  generality. 

In  addition  to  the  singling  out  of  Astronomy  as  a  leading 
science,  Comte*s  arrangement  has  these  two  farther  peculiari- 
ties, namely,  the  omission  of  Psychology,  as  a  separate  depart- 
mental science,  (it  being  appended  to  Biology,  under  '  Cerebral 
Functions,*)  and  the  inclusion  of  Sociology,  or  the  Science  of 
Society,  as  a  fundamental  department. 

Mr.  Herbert  Spencer,  in  his  recent  work  entitled  *  The 
Classification  of  the  Sciences,'  has  criticised  the  scheme  of 
Comte,  and  propounded  one  of  his  own,  which  he  has  devel- 
oped with  circumstantial  minuteness.  He  deals  exclusively 
with  the  Theoretical  sciences. 

Mr.  Spencer's  fundamental  idea  is  the  important  distinction 
of  Abstract  and  Concrete,  which  he  expresses  in  a  variety  of 
forms  ;  it  is  the  distinction  between  the  Relations  of  pheno- 
mena and  the  Phenomena  themselves,  between  the  Analytical 
and  Synthetical  ;  it  is  the  separation  of  one  or  a  few  sequences 
from  the  total  plexus  of  sequences ;  the  wholly  or  partially 
ideal  as  contrasted  with  the  real. 

Not  content,  however,  with  a  simple  binary  division  accord- 
ing to  this  leading  contrast,  Mr.  Spencer  proposes  a  three-fold 
division,  by  interpolating  between  the  extremes  a  middle  class 
partly  Abstract  and  partly  Concrete,  to  be  termed  Abstract- 
Concrete.  The  three  classes  are  Abstract,  Abstract-Concretk, 
and  Concrete.  The  only  way  that  this  is  competent  is  to  sub- 
divide the  Abstract,  according  to  degrees  of  Abstractness. 
*  Concrete  '  has  no  degrees  ;  it  means  the  phenomena  taken  in 
their  full  totality,  or  individuality, — Stars,  Mountains,  Mine- 
rals, Plants,  Animals;  and  there  can  be  but  one  way  of  giving 
these  totals,  one  mode  of  concreteness.     There  may,  however, 


HERBERT   SPENCER*S   CLASSIFICATION. 


631 


be  various  degrees  of  the  analytic  separation — more  or  less 
abstract  relatioas  indicated  ;  quantity  and  form  are  more  ab- 
stract than  weight,  hardness,  colour,  life. 

The  Abstract  Sciences  by  pre-eminence,  are  those  that  deal 
with  the  most  abstract  of  all  relations — Space  and  Time. 
Wichout  aflarming  that  Space  and  Time  are  intrinsically  mere 
forms,  conceived  by  us  without  any  particular  things  extended 
and  enduring,  Mr.  Spencer  holds  that  they  have  acquired  this 
character  by  hereditary  transmission,  and  that  we  do  actually 
possess  them  in  their  empty  condition,  or  apart  from  any  con- 
crete embodiments.  Hence,  whatever  relations  subsist  with 
reference  to  these  great  conceptions,  are  the  most  abstract  that 
the  mind  can  possibly  entertain  ;  they  are  pure  and  proper  ab- 
stractions ;  their  hold  of  the  concrete  world  has  been  almost, 
if  not  altogether,  severed.  Space  is  the  abstract  of  all  rela- 
tions of  co-existence.  Time  is  the  abstract  of  all  relations  of 
sequence.  Now  there  ai-e  two  sciences  that  are  occupied  with 
these  abstract  relations  of  co-existence  and  of  sequence — Logio 
and  Mathematics ;  which  accordingly  form  a  class  by  them- 
selves, being  removed  from  the  next  class  by  a  wider  interval 
than  separates  the  members  of  that  class  from  one  another. 

Proceeding  from  the  blank  Forms  of  existence,  to  Existences 
themselves,  from  the  relations  of  phenomena,  to  the  phenomena^ 
we  find  two  divisions,  having  different  aspects,  aims,  and 
methods.  In  fact,  we  have  the  distinction  of  Abstract  and 
Concrete  carried  out,  without  the  same  absolute  divorce  as  in 
the  previous  class.  Mr.  Spencer  illustrates  the  distinction 
thus : — Every  phenomenon  is  a  manifestation  of  force,  usually 
a  combination  or  complication  of  forces  (the  couree  of  a  pro- 
jectile depends  upon  at  least  three  forces).  We  may  study  the 
forces  either  in  separation,  or  in  combination — the  factors  or 
the  product.  On  the  one  hand,  neglecting  all  the  incidents  of 
special  cases  (say  of  falling  bodies),  we  may  aiin  at  educing 
the  laws  of  the  common  force  (gravity)  when  it  is  uninter- 
fered  with.  On  the  other  hand,  given  all  the  incidents  of  a 
phenomenon  (as  a  river),  we  may  seek  to  interpret  the  entire 
phenomenon,  as  o,  product  of  the  several  forces  simultaneously 
in  action.  The  truths  reached  through  the  first  kind  of  en- 
quiry,  though  concrete  inasmuch  as  they  have  actual  exist- 
ences for  their  subject-matter,  are  abstract  as  referring  to  the 
modes  of  existence  apart  from  one  another. 

Mr.  Spencer  thinks  it  proper  to  point  out  farther  that  the 
abstract  must  not  be  confounded  with  the  general.  Each  has 
its  peculiar  signification ;  *  abstract  *  means  detachment  from 


i 


A 


' 


632 


CLASSIFICA.TION  OF  THE   SCIENCES. 


particulars  ;  *  general '  means  manifestation  in  nnmerons  oases. 
The  law  of  uniform  rectilineal  motion  is  aj^tract ;  but  it  is 
never  realized  in  any  particulars,  consequently  it  is  not  gene- 
ral ;  while  rotation  on  an  axis  is  very  general.  Accordingly, 
he  disapproves  of  Comte's  expression  *  decreasing  generality/ 
as  belonging  to  the  phenomena  of  the  successive  sciences 
— Mathematics,  Physics,  &c.  This  criticism  indicates  a  point 
worth  noting,  but  as  regards  Comte's  remark  it  might  easily 
be  evaded.  There  can  be  no  abstraction  without  a  prior 
generalization ;  the  abstract  law  of  rectilinear  motion,  is  a 
generalization  of  the  very  highest  order  stating  what  would 
happen  in  every  case  when  a  body  is  projected  into  space  and 
left  to  itself.  The  other  kind  of  generality  is  something  more 
special  and  concrete,  in  fact,  much  less  of  a  generality  than 
this  great  primary  law. 

The  Sciences,  then,  that  treat  of  the  forces  of  phenomena,  as 
analyzed  and  handled  in  separation,  are  the  Abstract- Concrete 
Sciences ;  as  Mechanics,  Physics,  Chemistry.  The  sciences 
that  view  phenomena  in  their  aggregate,  or  their  full  actuality, 
are  Concrete  Sciences  ;  such  are  Astronomy,  Geology,  Biology, 
Psychology,  Sociology,  &c. 

A  few  words  now  as  to  the  more  precise  definitions  and 
divisions  of  the  leading  departments,  on  which  hang  various 
points  of  logical  interest. 

Abstract  Science  considers,  first,  what  is  common  to  all 
Relations,  and  next,  what  is  common  to  each  order  of  Relations. 
Between  each  kind  of  phenomenon  and  certain  other  kinds  of 
phenomena,  there  exist  uniform  relations.  It  is  a  universal 
abstract  truth—that  there  is  an  unchanging  order  among 
things  in  Space  and  in  Time.  This  is  the  most  abstract  truth 
of»  all,  the  subject-matter  of  the  highest  division  of  Abstract 
Science.  It  has  sub-divisions.  First,  and  next  in  abstractness, 
are  the  connexions  of  things  in  Space  and  Time,  irrespective 
of  the  things  connected.  This  is  the  subject-matter  of  Logic^ 
where  the  nature  and  amounts  of  terms  related  are  not 
considered,  but  only  the  relations  themselves.  The  other  sub- 
division takes  in  Quantity  or  amount,  without  any  farther 
qualities.  This  is  Mathematics,  which  is  a  statement  of  laws  of 
quantity  apart  from  any  real  things,  that  is,  as  occupying 
Space  and  Time.  This  statement  is  made  upon  certain  ultimate 
«m^  occupying  definite  positions  in  Space  and  in  Time.  The 
divisions  of  Mathematics  follow  according  as  the  units  are 
simply  separate,  or  according  as  they  are  both  separate  and 
equal  j    the  one  gives  birth  to  an  indefinite  Calculus  (applied 


ABSTRACT  AND   CONCRETE   SCIENCEa 


633 


in  Statistics),  the  other  to  the  Definite  Calculus,  whose  sub- 
divisions are  Arithmetic,  Algebra,  and  the  Calculus  of  Opera* 
tious.  When  tlie  computation  of  units  refers  to  occupation  of 
Space,  the  subject  is  Geometry.  When  Time  is  introduced,  we 
have  Kinematics  and  the  Geometry  of  Motion. 

So  much  for  the  sciences  of  pure  Abstraction.  The  second 
class,  the  Abstract- Concrete,  are  occupied  with  the  general 
laws  of  Motion,  Matter,  and  Force,  in  their  disentanglement 
from  the  concrete  phenomena,  where  iliey  re-act  upon,  and 
modify  one  another.  In  Mechanics,  for  example,  which  is  one 
of  the  sub-divisions,  the  laws  of  motion  are  expressed  without 
reference  to  friction  and  resistance  of  the  medium  (?).  So  in 
Chemistry,  another  sub-division,  the  laws  are  viewed  upon 
substances  absolutely  pure,  such  as  Nature  rarely  supplies. 

The  partition  of  this  group  is  conducted  on  the  same  prin- 
ciple as  in  the  former  group.  A  distinction  is  drawn  between 
Force  considered  apart  from  its  modes,  and  Force  considered 
under  each  of  its  modes, — a  more  abstract,  and  a  less  abstract 
department.  The  first  part  contains  a  statement  of  the  Laws 
of  Force,  as  deducible  from  the  fundamental  principle  of  the 
Persistence  of  Force,  together  with  the  theorems  of  the  Com- 
position and  Resolution  of  Forces.  The  second  part  comprises 
Molar  Mechanics  or  Molar  Forces  (Statics,  Hydrostatics, 
Dynamics,  Hydrodynamics),  and  Molecular  Mechanics — includ- 
ing the  properties  and  states  of  matter  (Physical),  and  Chemis- 
try ;  together  with  Heat,  Light,  Electricity,  and  Magnetism. 
[The  arrangement  is  a  questionable  one,  in  so  far  as  Chemistry 
is  interposed  between  the  Physical  properties  and  states  of 
bodies,  and  the  agencies — named  Heat,  Light,  &c]. 

The  division  of  Abstract- Concrete  Science  is  thus  co-ext^n- 
sive  with  what  we  have  formerly  termed  Inorganic  Physics. 

The  third  great  group,  the  Concrete  Sciences,  as  repeatedly 
stated,  embrace  the  totalities  of  phenomena.  Astronomy  is 
placed  in  this  group.  The  meaning  is,  that  the  astronomer 
does  not  stop  short  after  generalizing  the  laws  of  planetary 
movement,  such  as  they  would  be  if  there  existed  only  one 
planet ;  he  solves  this  abstract  concrete  problem,  as  a  step  to- 
wards solving  the  concrete  problem  of  the  planetary  movements 
as  affecting  one  another.  The  *  theory  of  the  Moon '  means 
an  interpretation  of  the  Moon's  motions,  not  as  determined 
simply  by  centripetal  and  centrifugal  forces,  but  as  perpetually 
modified  by  gravitation  towards  the  Earth's  equatorial  protu- 
berance, towards  the  Sun,  and  even  towards  Venus— forces 
daily  varying  in  their  amounts  and  combinations.     So  the 


I 


i 


634 


CLA.SSIFICATION  OF  THE  SCIENCES. 


geologist  does  not  confine  himself  to  the  separate  elements— 
water-action,  fire-action,  he  aims  to  interpvet  the  entire  structurs 
of  the  Earth's  crust.  And,  in  Biology,  if  different  aspects  of 
the  phenomena  of  Life  are  investigated  apart,  they  are  all 
helping  to  work  out  a  solution  of  vital  phenomena  in  their 
entirety,  both  as  displayed  by  individual  organisms  and  by 
organisms  at  large.  The  interpretation  is  no  longer  syntheti- 
cal but  analytical. 

These  explanations  premised,  the  enumeration  of  subjects  in 
the  Concrete  division  is  as  follows  : — First,  and  most  general 
of  all,  are  the  Universal  Laws  of  the  continuous  Re-distribution 
of  Matter  and  Motion.  Next  follows  the  application  of  these 
to  actual  Matter.  As  applied  to  the  Celestial  Bodies  (1)  treated 
as  masses,  it  is  Astronomy  ;  (2)  as  made  up  of  molecules — 
Astrogeny  (Solar  Mineralogy  and  Solar  Meteorology).  On  the 
earth,  the  same  actions  result  in  Mineralogy^  Meteorology, 
Geology ;  when  causing  organic  phenomena,  they  make  up 
Biology,  which  has  various  sub-divisions,  terminating  in 
Psychology  and  Sociology. 

Such  is  the  outline  of  Mr.  Spencer's  scheme.  By  way  of 
criticism,  the  following  remarks  may  be  offered. 

In  the  first  place,  objection  may  be  taken  to  his  language, 
in  discussing  the  extreme  Abstract  Sciences,  when  he  speaks 
of  the  empty  forms  therein  considered.  To  call  Space  and 
Time  empty  forms,  must  mean  that  they  can  be  thought  of 
without  any  concrete  embodiment  whatsoever ;  that  one  can 
think  of  Time,  as  a  pure  abstraction,  without  having  in  one's 
mind  any  concrete  succession.  Now,  this  doctrine  is  in  the 
last  degree  questionable.  For  although  we  might  concede  the 
hereditary  predisposition  to  fall  into  these  conceptions,  we  do 
not  thereby  affirm  that  they  can  be  bodied  forth  without  any 
concrete  examples  whatever.  We  might  rather  say  with 
Kant,  and  the  later  a  priori  schools,  that  when  particulars  are 
given  they  start  forth  into  full  view,  This  much  is  certain, 
however,  that  without  a  very  wide  and  familiar  converse  with 
particulars,  the  exceedingly  abstract  relations  of  these  Abstract 
Sciences,  are  wholly  incomprehensible  to  any  human  being. 
The  extreme  generalities  of  Logic,  in  order  to  be  intelligible, 
need  perpetual  reference  to  particulars.  The  same  is  true  with 
the  first  elements  of  Mathematics,  which  are  the  foundations 
of  all  the  rest. 

Mr.  Spencer's  account  of  the  subject-matter  of  Logic,  the 
first  of  all  the  sciences,  is  so  extremely  general  that  we  can 
hardly  discover  what  is  the  precise   scope  he  assigns  to  it. 


LINES  OF  DEMARCATION. 


635 


From  its  position,  however,  it  must  be  viewed  as  Theoretical 
Logic  purely ;  under  which  there  would  be  included  the  funda- 
mental aspects  of  all  knowledge— Diff-erence  (Relativity)  and 
Agreement  (Generality),  the  Laws  of  Consistency,  Mediate 
Inference,  the  Uniformity  of  nature  ;  and  the  various  deduc- 
tions or  consequences  of  those  primary  facts.  These  are  points 
common  to  all  sciences,  and  may  therefore  precede  them  all. 
At  the  same  time,  it  should  be  remarked  that  the  ascertaining 
of  these  very  high  generalities  has  been  a  great  inductive 
eff'ort,  considerably  aided  by  the  special  study  of  the  human 
mind,  or  the  science  of  Psychology.  This  observation  shghtly 
qualifies  Mr.  Spencer's  statement  that  none  of  the  truths  of 
the  third  group  are  of  any  use  to  the  problems  of  the  second, 
while  the  second  group  are  of  no  use  to  the  first. 

It  may  be  farther  noticed  that,  notwithstanding  the  strong 
terms  employed  to  contrast  the  Abstract  with  the  Abstract- 
Concrete  Sciences,  the  contiguous  subjects  of  each  show  but  a 
narrow  boundary  line.  The  geometry  of  Motion,  the  last  of 
the  Abstract  Sciences,  comes  very  close  upon  the  Universal 
Laws  of  Force,  the  first  subject  of  the  Abstract-Concrete  group. 

These  considerations,  if  they  have  any  weight,  tend  to  in- 
validate the  alleged  distinction  between  Abstract  and  Abstract- 
Concrete  Sciences,  a  distinction  without  an  adequate  difference. 
Practically,  however,  the  matter  is  of  no  moment.  The  succes- 
sion of  subjects  would  probably  be  regarded  as  the  same,  and 
the  manner  of  sub-dividing  and  treating  them  would  be  very 
much  the  same  with  or  without  this  particular  boundary. 
Mathematics  must  precede  Mechanics  ;  and  Logic,  conceived  m 
its  high  theoretic  aspects,  may  claim  to  precede  Mathematics.^ 

A  much  more  serious  dispute  arises  out  of  Mr.  Spencer  s 
proposed  boundary  line  between  the  Abstract-Concrete  and 
the  Concrete  Sciences.  No  one  ever  drew  the  hue  as  he  has 
done  it  The  Concrete  Sciences  have  always  been  typified  by 
the  so-called  Natural  History  Sciences— Mineralogy,  Botany, 
Zoology,  Geology— and  by  Geography.  These  are  Sciences 
whose  marked  features  are  Classification  and  Description. 
They  deal  with  large  collections  of  objects,  which  they  arrange 
and  describe  by  means  of  careful  generalization. 

It  is,  therefore,  with  a  little  surprise  that  we  find  inserted 
among  Concrete  Sciences,  not  merely  Astronomy,  but  the 
whole  of  Biology,  in  which  is  included  Psychology.  Certain 
parts  of  these  subjects  would  be  properly  concrete  ;  as  Celestial 
Geography  (under  Astronomy)  ;  and  the  Races  and  Charao- 
ters  of  men  (under  Psychology.) 


i 


"i 
i 
- 

V 

■r, 


ii 
i 

J 


I 


^«; 


636 


CLASSIFICATION  OF  THE   SCIENCES. 


Let  US  consider  how  the  case  stands  with  Astronomy.  This 
science,  since  Newton's  time,  is  avowedly  based  on  Theoretical 
Mechanics.  Newton,  in  the  First  Book  of  the  Principia,  which 
may  be  pronounced  Abstract  Mechanics  of  the  purest  type, 
went  far  beyond  Mr.  Spencer's  limits  to  an  Abstract-Concrete 
Science.  These  limits,  indeed,  are  not  a  little  arbitrary.  We 
can  suppose  a  science  to  confine  itself  solely  to  the  *  factors,'  or 
the  separated  elements,  and  never,  on  any  occasion,  to  combine 
two  into  a  composite  third.  This  position  is  intelligible,  and 
possibly  defensible.  For  example,  in  Astronomy,  the  Law  of 
Persistence  of  Motion  in  a  straight  line  might  be  discussed  in 
pure  ideal  separation  ;  and  so,  the  Law  of  Gravity  might  be 
discussed  in  equally  pure  separation — both  under  the  Abstract- 
Concrete  department  of  Mechanics.  It  might  then  be  reserved 
to  a  concrete  department  to  unite  these  in  the  explanation  of  a 
projectile  or  of  a  planet.  Such,  however,  is  not  Mr.  Spencer's 
boundary  line.  He  allows  Theoretical  Mechanics  to  make  this 
particular  combination,  and  to  arrive  at  the  laws  of  planetary 
movement,  in  the  case  of  a  single  planet.  What  he  does  not 
allow  is,  to  proceed  to  the  case  of  two  planets,  mutually  dis- 
turbing one  another,  or  a  planet  and  a  satellite,  commonly 
called  the  *  problem  of  the  Three  Bodies.'  This  problem  is 
not  to  be  touched  in  Theoretical  Mechanics,  but  to  be  remanded 
to  the  Concrete  Science  of  Astronomy.  Yet,  if  we  are  allowed 
to  combine  the  two  factors — projectile  motion  and  gravity  to 
one  centre — why  may  we  not  take  in  an  additional  factor,  a 
second  gravitating  body  ?  The  difference  is  not  between 
single  factors  and  their  combination,  but  between  two  grades  of 
combination. 

In  point  of  fact,  such  a  line  is  never  drawn.  Newton,  in  the 
First  Book  of  the  Principia,  took  up  the  problem  of  the 
Three  Bodies,  as  applied  to  the  Moon,  and  worked  it  to  ex- 
haustion. So  writers  on  Theoretical  Mechanics  continue  to 
include  the  Three  Bodies,  Precession,  and  the  Tides.  Nor  is 
any  reason  apparent  for  making  the  break  that  Mr.  Spencer 
suggests.  Increasing  complicacy  of  ded action  and  calculation 
attends  the  inclusion  of  new  factors,  but  this  special  difficulty 
is  not  supposed  to  take  the  subject  out  of  an  abstract  depart- 
ment and  to  insert  it  in  some  concrete  department. 

Again,  Mr.  Spencer  remarks  that  in  works  on  Mechanics, 
the  laws  of  motion  are  expressed  without  reference  to  friction 
and  resistance  of  the  medium.  Turning  to  *  Thomson  and 
Tait's  Mechanics,'  we  find  the  Laws  of  Friction  introduced, 
with  a  reservation  of  the  purely  Experimental  results  to  the 


CHEMISTRY  AND  BIOLOGY. 


637 


department  called  Properties  of  Matter.  In  Newton's  Second 
Book,  and  in  all  works  of  similar  compass,  the  operation  of  a 
Resisting  Medium  is  handled. 

The  law  of  the  radiation  of  light  (the  inverse  square  of  the 
distance)  is  said  by  Mr.  Spencer  to  be  Abstract-Concrete, 
while  the  disturbing  changes  in  the  medium  are  not  to 
be  mentioned  except  in  a  Concrete  Science  of  Optics.  We 
need  not  remark  that  such  a  separate  handling  is  unknown  to 
science. 

Mr.  Spencer's  illustrations  from  Chemistry  are  especially  at 
variance  with  usage,  while  it  is  difficult  to  reconcile  them 
with  reason.  Chemistry  is  an  Abstract-Concrete  Science. 
What  does  this  mean?  The  reply  is,  the  chemist  is  never 
satisfied  with  the  crude  substances  of  nature,  but  first  purifies 
them,  and  ascertains  the  properties  in  the  pure  state.  This,  of 
course,  is  a  necessary  precaution.  Bnt  if  the  insinuation  be, 
that  Chemistry  does  not  give,  or  ought  not  to  give,  the  pro- 
perties of  any  impure  substance,  or  any  alloy  or  mixture, 
the  fact  is  quite  different.  Every  chemical  writer  describes  all 
the  prevailing  species  of  carbon,  including  pure  and  impure 
kinds  ;  the  same  with  iron,  and  with  every  substance  found  in 
important  varieties.  Why  should  it  be  otherwise  ?  There  is  no 
dereliction  of  logical  principles  in  stating  the  properties  of 
the  iron  ores,  in  connexion  with  iron.  The  same  thing  may  be 
repeated  in  Mineralogy,  but  is  not  out  of  place  in  Chemistry. 
Again,  no  writer  on  Chemistry  ever  omits  to  describe  the 
Atmosphere,  which  is  the  actual  or  concrete  combination  of 
Oxj'gen,  Nitrogen,  &c. 

It  may  be  noticed  in  addition  that  a  sul^tance  purified  is 
obviously  not  a  substance  in  the  abstract.  Virgin  gold,  and 
the  purest  diamond  are  still  objects  in  the  concrete. 

These  remarks  on  Chemistry  pave  the  way  for  the  conside- 
ration of  the  place  assigned  to  Biology  among  the  Concrete 
Sciences.  Now,  Biology  is  a  science  of  increasing  complica- 
tion ;  living  bodies  are  subjected  to  all  the  Physical  and 
Chemical  Laws,  and  to  Biological  Laws  in  addition :  so  that  a 
rose  is  a  more  complicated  object  than  a  diamond.  But  the 
objects  of  Chemistry  and  the  objects  of  Biology  are  equally 
concrete,  so  far  as  they  go ;  the  simple  bodies  of  chemistry, 
and  their  several  compounds,  are  viewed  by  the  Chemist  as 
concrete  wholes,  and  are  described  by  him,  not  with  reference 
to  one  factor,  but  to  all  their  factors.  The  isolation  of  the  one 
property,  named  Chemical  combination,  which  would  be  an 
abstract  handling  of  bodies  in   the  chemical   point  of  view. 


I 


038 


CLASSmCATlON  OF  THE  SCIENCES 


mnst  be  considered  to  be  impracticable;  at  all  events  it  is 
never  done.  We  may  doubt  whether  anything  would  be  gained 
by  attempting  it.  But,  whatever  abstractive  operation  of  this 
kind  is  possible  in  Chemistry,  might  be  repeated  in  Biology  ; 
there  might  be  general  laws — isolated  factors — of  life,  as  well 
as  of  inorganic  matter.  If  so,  to  place  one  of  these  two  leading 
departments  among  Abstract  Concrete  Sciences,  and  the  other 
among  the  proper  Concrete  departments  is  to  make  a  dis- 
tinction without  a  sufficient  difference. 

I^or  is  it  possible  to  justify  the  placing  of  Psychology  wholly 
among  Concrete  Sciences.  It  is  a  highly  analytic  science,  as 
Mr.  Spencer  thoroughly  knows.  The  totality  of  mind  is  sepa- 
rated into  factors,  each  discussed  in  isolation,  before  they  are 
brought  together.  There  are  many  strictly  abstract  discussions 
to  show  the  difference  between  the  effect  of  a  motive  (as  selfish- 
ness) acting  in  ideal  purity  or  separation,  and  the  same  motive, 
combined  with  many  others,  in  the  concrete  human  being. 
But  the  force  of  the  remark  would  appear  to  be  dissipated  if 
all  the  laws  of  Psychology  are  to  be  considered  as  expressions 
of  the  concrete  facts  of  mind. 

A  separation  may  be  temporarily  made  between  the  purely 
theoretical  and  deductive  treatment  of  a  science,  and  the  ex- 
perimental treatment.  In  Theoretical  Mechanics,  (as  Hydro- 
Dynamics),  the  laws  of  a  resisting  medium  may  be  inferred 
and  computed  from  primary  assumptions  as  to  the  nature  of 
fluid  particles ;  while,  on  the  other  hand,  the  subject  may  be 
investigated  by  experiments,  as  in  gunnery.  But  the  science 
is  not  completely  presented  unless  both  are  taken  account  of 
^ogethe^ :  the  theoretical  deductions  have  to  be  confronted, 
checked  and  verified,  by  the  experimental  results,  in  order  to 
have  any  standing  as  laws  of  the  department. 

Yet  another  method  is  possible.  A  subject,  as,  for  example, 
Astronomy,  may  be  exhaustively  handled  in  a  separate  treatise ; 
wherein  there  shall  be  brought  together  from  every  department 
whatever  bears  upon  the  celestial  bodies.  This  would  be  a 
highly  mixed  department,  yet  not,  on  that  account,  a  strictly 
concrete  science.  It  would  be  full  of  the  most  abstract  discus- 
sions ^  witness  the  'Mechanique  Celeste  '  of  Laplace.  It  would 
draw  contributions  from  various  sciences,  besides  its  parent 
science.  Mechanics  ;  it  would  introduce  Optics,  Heat,  Magnet- 
ism, and  Chemistry ;  yet  it  would  not  treat  the  heavenly 
bodies  as  Minerals  are  treated  in  Mineralogy,  or  Plants  in 
Botany.  It  would  have  many  practical  bearings ;  in  fact,  it 
would  have  considerable  claims  to  be  a  Practical  Science.     Any 


I 


PRETENSIONS   OF  FORMAL   LOGIC. 


639 


scientific  department  exhaustively  treated  would  eschew  purity, 
and  draw  contributions  from  many  sources. 

Thus,  it  appears  that  Mr.  Spencer,  in  abandoning  the  usual 
partition  of  the  sciences,  into  the  departmental  or  fundamental 
sciences,  on  the  one  hand,  and  the  concrete  or  derived  on  the 
other,  has  abandoned  the  more  real  distinction  in  search  of  a 
fanciful  and  untenable  boundary  line  of  the  Abstract  and  the 
Concrete.  We  see  reason  still  to  abide  by  the  old  specification 
of  the  Concrete  Sciences,  typified  by  Mineralogy,  Botany, 
Zoology,  Geology,  &c.  These  sciences  have  marks  peculiar  to 
themselves ;  they  are  the  class ificatory  and  the  descriptive 
sciences.  They  embrace  large  collections  of  individuid  things, 
which  have  to  be  classified,  and  to  be  described  as  concrete 
wholes.  Moreover,  they  contain  no  new  fundamental  operation 
of  nature ;  every  variety  of  natural  agent  has  been  previously 
exhausted  in  the  departmental  sciences — Mathematics,  Physics, 
Chemistry,  Biology,  Psychology. 

B. — THE   PROVINCE    OF  LOGIC. 

It  is  contended  by  some  logicians  that  the  Province  of  Loo-io 
is  Formal  Reasoning  and  Thinking ;  by  which  they  mean 
mainly  the  Syllogism,  and  what  is  subsidiary  thereto.  They 
would  exclude  everything  that  refers  to  the  Matter,  that  is  to 
say — Induction,  and  the  greater  part  of  Definition  and  Classifi- 
cation. 

We  have,  however,  just  grounds  to  complain  that  the  dis- 
tinction of  Form  and  Matter  is  too  vague  and  unsteady  to  con- 
stitute a  clear  line  of  demarcation  between  the  two  departments 
of  Evidence — Deductive  and  Inductive.  It  \fill  be  expedient 
for  us,  therefore,  to  ascertain  what  precise  meanings,  if  any, 
can  be  assigned  to  these  phrases. 

Perhaps  the  most  thorough  and  consecutive  account  of  the 
severance  of  Formal  Logic  from  Material  Logic  is  that  con- 
tained in  the  Introduction  to  Mansel's  edition  of  Aldrich.  In 
that  work,  the  author  adduces  every  consideration  that  is  of 
any  avail  in  widening  the  distinction  in  question. 

Adverting  to  the  first  question  raised  in  the  definition  of 
Logic,  namely,  whether  it  be  a  Science  or  an  Art — whether  it 
is  principally  theoretical  or  principally  practical — Mr.  Mansel 
holds  that,  in  its  essence,  it  is  speculative  or  theoretical,  and, 
in  its  accidents,  practical.  There  would  be  a  body  of  prin- 
ciples or  laws,  although  no  one  cared  to  apply  them  to  the 
discipline  of  the  mind,  or  to  the  improvement  of  the  thinking 
faculties, 

29 


•'ifer 


:i 


640 


THE  PROVINCE  OF   LOGIC. 


Nevertheless,  the  science  is  susceptible  of  apphcation  to 
practice ;  it  may  be  brought  to  bear  on  our  intellectual  pro- 
cesses. Such  is  its  scope  as  expressed  in  the  second  part  of 
Whately's  definition -the  AH  of  Feasonmg  ;  y^hich  de^mtioii, 
however,  as  regards  the  word  *  Reasoning,'  Mr.  Mansel,  in 
common  with  Hamilton  and  Mill,  objects  to  as  narrowmg  the 
province  too  much.  Even  as  a  Formal  Science,  Logic  in- 
eludes  the  processes  named  Apprehension  and  Judgment,  and 
these  not  as  mere  aids  to  Reasoning,  but  as  independent  acts 
of  thought.  Accordingly,  Mansel  agrees  with  Hamilton  m 
substituting  for  '  Reasoning,'  with  suitable  qualifications,  the 
larger  term  *  Thought.*  , 

He  then  proceeds  to  lay  out  the  distinction  between  the 
Form  and  the  Matter  of  the  thought.  His  first  indication  of 
the  difference  is  to  this  effectr-Thought  may  violate  its  own  laias, 
and  so  dtstroy  itself;  something  may  be  set  np  that  turns  out 
wholly  unthinkaUe,  On  the  other  hand,  a  Thought  may  be  per- 
fectly  consistent  with  itself,  but  at  variance  with  facts  of 
experievce;  which,  although  quite  thinkable  would  be  empiri- 
cally  illegitimate,  or  unreal.  [This  is  the  distinction  between 
Self-Consistency-Immediate  or  Equivalent  statements,  and 
Inductive  or  matter-of-fact  certainty].  . 

The  next  remark  is  that  there  must  be  material  data  m  order 
to  thought  of  any  kind,  even  formal  thought ;  there  must  be 
concrete  experience  of  things  external  and  things  internal,  in 
order  to  understand  even  a  syllogism.     But  the  materials  being 
riven,  there  is  a  vital  difference  between  two  modes  of  using 
them.   The  distinction  of  Presentative  and  Bepresentahve  thought 
is  an  aid  here  ;  the  distinction  between  the  mdividual  concrete 
thines-a  building,  a  man,  a  star,  and  the  generalities  or  con- 
ceptl-height,  figure,  brightness,  which  we  may  form  by  the 
comparison  of  the  concrete  objects.    The  consideration  of  the 
Matter  is  the  reference  to  the  individual  things ;  the  considera- 
tion  of  the   Form  is  the  general  concept,  or  representative 
thought.     [So  far  we  have  the  ordinary  distinction  between 
Concrete  and  Abstract,  only  it  is  apparently  pushed  to  a  kind 
of  Conceptualism ;    there  being  implied  that  the  concept,  or 
notion,  is  something  more  than  an  agreement  among  individuals. 
If  it   bo  true  that  a  notion  is  unthinkable,  except   as  que  or 
more  individuals,  the  *  Form '  is  still  '  Matter,'  only  in  a  some- 
what different  arrangement],  •  i    j  „„ 
But  farther,  the  thinking  process  may  be  distinguished  as 
material  or  formal.     It  is  forvml  when  the  matter  given  it 
sufficient  for  the  product  derived,  with  bo  other  addition  but 


FORM^Ui  THINKING  EXPLAINED. 


6^1 


the  ant  of  thinking.  It  is  material  when  the  data  are  insuffi- 
cient, and  the  mind  has  to  take  in  more  matter,  in  the  act  of 
thinking.  Given  the  attributes,  A,  B,  C,  we  can  think  them 
as  co-existing  iu  an  object,  without  any  fresh  appeal  to  facts  ; 
which  informal  conceiving.  [This  is  quite  intelligible  too  ;  all 
the  operations  of  Arithmetic  are  formal  in  this  sense  ;  we  pro- 
nounce six  times  four  to  be  twenty  four,  without  an  appeal  to 
pebbles  or  coins,  or  any  real  objects.  We  have  put  together 
from  primary  realities  a  machinery  that  can  operate  independ- 
ently of  the  realities]. 

As  conditions  of  formal  conceiving,  are  laid  down  the  laws 
of  Contradiction  and  Identity.  We  must  not  introduce  Con- 
tradictory attributes — A  and  not-A.  The  author  is  a  little 
more  obscure  as  regards  the  condition  of  Identity.  Thought, 
he  says,  is  representative  of  all  possible  objects  ;  but  Intuition 
(cognition  of  the  individual,  as  opposed  to  Thought,  or  the 
general)  must  be  conscious  of  differences;  every  object  of 
intuition  is  marked  off,  limited,  and  individualized  ;  it  is  itself 
and  no  other.  To  this  circumstance  corresponds  the  Law  of 
Identity,  *  A  is  A  ' ;  *  every  object  of  thought  is  conceived  as 
itself  A  somewhat  novel  rendering  of  that  well-known  Law 
of  Thought. 

These  laws  are  the  key  to  logical  conceiving  (Conception  is 
the  first  logical  product).  Next,  as  to  formal  judging^  or  the 
forming  of  Judgments.  Affirmation  takes  place  when  one 
.  concept  is  contained  in  another ;  Negation,  when  one  contra- 
dicts another.  Here,  too,  are  involved  the  laws  of  Identity 
and  Contradiction. 

Finally,  as  to  reasoning.  This  is  formal^when  the  given 
judgments  are  connected  by  a  middle  term,  under  such  condi- 
tions of  quantity  and  quality  that  the  mere  act  of  thought 
necessarily  elicits  the  conclusion.  If  there  be  required  any 
addition  to  the  data,  the  consequence  is  material.  Formal 
Mediate  reasoning,  no  less  than  Immediate  inference,  is  achieved 
through  the  laws  of  Identity  (for  affirmative  syllogisms),  and 
of  Contradiction  (for  negative  syllogisms).  In  the  immediate 
inferences  of  Opposition  [Obversion]  and  Conversion,  there  is 
a  further  demand  for  the  subordinate  law  of  Excluded  Middle. 

Thus,  then,  if  a  thought  professes  to  be  based  on  formal 
grounds,  to  be  guaranteed  by  the  laws  of  thought  alone,  its 
pretensions  can  be  adjudicated  on  by  Logic ;  if  it  professes  to 
rest  on  sensible  experience,  or  on  suppressed  premises,  it  must 
come  before  another  tribunal. 

It  is,  of  course,  open,  the  author  remarks,  for  any  innovator 


6i2 


THE  rROVlNCE  OF  LOGIC. 


to  propose  an  extension  of  bonndaries,  by  the  inclnsion  of  tbe 
Matter  of  propositions ;  but  he  does  so  in  the  t^eth  ot  Kant  s 
demonstration,  that  a  critenon  of  material  tndh  u  not  only 
impossible,  hut  self-contradictory.  Moreover,  the  attempt  to 
enlarge  the  field  renders  impossible  the  assigning  of  any  dejinite 

field  whatever.  .        , 

We  are  interested  to  know  in  what  way  Mr.  Mansel  makes 
eood  these  very  strong  allegations.     The  steps  are  these. 

( 1 )  The  Aristotelian  or  Formal  Logic  seeks  the  laws  whereby 
the  mind  thinks ;  the  Baconian  seeks  the  laws  whereby  the 
phenomena  oi  outimrd  things  take  place;  that  is  to  say  the  one 
refers  to  mind,  the  ego,  the  other  to  matter,  the  object,  or  7wn. 
eno.  Consequently,  the  one  enquiry  is  the  mterrogation  ot 
B"clf-consciousness,  the  other  is   an   examination  of  external 

nature.  .  ^.  .     •       i   ^„^«n.^ 

Such  is  Mr.  Mansers  first  position.  It  seems  to  involve  some 
confusion  of  ideas.  We  strongly  doubt  whether  the  contrast  ot 
Formal  Loirio  and  Inductive  Logic  can  be  reduced  under  tbe 
contrast  of'  Subject  and  Object,  or  Mind  and  Matter.        ^ 

For  one  thing,  the  study  of  Mind,  or  Psychology,  is,  in 
modern  times,  universally  considered  to  be  properly  Inductive. 
How  can  we  reach  the  important  laws  of  Mind— such  as  Rela- 
tivity, Association  of  Ideas,  tbe  operation  of  the  Feelings,  and 
the  Will— except  by  observation  and  induction  of  the  tacts  ot 
self-consciousness,  occasionally  aided  by  external  indications. 

Acrain,  ih^  laws  of  Thought,  called  Identity,  Contradiction, 
and  "Excluded  Middle,  apply  alike  to  the  outer  world  and  to 
llie  mind.  If  so,  they  may  be  gathered  from  either  source 
Probably,  however,  the  supposition  is  that  these  laws  are  got 
at  without  investigation  ;  that  they  work  themselves  out  with- 
out being  expressly  studied.  We  unconsciously  and  irresistibly 
declare  that  the  same  thing  is  not  at  the  same  instant  white 
and  black  ;  just  as  we  walk  without  thinking  how  we  walk. 

These  invincible  tendencies  of  the  mind,  if  such  there  oe,  are 
no  doubt  facts  of  our  mental  naturft^)ut  so  is  our  belief  that 
Nature  is  uniform,  or  that  every  ^Oept^must  have  a  cause  ;  on 
which  reposes  all  Inductive  investigation.  In  both  cases,  the 
mind  is  the  instrument,  although  the  material  may  be  some- 
times mental  phenomena  and  sometimes  phenomena  of  the 
outer  world.  Deduction  and  Induction  have  equally  their  seat 
in  laws  of  the  thinking  mind ;  and  have  equally,  for  their 
field  of  operation,  both  mind  and  matter. 

(2)  The  next  position  is  this— The  Aristotelian  laws  are  laws 
oftlioughtas  it  o^ight  to  he;  the  Baconian  laws  are  laws  of 


hansel's   ARGUMENTa 


613 


nature  as  it  is.  The  author  adds,  as  explanatory  and  synonym- 
ous statements,  what  seems  to  involve  a  new  and  distinct  idea, 
namely,  that  the  one  rest  on  their  own  evidence,  the  other  on 
the  evidence  of  the  facts  concerned. 

To  this  we  may  reply  that  *  thought  as  it  ought  to  be  *  is 
certainly  not  confined  to  Formal  Reasoning.  Wherever  we 
think  wrong,  and  have  to  be  put  right,  we  are  in  the  domain 
of  *  thought  as  it  ought  to  be.*  Lord  Bacon's  inductive  logic 
professed  to  substitute  right  thinking  for  wrong.  We  commit 
fallacies  of  Deduction  and  of  Induction  equally  ;  and  if  Logic 
does  not  put  us  right  upon  both,  it  must  be  for  some  other  rea- 
son than  the  one  now  assigned. 

The  addendum  given,  professedly  to  explain  the  above  posi- 
tion, namely — that  the  Aristotelian  laws  are  self-evident,  and 
irreversible  in  thought,  while  the  Baconian  laws  are  inductions 
from  facts  and  contingent  or  reversible — is  merely  a  re-state- 
ment of  the  general  thesis  as  between  self-evident  or  necessary- 
truth,  and  inductive  or  contingent  truth. 

(3)  The  third  position  is  that  ths  Aristotelian  Logic  pro- 
ceeds from  the  law  to  the  facts,  constructing  types  or  genera- 
lities, and  rejecting  what  does  not  conform  thereto ;  while  in 
the  Baconian  Logic,  the  procedure  is  from  the /ac/5  to  the  law, 
rejecting  every  law  that  does  not  account  for  the  facts.  This 
is  a  direct  opposition  of  MetJwd. 

Now,  we  may  readily  grant  this  position.  But  what  is  its 
bearing  on  the  question  in  dispute  ?  The  methods  are  different, 
but  both  are  methods  of  arriving  at  truth  ;  both  may  be  alike 
in  want  of  precautions,  and  if  so,  both  may,  so  far  as  appears, 
equally  receive  attention  from  the  logician. 

(4)  The  fourth  position  is  perhaps  the  most  remarkable. 
It  is  this :  Law,  in  the  Aristotelian  system,  implies  a  conscious- 
ness of  obligation;  whereas,  in  the  Baconian  system,  Law 
means  only  uniform,  sequence. 

Here  is  that  confusion  of  thought,  so  well  pointed  out  by 
John  Austin,  in  connexion  with  the  term  *  Law,*  whereby 
there  is  introduced  into  the  order  of  natural  phenomena  the 
notion  of  authority  and  obedience.  Law,  as  regards  the  order 
of  nature,  whether  in  mind  or  matter,  is  purely  figurative  ;  it 
is  applicable  merely  as  expressing  uniformity  of  sequence ;  the 
Ethical  and  Political  definition — a  rule  set  by  intelligent 
superiors  to  intelligent  inferiors,  accompanied  by  the  infliction 
of  pain  on  neglect — cannot  be  transferred  to  the  sequences  of 
nature,  whether  mental  or  material ;  the  application  to  these 
contains  only  the  single  incident  of  law — uniformity.     There 


Q4A: 


THE  PROVINCE   OF  LOGIC. 


can  be  no  moral  right  or  wrong  in  Logic,  except  only  in  so  far 
as  we  are  all  morally  bound  to  seek  the  truth,  an  obligation 
extending  equally  to  truth  Deductive  and  to  truth  Inductiv©. 

(5)  A  tifth  position  maintained  by  the  author  is,  that,  in  the 
field  of  Thought,  the  cause  is  the  conscious  self;  the  effects,  the 
thoughts  produced  by  that  self,  through  its  own  power,  and 
under  its  own  laws.  To  which  we  may  reply,  that  both  causes 
and  effects  are  equally  self,  equally  mental,  but  not  thereby 
radically  contrasted,  in  manner  of  investigation,  with  external 
nature.  Cause  and  efiect  in  mind  must  be  discovered  induct- 
ively,  if  at  all.  Should  the  sequences  be  very  prominent,  little 
attention  may  suffice  for  their  discovery ;  but  that  does  not 
alter  the  method  of  proceeding. 

So  much  is  Mr.  Mansel  cai-ried  away  by  the  application  of 
the  term  Law,  in  its  Ethical  sense,  to  the  process  of  thinking, 
that  he  censures  Mr.  Mill  for  applying  *  physical  causation ' 
(meaning  uniformity  of  sequence,  ascertained  by  induction)  to 
the  moral  and  intellectual  world ;  as  if  there  ever  was  any 
other  mode  of  discovering  the  facts  and  laws  of  mind  than  the 
same  processes,  observation,  and  generalization,  that  apply  to 
the  material  world.  In  short,  he  brings  us  round  by  a  series 
of  verbal  ambiguities  to  the  question  of  Free- Will  and  Neces- 
sity, which  becomes  thus  a  principal  turning-point  of  the 
controversy  as  to  whether  Logic  should,  or  should  not,  be 
confined  to  Deduction. 

The  combined  force  of  these  five  positions  does  not  appear 
to  establish  either  of  the  two  allegations,  namely  (1)  that  a 
criterion  of  material  truth  is  not  only  impossible,  but  self- 
contradictory,  or  (2)  that  to  enlarge  the  field  of  Logic,  is  to 
assign  it  no  definite  field.  We  shall  not  here  attempt  a  direct 
reply  to  the  first,  inasmuch  as  the  exact  basis  of  inductive 
truth  will  be  fully  considered  in  another  place.  (Appendix  D.) 
The  second  allegation  is  a  challenge  to  assign  a  definite  boun- 
dary to  Logic,  while  over-stepping  the  limits  of  the  Formal 

Logic.  T         rm-  j_?      1 

Mr.  Mansel  puts  so  much  more  stress  on  the  Theoretical 
than  on  the  Practical  side  of  Logic,  that  he  would  not  be  satis- 
fied with  a  reply  based  on  the  practical  side.  Let  us  enquire, 
then,  whether  a  Theoretical  Logic,  embracing  Induction,  could 
be  laid  out  and  so  circumscribed  as  not  to  be  confused  with 
any  other  scientific  department,  such,  for  example,  as  Mathe- 
matics, Physics,  or  Psychology. 

In  the  Introduction,  we  have  indicated  a  field  of  Theoretical 
Logic,  according  to  the  larger  meaning  of  the  Province  ;    and 


SCOPE   OP  THEORETICAL  LOGIC. 


645 


in  Appendix  A,  we  have  given  Mr.  Spencer's  survey  of  the 
field  in  the  same  larger  meaning.  In  summary,  we  may  repeat 
the  topics. 

I.  The  Laws  of  Consistency,  or  Equivalence  of  Propositions, 
commonly  understood  as  the  Laws  of  Thoughts  These  give 
necessary  (in  the  sense  of  analytic)  inferences.  They  also 
give,  in  the  view  of  Hamilton  and  Mansel,  the  basis  of  the 
Syllogism. 

II.  The  Laws  of  Deductive  or  Mediate  Inference,  as  repre- 
sented by  the  Dictum  de  omni  et  nullo.  This  we  hold  to  be 
more  than  mere  Self-consistency,  or  Equivalence.  It  might  be 
called  Mediate  Consistency,  the  consistency  of  a  conclusion  with 
two  conjoint  premises,  as  contrasted  with  the  consistency  of 
an  equivalent  transmutation  of  a  single  proposition.  Mr. 
Mansel  would  hold  that  this  consistency  is  necessitated  and 
self-evident ;  and  such  an  impression  is  not  uncommon  with 
thinkers  generally.  In  opposition  to  that  view,  we  have  con- 
tended that  nothing  less  than  the  induction  of  material  in- 
stances would  justify  the  conclusion. 

III.  The  Law  of  the  Unifoumitt  of  Nature,  which  is  the 
basis  of  all  material  truth,  and  of  all  induction ;  consequently 
the  basis  of  the  syllogistic  axiom  of  mediate  consistency.  The 
consideration  of  this  law  may  well  precede  the  ordinary  sciences, 
for  it  is  an  assumption  running  through  them  alL  It  may,  there- 
fore, receive  its  first  announcement  in  the  science  that  deals 
with  the  criteria  of  all  truth,  namely,  the  separate  science  of 
Logic.  It  is  followed  out  into  a  series  of  formulae,  known  as 
the  Inductive  Canons,  which,  in  their  own  sphere,  may  be  com- 
pared with  the  syllogistic  forms,  in  the  Deductive  sphere. 

Now,  it  seems  to  us,  that  a  science  may  be  constructed  so  as 
to  include  the  Laws  and  Formulae  of  Immediate  Consistency, 
Mediate  Consistency,  and  General  Uniformity,  without  trans- 
gressing the  sphere  of  any  other  science.  It  need  not  ran  into 
Mathematics,  the  kindred  Formal  Science ;  it  need  not  trespass 
on  the  Physical  Sciences,  merely  because  it  considers  the  pos- 
tulate necessary  to  them  all,  that  is,  Uniformity ;  it  need  not 
run  into  Psychology,  although  it  derives  from  that  science  the 
explanation  of  the  ultimate  nature  of  Knowledge,  as  Difference 
and  Agreement.  And  there  does  not  appear  to  be  any  other 
conterminous  region. 

But  we  cannot  concede  to  Mr.  Mansel  that  Logic  is  essen- 
tially, or  in  the  main,  a  theoretical  science,  and  only  incident- 
ally practical.  We  contend  that  the  science  would  never  hkve 
"heen  called  into  existence,  but  for  its  supposed  practical  utility. 


646 


THE  PROVINCE   OF  LOGia 


Indeed,  the  same  might  be  said  of  its  splendid  giant  brother, 
Mathematics.  However  agreeable  and  recreative  to  some 
minds  may  be  the  contemplation  of  this  great  creation  of  ages, 
yet,  but  for  the  necessities  and  difficulties  of  measurement,  it 
would  never  have  been  heard  of.  Mr.  Mansel  supposes  a  race 
of  intelligent  beings,  subject  to  the  same  laws  of  thought  as 
we  are  now,  but  incapable  of  transgressing  these  laws  ;  and 
declares  that  in  the  presence  of  such  a  race,  the  Logic  of  the 
Formal  Concept,  Judgment,  and  Syllogism,  would  remain  the 
same.  Unfortunately  even  for  the  illustration,  there  is  a 
fallacy  of  Relativity  in  the  very  statement  of  the  case.  To  a 
being  that  never  committed  an  error,  truth  and  error  would 
be  alike  unmeaning ;  to  appreciate  the  valid  moods  of  the 
syllogism,  as  contrasted  with  the  invalid,  such  a  being  would 
have  first  to  be  told  of  an  erring  race,  capable  of  confounding 
the  two.  Only  after  Adam  fell  did  he  know  good  and  evil ; 
only  by  committing  fallacies  is  any  one  competent  to  under- 
stand Logic 

Postponing  for  a  little  the  enquiry  into  the  practical  utility 
of  the  Inductive  extensions  of  Logic,  we  shall  advert  more 
particularly  to  the  distinction  of  Form  and  Matter,  on  which 
so  much  stress  is  laid  in  the  present  dispute.  To  some  Formal 
Logicians  the  distinction  does  not  appear  in  all  respects  satis- 
factory. Thus,  Dr.  Thomson  (Outline  of  the  Laws  of  Thought, 
§  15)  remarks  : — *  The  philosophic  value  of  the  terms  matter 
and  form  is  greatly  reduced  by  the  confusion  which  seems  in- 
variably to  follow  their  extensive  use.  Whilst  one  writer  ex- 
plains form  as  '  the  mode  of  knowing '  an  object,  another  puts 
it  for  *  distinctive  part,*  which  has  to  do  with  the  being  or 
nature  of  the  thing  rather  than  with  our  knowledge  of  it ; 
where  it  means  *  shape  *  in  one  place,  which  is  often  a  mere 
accident,  in  another  it  means  *  essence ;'  so  that  it  may  be 
brought  to  stand  for  nearly  opposite  things.  I  will  add,  that 
probably  there  is  no  idea  which  these  terms  represent  that 
cannot  be  conveniently  expressed  by  others,  less  open  to  con- 
fusion/ 

Mr.  De  Morgan  says  : — *  When  it  shall  be  clearly  pointed 
out,  by  definite  precept  and  sufficiently  copious  example,  what 
the  logicians  really  mean  by  the  distinction  of  form  and  matter, 
I  may  be  able  to  deal  with  the  question  more  definitely  than 
I  can  do  at  this  time.'  (Cambridge  Transactions,  vol.  X.  Part 
IL  p.  8.)  Again,  *  The  truth  is,  the  mathematician  as  yet,  is 
the  only  consistent  handler    )f  the  distinction,  about  which, 


FORM  ANDMATTEU. 


617 


nevertheless,  he  thinks  very  little.  The  distinction  of  form 
and  matter  is  more  in  the  theory  of  the  logician  than  in  his 
practice  ;  more  in  the  practice  of  the  mathematician  than  in 
his  theory.'     (Syllabus,  p.  48). 

Hamilton  illustrates  Formal  Truth  in  Mathematics  thus: — 
*  To  the  notions  of  Space  and  Time,  the  existence  or  non- 
existence of  matter  is  indifferent.  If  matter  had  no  existence, 
nay,  if  space  and  time  existed  only  in  our  minds,  mathematics 
would  be  still  true ;  but  their  truth  would  be  of  a  purely 
formal  or  ideal  character, — would  furnish  us  with  no  know- 
ledge of  objective  realities/  (Logic  II,  p.  'o^).  But,  in  another 
place,  he  quotes,  with  approbation,  from  Esser,  a  passage  to 
the  effect  that  truth  consists  not  in  any  absolute  harmony  of 
thought,  but  in  the  correspondence  of  our  thoughts  with  their 
objects.  *  The  distinction  of  formal  and  material  truth  is  thus 
not  only  unsound  in  itself,  but  opposed  to  the  notion  of  truth 
universally  held,  and  embodied  in  all  languages.'  (Logic  I. 
106).  And  again  (Reid's  works,  p.  687),  he  remarks  of 
Reid's  criticism  on  the  Predicables,  that  Reid,  like  our  British 
philosophers  in  general,  was  unaware  of  the  difference  between 
the  Logical  or  Formal^  and  the  Metaphysical  or  Real.  The 
Predicables  are  forms  or  modes  of  predication,  and  not  tilings 
predicated :  in  the  language  of  the  schools,  second  notions,  not 
first.' 

Let  us  adopt  Mr.  de  Morgan's  suggestion,  and  refer  to 
Mathematics  for  examples  of  Form,  in  the  opposition  to  Matter. 
In  so  doing,  however,  we  are  merely  taking  up  an  old  subject 
under  a  new  name.  In  Mathematics,  we  have  the  most  com- 
plete development  of  reasoning  by  Symbols,  called  also  Abstract 
reasoning.  There  will  be  other  opportunities  for  examining 
the  special  processes  of  Mathematics  (Logic  of  the  Sciences, 
Mathematics).  For  the  present,  let  us  note  what  bears  upon 
the  question  before  us.  The  abstractions  of  Mathematics,  like 
all  other  abstractions,  are  embodied  in  concrete  instances  ;  the 
Form  is  always  given  in  some  kind  of  Matter.  But  the 
matter  needed  is  so  very  spare  and  attenuated,  that,  by  a 
stretch  of  language,  we  may  say  it  is  no  matter  at  all.  Yet, 
the  circles  of  Euclid  are  circles  of  printer's  ink ;  they  have 
colour  and  a  definite  size.  If  we  compare  them  with  the 
round  shield  of  Achilles,  or  a  gorgeous  centre  ornament  in  the 
roof  of  a  palace,  we  may  describe  them  as  void  of  matter  and 
substance  ;  but  they  have  their  own  substance,  nevertheless. 

The  symbols  of  Arithmetic  (still  more,  of  Algebra)  are 
material,  although  their  peculiar  shape  has  nothing  representa- 


i  ii 


648 


THE  PKOVINCE  OF  LOGia 


tive  in  it.  They  are  the  signs  of  concrete  f^fr'^^^l^^Z^ 
three-which  are  inconceivable  by  ns,  except  m  concrete 
nstances.  The  sin^plest  material  will  answer  tbe  PYPOse- 
bread  crumbs,  pebbles,  mud  specks;  but  we  mnst  have  m  the 
mind,  a  series  of  discrete  impressions,  derived  somehow  or 
^ther  ;  even  thoughts  wonld  do ;  but  we  find  it  easier  to  work 
upon  things  of  sense.  Without  some  concrete  bas.8,  we  cannot 
JLess  i/ thought  any  number  whatever  This  is  merely  to 
repeat  the  received  nominalistic  view  of  Absti-act  Ideas. 

There  is,  however,  an  important  step  that  can  be  made  in 
Mathematical  R^^sonings,  whereby  we  can  altogether  leave  out 
of  si-ht  the  concrete  things  (which  is  to  refrain  from  reahzmg 
the  verv  meanings  of  the  numbers  that  we  are  handhng).  We 
can  devise  r.Zes  0/  operating  upon  the  symbols,  which,  when 
Tuly  cortructed  Ld^hecked  by  the  P-per  precautions,  wiU 
give  us  the  same  results  as  actual  experiments  upon  the  con- 
Crete  numbers.  Having  constructed  our  aecimal  notation, 
^e  can  base  upon  it  a  m^tiplication  table,  containing  equiva- 
knt  formations  of  numbers;  and  by  mere  force  of  memory, 
recalling  these  symbolical  equivalents,  we  can  perform  opera- 
Jfls  of  multiplying,  without  thinking  of  the  concrete  numbers 
at  all  Tn  gettfng  out  the  product  of  94  by  116,  we  ^^^  ^^^^^ 
the  world  of  numbered  realities  out  of  view  for  the  time  :  coxn- 
ing  back  to  it  only  when  the  product  has  to  be  practically 

^"^  Not ,*by  this  dwelling  among  symbols,  and  rules  and  signs 
of  operLtion,  we  are  as  far  away  from  Matter,  or  thmgs  m  the 
concrete,  as  we  can  possibly  be.  If  anything  represents  pure 
Form,  the  multiplication  table  does.  The  higher  operations  of 
Algebra  keep  us  for  longer  periods  withdrawn  frona  concrete 
feality;  but  the  principle  is  the  same.  The  symbolical  creations 
are  mo;e  numerous,  the  rules  of  operation  more  complicated, 
the  operations  themselves  more  protracted  ;  yet  there  is  no- 
thine  new  in  the  principle  of  working. 

The  question  then  arises,  Do  these  rules  of  operation  upon 
eymbols  bear  out  the  pretensions  of  Formal  Logic,  as  to  th^ 
self-evident,  necessary,  and  non-material  character  of  Formal 
Thinkincr  ?  Are  all  such  rules,  in  their  origm,  completely 
withdrawn  from  the  tests  of  concrete  experience,  as  ^^y  are  in 
the  working  ?  The  full  answer  to  this  question  is  the  theory 
of  Deductive  Reasoning  in  general,  and  of  Mathematical  Rea- 
soning in  particular.  It  is  enough  here  t«  make  two  observa- 
tions  First.  If  it  be  true,  as  the  a  i^osfmon  thinkers  maintain, 
that  the  final  axioms  of  all  Mathematics,— on  which  repose  the 


FORMAL   RULES  OF  OPERATION. 


649 


rules  for  Arithmetical  sums,  for  Algebraic  equations,  and  for 
Geometrical  demonstrations, — are  inductions  from  experience, 
then  these  various  rules  of  operation  have,  after  all,  a  purely 
material  source,  and  are  not  evolved  by  the  mind  iu  abstraob 
or  formal  thinking. 

But  secondly.  It  is  notorious  and  undeniable,  that  the  rules 
of  operation,  before  they  are  trusted  to,  are  tried  and  checked 
by  the  results.  A  great  many  of  them  are  so  paradoxical,  so 
unpromising,  and  even  repugnant,  to  the  ordinary  mind,  that 
they  are  admitted  only  because  of  their  being  instrumental  in 
bringing  out  true  results  (as  proved  by  reference  to  the 
matter).  Who  would  put  faith  in  such  a  rule  as  *  minus  mul- 
tiplied by  minus  gives  plus,'  unless  fully  assured  by  concrete 
trials  that  it  leads  to  correct  conclusions  ?  The  impossible 
quantities  of  common  Algebra,  the  infinitesimals  of  the  higher 
Calculus,  have  been  a  perpetual  stumbUng-block,  as  regards 
their  Form  ;  their  sole  justification  is  the  test  of  actual  facts. 

Seeing  how  many  ingenious  tricks  can  be  played  upon  us 
by  formulas  and  formalities,  the  most  unexceptionable  in  their 
appearance,  there  probably  is  not  a  single  rule  in  the  whole 
compass  of  Mathematics  that  any  reflecting  person  would  trust 
to  merely  as  a  *  Law  of  Thought,*  without  an  appeal  to  the 
matter  by  actual  trials.  The  reason  why  we  are  so  confident 
in  these  rules,  is  that  their  verification  is  so  easy,  and  has  been 
so  complete.  But  in  the  absence  of  verification,  we  should  be 
very  chary  indeed  in  admitting  such  rules  as  the  multiplica- 
tion and  division  of  fi:uctions,  vulgar  and  decimal,  the  extrac- 
tion of  the  cube  root,  and  the  like.  We  have  often  been 
deceived  by  more  plausible  formalities  than  these  ;  dolus  latet 
in  generalihm,  is  true  of  all  alleged  *  Laws  of  Thought* 

The  same  remark  as  to  the  necessity  of  inductive  verifica- 
tion applies  to  Logical  Forms.  Not  one  of  the  valid  moods 
would  be  received  by  mankind  upon  formal  evidence  alone. 
The  dictum  seems  very  evident,  the  nota  noice  even  more  evi- 
dent ;  but  the  nota  notce  conducts  us  most  plausibly  to  false 
conclusions,  until  by  examination  of  the  actual  cases  we  have 
laboriously  fenced  it  with  circumlocutions  and  qualifications. 

When  we  examine  carefully  the  various  processes  in  Logic, 
we  find  them  to  be  material  to  the  very  core.  Take  Conversion. 
How  do  we  know  that,  if  No  X  is  Y,  No  Y  is  X  ?  By  exam- 
ining cases  in  detail,  and  finding  the  equivalence  to  be  true. 
Obvious  as  the  inference  seems  on  the  mere  formal  ground,  wo 
do  not  content  ourselves  with  the  formal  aspect.  If  we  did, 
we  should  be  as  likely  to  say.  All  X  is  Y  gives  All  Y  is  X ;  we 


650 


THE    PROVINCE  OF  LOGia 


VALUE   OF  A  LOGIC   OF   INDUCTION. 


651 


f 


ii 


are  prevented  from  this  leap  merely  by  the  examination  of  . 

""^Again,  the  laws  of  Hypothetical  Equivalence  ^f /^P^^f,^^^ 
on  our  knowledge  of  the  material  circumstance  called  Plurality 
of  Causes,  but  for  which  the  formal  directions  as  to  Hypo- 
thetical Inference  would  be  quite  different. 

Mr.  Mansel  complains  that  the  rules  of  Definition  commonly 

ffiven  in  logical  treatises  are  extra-logical ;  that  is,  they  step 

out  of  Form  into  Matter.     The  charge  is  well  founded ;  the 

writers   obviously   felt   that   Definition,   confined   withm   tbe 

narrow  limits  of  the  Formal,  would  be  a  very  meagre  afiair. 

What    would    be    logical    defining   in    strict  form  f      W  by, 

this.     A  Formal  Definition  consists  in  giving,  as  the  marks  oi 

the  thing  defined,  the  marks  of  some  higher  Genus,  together 

with    the   Difference.      We   have,    then,   these   forms  :--The 

Genus  together  with  the   Difference  (in  Connotation)  is  the 

Species  ;   the  Species  minus  the  Difference  is  the  Genus  ;  the 

Species  m/m(.  the  Genus  is  the  Difference.     This  is  the  whole 

theory  of  Defining,  according  to  Formal  L.^gic  ;  and  it  is  worth 

""""stilfmore  would  a  logic  of  Classification,  tobe  of  any  value, 
trench  upon  material  considerations.  Logical  Div^^sion  is 
another  name  for  classification.  The  rules  of  Logical  Division 
are  Formal,  but  they  have  to  be  held  in  check  by  the  matter, 
otherwise  they  may  lead  us  astray. 

It  may  be  maintained  that  Deduction  and  Induction  are 
properly  conilnuous  operations;  they  are  the  parts  ol  one 
whole.  Within  certain  small  limits,  Deductive  processes  are 
possible,  upon  rules  of  symbolical  operation  solely,  these  having 
been  well  fenced  by  a  study  of  the  matter  ;  but  real  deduction, 
the  extension  of  a  principle  to  new  cases,  supposes  an  exami- 
nation  of  the  cases  in  their  concreteness  or  ac tn ah ty,  exactly 
as  in  the  inductive  generahzation  of  the  rule.  The  judge  who 
applies  the  law  must  look  to  the  matter ;  he  must  not  commit 
paralogisms  of  form  ;  but  he  cannot  stop  short  at  mere  tormal 

correctness.  .  ,  _  ,       ,       i^„  ^z? 

Within  the  Inductive  sphere,  we  might  construct  rules  ot 
Formal  operation,  such  as  ought  to  commend  themselves  to  a 
ripid  formalist.  Thus,  A,  B,  and  C,  being  joint  causes  ot  an 
effect  X  ;  if  A  be  reduced  in  amount,  B  or  C  must  be  corres- 
pondingly  raised  to  keep  up  the  effect ;  if  A  be  increased,  the 
others  are  so  far  dispensed  with,  and  so  on.  These  are  easy 
mathematical  considerations,  which  we  know  to  be  correct 


generally,  and  can  therefore  use  formally  without  regard  to 
the  matter. 

But  the  question  at  issue  cannot  be  adequately  stated,  unless 
we  view  Logic  as  a  Practical  Science.  If  its  practical  charactei 
is  conceded,  the  propriety  of  extending  the  Province  rests 
upon  the  utility  of  rules  for  Induction.  The  presumptions  in 
favour  of  such  rules  are  these  : — 

First.  It  is  admitted  that  Aristotle  included  in  his  scheme 
both  Deduction  aud  Induction,  however  imperfect  may  have 
been  his  view  of  their  respective  spheres,  and  however  inade- 
quate may  have  been  his  handling  of  Induction.  Thus,  the 
testimony  of  the  Founder  of  Deductive  Logic  is  opposed  to  its 
exclusive  pretensions. 

Secondly.  In  the  table  of  Fallacies,  sketched  by  Aristotle, 
and  retained  by  the  scholastic  logicians,  with  sHght  modifica- 
tions, there  are  comprised  Fallacies  of  the  Matter,  and  of 
these  some  are  fallacies  of  Induction  [non  causa  pro  causa,  8fc.), 
From  this  we  may  infer,  that,  in  the  opinion  of  logicians 
generally,  people  are  liable  to  commit  mistakes  in  regard  to 
matter,  no  less  than  in  regard  to  form.  We  may  infer  farther, 
that  it  is  not  useless  to  give  a  reminder  of  these  material  and 
inductive  mistakes,  which  is,  in  fact,  a  Logic  of  Induction. 

Thirdly.  The  scholastic  period  was  marked  by  an  almost 
exclusive  attention  to  the  formal  or  Syllogistic  part  of  Logic. 
At  the  revival  of  letters  and  philosophy  in  the  15th  and  IGth 
centuries,  public  opinion  revolted  against  the  narrowness  of 
the  conception,  and  found  a  spokesman  in  Bacon,  who  inaugu- 
rated, amid  very  general  applause,  a  Logic  of  Induction.  For 
the  last  two  centuries  and  a  half  it  has  been  the  pride  of 
both  physical  and  metaphysical  philosophers  to  call  themselves 
his  disciples  as  regards  the  methods  of  pursuing  science  and 

philosophy. 

Fourthly.  The  renovated  Physics,  or  Natural  Philosophy,  ot 
Galileo  and  Newton  was  accompanied  with  a  professed  Logic 
of  Induction—the  famous  Eegnlcs  Philosophandi  prefixed  to 
the  Third  Book  of  the  Princlpia.  These  rules,  meagre  as  they 
are,  were  a  guiding  star  in  physical  research  to  the  enquiries 
of  the  18th  century. 

Fifthly.  In  the  present  day,  when  physical  science  has  been 
BO  far  advanced  as  to  exemplify  sound  methods  of  procedure, 
the  most  distinguished  physical  philosophers  still  feel  and  ac- 
knowledcre  the  need  of  a  systematic  guide  to  research,  for  the 
more  abstruse  and  subtle  departments.     The   Introduction  to 


652 


THE  PROVINCE  OF  LOGia 


BASIS  OF  RELATIVITY. 


653 


^k 


Natural  Philosophy,  by  Sir  John  Herschel,  and  the  History 
and  Logic  of  the  Inductive  Sciences,  by  the  late  Dr.  Whewell, 
are  testimonies  to  this  want. 

Sixthly.  Since  the  publication  of  the  work  of  Mr.  John 
Stuart  Mill,  in  which  the  Inductive  Logic  is  methodized  with 
a  completeness  previously  unknown,  applications  have  been 
extensively  made  of  the  Inductive  canons  to  the  Experimental 
Sciences.  The  investigations  of  lledical  science  have  especi- 
ally profited  by  Mr.  Mill's  teaching  ;  a  higher  and  surer  stan- 
dard of  evidence  has  taken  the  place  of  the  loose  methods  of 
reasoning  formerly  prevalent. 

Seventhly.  The  Science  of  Politics  is  an  equally  striking  ex- 
ample. The  valuable  work  of  Sir  George  Cornwall  Lewis  on 
the  '  Methods  of  Observation  and  Reasoning  in  Politics,'  makes 
perpetual  reference  to  the  Inductive  Logic  of  Bacon,  Her- 
schel, Whewell,  and  Mill,  and  only  once  or  twice  alludes  to 
Formal  Logic,  although  the  author's  education  was  such  as  to 
incline  him  to  view  that  department  with  the  utmost  possible 
favour.  He  complains  strongly  of  the  wide-spread  abuse  of 
the  Method  of  Agreement  (the  enumeraiio  simplex  of  Bacon) 
in  Politics,  as  in  other  snbjects ;  and  endeavours  by  precept, 
and  by  example,  to  counterwork  the  vicious  tendency. 

Eighthly.  Sir  William  Hamilton  occupies  a  considerable 
portion  of  his  Course  on  Logic  (nine  Lectures  out  of  Thirty- 
six),  with  Modified  Logic,  in  which  he  considers  Truth  and 
Error,  on  the  material  side ;  Observation  ;  Induction ;  the 
Credibility  of  Testimony ;  and  various  other  points  related  to 
the  acquisition  and  communication  of  knowledge.  The  plan 
of  his  course  would  have  allowed  him,  without  contradicting 
bis  views  of  the  Province  of  Logic,  to  have  gone  as  minutely 
as  Mr.  Mill  does,  into  Induction,  and  the  operations  subsidiary 
to  Induction,  such  as  Classification  and  Naming. 

Dr.  Thomson,  in  his  Laws  of  Thought,  follows  the  example 
of  Hamilton,  in  the  enlargement  of  the  Province.  In  Part  IV., 
entitled  *  Applied  Logic,'  he  considers  (shortly)  the  Search  for 
Causes,  the  Inductive  Methods,  Definition,  Analogy,  Chance, 
Classification,  Fallacies  generally,  and  the  Division  of  the 
Sciences. 

C— ENUMERATION   OF  TIIINGS. 

The  Classification  of  Names  (p.  61)  leads  by  a  natural 
transition  to  the  Classification  of  Things.  Moreover,  in  order 
to  establish  the  most  generalized  propositions,  we  must  possess 
correspondingly  generalized  Notions. 


The  totality  of  Existing  Things  may  be  divided  in  yarious 
ways,  under  difierent  principles  of  classification  and  division. 
We  may  partition  the  whole  universe  into  Celestial  Bodies 
and  Terrestrial  Bodies  ;  into  Minerals,  Plants,  Animals  ;  into 
Solid,  Liquid,  Gas  ;  into  Ponderable  and  Imponderable  ;  into 
the  Four  Elements  of  the  ancients,  which  division  crudely 
gives  the  three  states  of  matter,  and  the  imponderables — Heat, 
Light,  &c.  Lastly,  we  may  make  a  division  into  Matter  and 
Mind.  These  various  modes  of  sub-dividing  the  totality  of 
things  are  useful  for  their  special  purposes.  The  purpose  of 
the  Logician  is  to  arrive  at  a  division  that  will  correspond  to 
the  distinct  methods  of  enquiry,  so  as  to  partition  the  field  of 
knowledge  according  to  the  best  division  of  intellectual  labour. 

We  begin  by  re-stating,  as  an  essential  preliminary,  the 
principle  of  Universal  Relativity,  by  which  all  objects  of  know- 
ledge are  two-sided,  or  go  in  couples.  This  statement  is 
necessary  to  obviate  the  error,  committed  by  Aristotle  and 
others,  of  placing  *  Relation  '  in  an  inferior  or  subordinate 
place  in  the  classification.  If  Relation  is  recognized  at  all,  it 
is  fundamental  and  independent ;  everything  comes  under  it, 
it  comes  under  nothing.  The  supreme  position  given  by 
Logicians  to  the  *  Law  of  Contradiction  '  is  a  mode  of  admit- 
ting this  primary  fact 

I.  The  deepest  of  all  Relations  is  Object  and  Subject,  com- 
monly called  Mind  and  Matter,  the  External  World  and  the 

Internal  World. 

When  we  pass  from  being  engrossed  with  pleasure  or  pam 
to  the  consciousness  of  some  extended  thing,  as  a  tree,  we  are 
affected  with  a  marked  shock  of  difference ;  we  have  made  a 
transition  the  broadest  and  deepest  that  the  mind  can  ever 
pass  through.     These  typify  the  two  ultimate  or  final  modes  of 
the  human  consciousness  ;  they  mutually  constitute  each  other, 
on  the  principle  of  Difference  or   Relativity;    they   cannot, 
therefore,  be  resolved  one  into  the  other,  or  into  any  more 
fundamental  experience.      The  contrast  must  be  accepted  as 
the  chief  division  of  all  things,  on  the  principle  of  dividmg 
upon  the  maximum  of  difference.     One  portion  of  knowledge 
we   term   the   Object   world,  the    Extended   World,  and,  less 
correctly.  Matter,  and  the  External  World.     The  other  portion 
we  call   the  Subject  world,  the   Unextended  Mmd,  and,  less 
properly,  the  Internal  World.     Indeed,  when  we  talk  of  these 
two  departments  as  dividing  between  them  the  universe  of 
existence,  we  are  using  fictitious  and  unmeaning   language; 
the  ultimate  universe,  according  to  the  law  of  Relativity,  is  a 


654: 


ENUMERATION  OF  THINGS. 


couple :  the  highest  real  grouping  of  things  is  this  two-fold 
grouping,  called  Object  and  Subject,  &c.  These  are  the 
proper  summa  genera.     Existence  is  a  mere  name. 

11.  Object  has  been  variously  represented  and  analyzed. 
Some  have  contended  that  it  is  an  ultimate  fact,  given  in  our 
earliest  consciousness.  Others  have  resolved  it  into  simpler 
states  of  the  mind.  The  different  views  on  this  subject  be- 
long to  the  Metaphysical  and  Psychological  question  called 
the  'Theory  of  External  Perception.'  We  here  assume  that  the 
notions  expressed  by  *  Object'  and  *  Subject,'  can  be  analyzed 
and  we  give  one  mode  of  the  analysis.  Object  means  (1) 
what  calls  our  muscular  and  bodily  energies  into  play,  as  opposed 
to  passive  feelings  ;  (2)  the  uniform  connexion  of  definite  feel- 
ings with  definite  energies,  as  opposed  to  feelings  unconnected 
with  energies ;  and  (o)  what  affects  all  minds  alike,  as  opposed 
to  what  varies  in  different  minds. 

(1)  The  greatest  antithesis  existing  among  the  phenomena 
of  our  mental  constitution  is  the  antithesis  between  the  Active 
and  the  Passive ;  the  muscles  (with  tlie  out-carrying  nerves) 
being  the  bodily  instniment  for  the  one,  the  senses  (with  the 
in-bringing  nerves)  being  the  bodily  instrument  for  the  other. 
To  this  fundamental  antithesis  we  are  able  to  link  the  opposi- 
tion of  Object  and  Subject.  Although  developed  by  other 
circumstances,  the  contrast  appears  to  be  rooted  in  our  greatest 

Psychological  contrast.  /?   •    i      i.         a 

(2)  The  circumstance  of  our  feelings  being  definitely  changed 
with  dctinite  active  exertions  on  our  part  is  a  most  notable  ac- 
companiment of  our  objectivity.  When  we  move  across  a 
room,  and  feel  our  optical  prospect  definitely  changing  with 
every  step,  and  always  going  through  the  same  definite  changes 
with  the  same  movements,  we  put  this  experience  m  contrast 
with  feelings  that  fluctuate  when  we  are  perfectly  still,  and 
have  no  relation  to  our  movements ;  as  the  stages  of  an  illness, 
the  periodic  sensations  of  hunger  and  fatigue,  and  the  various 

passions  and  emotions.  ,    ^  j.«.        j. 

(8)  It  is  a  characteristic  of  the  Object  world,  that  dilierent 
persons  are  afiected  in  the  same  way.  Those  definite  changes  of 
sense,  accompanying  definite  movements,  as  in  walking  down 
a  street,  or  in  entering  a  room,  arise  in  each  person  alike ;  the 
other  class  of  feelings— hunger,  fatigue,  fear— run  a  different 
oourse  in  different  persons. 

These  are  probably  the  main  features  of  the  fundamental  con- 
trast of  Subject  and  Object;  other  subsidary  circumstances  have 
been   pointed  out,  but  their  discussion  is  not  suitable  to  this  place. 


ATTRIBUTES   OF  BOTH   OBJECT  AND   SUBJECT. 


655 


III.  The  Subject  is  explained  by  what  has  been  said  of  the 
Object ;  it  concerns  our  passive  states ;  our  feelings  not  de- 
finitely changed  with  definite  energies ;  and  the  states  wherein 
different  persons  vary  in  the  same  circumstances. 

IV.  There  are  attributes  common  to  Object  and  to  Subject, 
and  attributes  special  to  each. 

Notwithstanding  the  fundamental  contrast  of  these  two  ex- 
periences, we  can  affirm  some  attributes  of  both.  Thus,  within 
the  sphere  of  each,  we  are  variously  affected ;  we  recognize 
object  distinctions  and  subject  distinctions.  So  we  identify 
and  compare  object  facts  with  one  another,  and  subject  facts 
•with  one  another.  From  the  very  nature  of  human  know- 
ledge, these  possibilities  of  discerning  agreement  and  difference 
must  hold  in  both  departments.     Hence  : — 

First.  The  contrasting  attributes  of  Likeness  and  IJnlike- 
NESS  belong  equally  to  Object  states  and  to  Subject  states.  We 
identify  and  discriminate  magnitudes,  forms,  colours,  &c., 
which  are  object  facts ;  we  identify  and  discriminate  pleasures, 
pains,  volitions,  ideas,  which  are  subject  facts.  Hence,  affir- 
mations of  likeness  or  of  unlikeness  may  apply  to  every  kind 
of  knowledge  whatsoever.  Being  in  fact  the  fundamental  cir- 
cumstances that  define  and  constitute  knowledge,  such  affirma- 
tions are  analytical  propositions. 

Secondly.  Quantity  or  Degree  belongs  to  both  states.     This 
is  Ao'reement  and  Difference  in  one  important  fact  or  feature, 
called  more  and  less ;   the  states  of  the  subject  mind  are  all 
of  varying  amount  or  intensity,  as  well  as  the  states  of  the 
object  consciousness,   which  we  call  object  properties —size, 
weight,  hardness,  &c.     We  may  and   do  predicate  quantity, 
therefore,  of  everything  knowable.     The  laws  of  Quantity,  of 
which  Mathematics  is  the  complete  developement,  pervade  all 
modes  of  existence.     It  is  true  that  numerical  calculations  are 
mostly  confined  to   object  properties — as  space,   dimensions, 
weif^ht,  and  so  on ;  we  have  no  numerical  ratios  in  pleasures 
and  pains.       This  circumstance,    however,   which  is  a  groat 
drawback  to  the  science  of  mind,  is  not  due  to  the  absence  of 
degree  from  mental  phenomena,  but  springs  from  our  inability 
to  set  up  an  exact  common  standard  of  degree  in  the  states  of 
the  mind,  and  to  take  precise  measures  according  to  that  stan- 
dard.     We  are  conscious  of  inequalities  in   our  pleasures, 
emotions,  and  desires,  but  we  have  a  difficulty  in  fixing  the 
degrees  in  an  understood  expression,  feuch  as  may  be  commoni- 
oated  to  others,  and  permanently  recorded. 

It  is  nsnal  to  specify  the  leading  modes  of  Quantity  under 


,-f 


\ 


\ 


656 


BNUMERATION   OF  THINGS. 


Intensity,  Duration,  and  Extension :  the  last  being  a  mode 
special  to  the  object.  Intensity  and  Duration  apply  in  both 
regions  of  phenomena.  Iniemitxj  is  usually  marked  with  re- 
gard to  each  special  property— intensity  in  colour,  heat,  pres- 
sure,  &c.  DuTdiion,  which  is  a  degree  of  contmuance,  is  more 
commonly  abstracted  from  things,  and  enters  into  that  great 
and  all-comprehending  generality,  called  Time,  to  be  noticed 
more  fully  under  next  head. 

Thirdly.  The  great  and  important  contrast  named  Lo-exist- 
BNCE  and  Succession  is  found  in  both  departments  of  pheuo- 

Co-existence  is  not  an  ultimate   experience  of  the  mind. 
We  begin  with  modes  of  Succession,  which  are  developed  mto 

Co-existences.  . 

To  the  mind,  which,  with  very  shght  qualification,  can 
attend  to  but  one  thing  at  a  time,  all  distinctive  stotes  of  con- 
sciousness  are  successive.  Succession  is  the  law  of  our  mental 
being  The  succession  may  be  rapid  or  slow,  which  supposes 
the  estimate  of  duration  above  noticed.  In  succession  is 
grounded  the  important  fact  caUed  Number  or  Discrete  ^ nan- 
tity,  as  opposed  to  the  measure  of  continuance,  or  Continuous 
Quantity.  We  identify  groups  of  successions  as  twos,  or 
threes,  fours,  and  so  on.  Thus  the  forms  and  modes  of  Quan- 
tity are  involved  in  the  modes  of  succession  of  our  sensations, 

feelings,  and  thoughts.  ,     ^    i        ,    i  i-i 

Duration  and  Succession  (with  Number)  thus  belong  alike 
to  states  of  the  Object  and  states  of  the  Subject.  The  element 
of  Time,  which  is  duration  and  succession  generalized  to  the 
utmost,  and  reduced  to  a  common  measure,  is  a  property  of 
both  worlds  ;  a  circumstance  that  has  been  noticed  from  the 
very  beginning  of  philosophy.  c     -    -*. 

The  predicate  of  Succession  also  involves  order  ot  priority, 
which  can  apply  to  object  and  to  subject  states  equally. 

Co  existence  is  an  artificial  product,  a  peculiar  mode  of  suc- 
cession, which  in  its  highest  form  is  Simultaneity  in  Space,  or 
Extension,  a  property  of  the  Object  sphere  exclusively.  There 
attaches  to  Mind  an  inferior  mode  of  Co-existence,  the  co- 
existence of  two  or  more  awakened  sensibilities  atone  moment 

of  time.  ,  ,_        .1       T  1 

Of  Attributes  common  to  both  spheres,  we  have  thus  ljik&- 
Unlike,  Quantitv,  Succession,  Co-existence ;  but  as  the  predi- 
cation of  Like-Unlike  in  the  widest  sense  is,  from  the  nature 
of  knowledge,  a  purely  identical  proposition,  we  need  state 
only  Quantity,  Succession,  and  Co-existence.     These  are  the 


ATTRIBUTES  SPECIAL  TO  THE  OBJECT. 


657 


three  attributes  assumed  as  distributing  knowledge  into  differ* 
ent  heads  of  Logical  Method. 

V.  The  attributes  special  to  the  Object,  are  as  follows  : — 

(1)  Extension. — This  property  is  the  fundament^il  circum- 
stance of  the  object  world,  the  one  fact  common  to  whatever 
is  not  mind,  or  not  subject.  When  we  are  in  a  purely  subject 
state,  as  a  pleasure  or  a  pain,  we  have  no  consciousness  of  ex- 
tension or  space.  The  distinction  between  extended  matter 
and  the  unextended  mind,  explicitly  made  in  the  5th  century, 
A.D.,  was  the  commencement  of  correct  views  of  mind  and 
matter. 

Psychologically  considered.  Extension  is  a  mode  of  our  active 
or  moving  energies,  assisted  by  our  senses.  Motion  is  essen- 
tial to  the  consciousness  of  things  as  extended.  Extension  is 
a  real  property  whether  with  or  without  matter  ;  as  scope  for 
motion,  even  empty  space  is  an  actuality.  The  total  of  the 
Extended  World  is  sub-divided  into  Extended  Matter  and 
Extended  Space  without  matter. 

(2)  Besistance,  Inertia,  Momentum,  or  Force. — This  is  the 
characteristic  property  of  Extended  Matter,  in  its  opposition 
to  an  Extended  void.  The  putting  forth  of  our  energies  in 
the  peculiar  mode  called  Eesistance  is  perhaps  the  simplest 
situation  that  we  can  be  in,  as  regards  the  active  side  of  our 
being ;  hence,  resistance  may  be  considered  our  fundamental 
consciousness  of  the  object  world.  Resistance  is  Matter ;  the 
giving  way  of  resistance,  followed  by  movement,  is  Space.  In 
no  subject  state  have  we  the  peculiar  sensibility  called  force, 
energy,  or  resistance  ;  where  that  feeling  is  present,  we  apply 
the  name  matter.  i 

Extension  and  Inertia  are  the  two  generic  facts  entering  into 
the  long  known  group  of  attributes  called  the  jprimai-y  qualities 
of  matter;  the  radical  and  identifying  peculiarities  of  the 
so-called  external  and  material  world.  Still,  these  are  in  close 
association  with  other  properties,  based  on  passive  sensibility, 
or  sense  proper,  as  colour,  tactile  feeling,  &c.  {secondary 
qualities);  which  properties,  of  themselves,  would  not  be 
object  properties,  but  become  so  by  their  dependence  upon  the 

object  class. 

(3)  Colour. — The  pure  and  proper  sensibility  of  the  eye,  the 
susceptibility  to  mere  light,  is  not  properly  an  object  fact. 
The  conjunction  of  the  feeling  with  visual  extension  (the  mus- 
cular sensibility  of  the  eye),  and  with  locomotion,  is  necessary 
to  give  objectivity  to  light  and  colour.  Our  notion  of  the 
extended  or  simultaneous  in  space  is  based  on  movements,  but 


658 


ENCMEKATION   OF  THING3. 


filled  up  and  defined  by  our  optical  sensibility  to  varieties  of 
light.  Our  feelings  of  illumination  are  definitely  connected 
with  definite  movements  and  in  that  way  comply  with  one  of 
the  grand  conditions  of  objectivity. 

(4)  Touch. — The  commonly  recognized  sense  of  Touch  is  a 
compound  of  muscular  energy  with  pure  skin  sensibility. 
This  last,  or  touch  proper,  is  scarcely  ever  separated  from  the 
fundamental  experience  of  Force  or  Resistance  (we  may  make 
the  separation  by  supporting  the  outstretched  arm  or  leg). 
Hence,  touch  is  adopted  and  embodied  among  object  properties. 
The  tactile  efiects,  called  hard,  soft,  rough,  smooth,  are  quali- 
ties of  Matter. 

Sight  and  Touch  are  the  senses  most  completely  incorporated 
with  our  activity,  or  with  our  object  experience.  The  remain- 
ing senses  have  a  looser  connexion  with  our  energies,  but,  so 
far  as  connected,  we  rank  their  indications  among  object 
qualities. 

(5)  Sound. — More  noise  might  be  a  form  of  simple  subjec- 
tivity. When  related  to  movements,  as  when  steadily  increasing 
or  diminishing  with  our  locomotion,  it  fiills  into  a  connexion 
with  objectivity.  So  regularly  is  this  connexion  observed,  that 
the  fact  is  enrolled  among  properties  of  matter. 

(6)  Odour.— An  exact  parallel  to  Sound.  The  objectivity 
of  odour  is  established  by  its  definite  changes  under  definite 
movements  on  our  part. 

(7)  Taste. — There  is  here  a  compound  of  a  peculiar  sensibility 
-—the  proper  gustatory  feeling — with  touch  proper ;  whence 
it  comes  readily  into  the  object  sphere. 

(8)  Heat  and  Cold. — This  property  needs  no  other  comment 
than  the  foregoing  remarks  on  Sound  and  on  Odour. 

The  various  organic  sensibilities  of  our  body — Digestion, 
Respiration,  &c. — have  a  strongly  subject  character;  yet,  they 
contract  object  relationships  whenever  they  are  definitely 
changed  with  definite  movements,  as  when  we  connect  reple- 
tion  with  taking  food,  or  suffocation  with  impeded  breathing. 
But,  in  so  far  as  they  suggest  no  activities,  or  attitudes  of 
energy,  they  are  pure  subject  states,  modes  of  self-consciousness. 

These^  are  the  various  sensible  properties  of  the  species 
'matter'  in  the  genus  'extended;'  they  are  the  modes  of 
primitive  sensibility  that  we  call  material.  There  are  other 
properties  of  a  more  subtle  and  abstruse  kind,  arrived  »t,  by 
the  help  of  our  intellectual  processes— such  as  we  call  Attrac- 
tions.  Repulsions,  Molecular  structure  and  arrangements — 
which  are  necessary  to  completeness  in  the  enumeration. 


ATTKIBUTES   SPECIAL  TO   THE  SUBJECT. 


659 


The  Sciences  of  the  so-called  External  world  are  occupied 
with  the  various  attributes  now  described.  One  portion  of 
Mathematics  is  occupied  with  quantity  in  Extension ;  Mechanics 
embraces  the  essential  fact  of  Matter,  together  with  its  other 
incidents;  Physics  and  Chemistry  include  Light,  Sound,  Odour, 
Heat,  &c. 

VI.  The  attributes  special  to  the  Subject  are  the  defining 
marks  or  essential  attributes  of  Mind — Feeling,  Willy  and 
Thought.  All  these  are  in  full  antithesis  to  the  great  object 
facts,  as  above  detailed. 

Of  Feelings,  the  greater  part  are  pleasures  and  pains,  which 
are  our  most  unequivocal  types  of  subjectivity.  We  never 
confound  two  such  things  as  comfortable  warmth,  and  lifting  a 
chair ;  the  heterogeneous  is  at  its  utmost  stretch  in  such  a 
contrast  as  this. 

Our  states  of  Will,  or  Volitions,  have  a  purely  subject 
origin,  namely,  our  feelings,  with  outcomings  in  the  object 
sphere.  The  two  departments  are  here,  as  often  happens,  in 
close  proximit}^  but  are  not  therefore  confused.  Voluntary 
action  is  always  reckoned  a  special  characteristic  of  mind. 
For,  although  it  is  activity,  directed  often  upon  material  things, 
yet  its  origin  in  the  pleasurable  and  painful  modes  of  sensi- 
bility gives  it  an  indelible  stamp  of  the  subject. 

Our  Thoughts,  Ideas,  or  Intellectual  states,  have  in  them  a 
considerable  amount  of  object  reference ;  still  there  is  a  broad 
distinction  between  Sensations  and  Ideas,  in  the  circumstance 
that  the  one  class  is,  and  the  other  is  not,  connected  with  de- 
finite bodily  movements.  The  succession  of  our  sensations  is 
in  uniform  accordance  with  our  locomotive  and  other  move- 
ments; the  succession  of  our  thoughts  is  totally  different. 
Hence,  although  our  ideas  are  the  reflexion  or  repetition  of  our 
sensations,  yet  their  manner  of  occurrence  assimilates  them 
with  subject  states. 

In  the  complex  fact  called  Sensation,  we  have  incessant 
shiftings  of  the  scene,  from  the  object  to  the  subject.  A  sen- 
sation, as  cognisant  of  extension,  resistance,  colour,  &c.,  is  an 
object  fact ;  as  a  pleasure  or  a  pain,  it  is  subject.  Now,  un- 
mistakeable  as  the  contrast  is,  wide  as  is  the  chasm,  we  may 
leap  it  a  great  many  times  in  a  minute  ;  we  flutter  to  and  fro, 
between  the  pleasurable  consciousness  of  a  sensation,  and 
the  intellectual  measure  of  it  as  a  thing  of  size,  form,  op 
colour. 

The  sciences  of  the  Subject  World  have  thus  to  deal  with 
our  Feelings,  Volitions,  and  Thoughts.     They  have,  moreover, 


660 


ENUMEEATION  OF  THINGS. 


to  draw  the  delicate  boundary  line  between  the  two  worlds, 
to  divide  the  spheres,  where  they  become  entangled. 

If  it  were  now  asked  what,  in  the  final  analysis,  is  the 
nature  of  predication,  we  are  able  to  afl&rin — Attributes  of  the 
Object,  and  Attributes  of  the  Subject,  declared  as  related  in 
Quantity,  as  Co- existing  or  as  Successive. 

VII.  Substance  is  not  the  antithesis  of  all  Attribute?,  but 
the  antithesis  between  the  fundamental,  essential,  or  defining 
attributes,  and  such  as  are  variable  or  inconstant. 

From  the  relative  character  of  the  word  Attribute,  the  fancy 
grew  up  that  there  must  be  a  substratum,  or  something  dif- 
ferent from  attributes,  for  all  attributes  to  inhere  in.  Now  as 
anything  that  can  impress  the  human  mind  —  Extension, 
Resistance,  &c.,  may  be,  and  is,  termed  an  attribute,  we  seem 
driven  entirely  out  of  reality,  if  we  would  find  a  something  that 
could  not  be  called  an  attribute,  and  might  stand  as  a  sub- 
stance. 

But  *  substance  *  cannot  be  rendered  by  non-entity.  The 
antithesis  that  we  are  in  search  of  is  made  up  without  so 
violent  a  supposition.  Substance  is  not  the  absence  of  ail 
attributes,  but  the  most  fundamental,  persisting,  inerasible,  or 
essential  attribute  or  attributes  in  each  case.  The  substance 
of  gold  is  its  high  density,  colour,  lustre,  &c. — everything  that 
we  consider  necessary  to  its  being  gold.  Withdraw  these,  and 
gold  itself  would  do  longer  exist ;  substance  and  everything 
else  would  disappear. 

The  substance  of  Body  or  Matter,  is  the  permanent,  or 
essential  fact  of  Matter — Inertia  or  Resistance.  This  is  the 
feature  common  to  everything  we  call  Body — whether  Solid, 
Liquid,  or  Gas  ;  the  most  generalized,  and  therefore  the  defin- 
ing property  of  Matter.  The  remaining  attributes  of  matter 
vary  in  each  separate  kind  ;  they  make  the  kinds  or  specific 
varieties — air,  water,  rock,  iron,  &c.  The  real  distinction  is 
thus  between  the  Essence  and  the  Concomitants,  the  Invariable 
and  the  Variable,  the  Genus  and  the  Species. 

The  substance  of  Mind  is  no  other  than  the  aggregate  of  the 
three  constituent  powers  —  Feeling,  Will,  Thought.  These 
present,  mind  is  present ;  these  removed,  mind  is  gone.  If  the 
three  facts  named  do  not  exhaust  the  mind,  there  must  be 
some  fourth  fact ;  which  should  be  produced  and  established  as 
a  distinct  mode  of  our  subjectivity.  The  substance  would  then 
be  four-fold.  But  the  supposition  of  an  *  ego  *  or  *  self,'  for  the 
powers  to  inhere  in,  is  a  pure  fiction,  coined  from  non-entity. 


MILL  S  CLASSIFICATION. 


661 


by  the  illusion  of  supposing  that  because  attribute  applies  to 
something,  there  must  be  something  that  cannot  be  described 
as  an  attribute. 

Mr.  Mill,  as  the  result  of  his  analysis,  gives  the  following  as 
an  enumeration  and  classification  of  all  Nameable  Things  : — 

*  1st.  Feelings,  or  States  of  Consciousness. 

*  2nd.  The  Minds  which  experience  those  feelings. 

*  3rd.  The  Bodies,  or  external  objects,  which  excite  certain 
of  those  feelings,  together  with  the  powers  or  properties 
whereby  they  excite  them  ;  these  last  being  included  rather  in 
compliance  with  common  opinion,  and  because  their  existence 
is  taken  for  granted  in  the  common  language  from  which  I 
cannot  prudently  deviate,  than  because  the  recognition  of  such 
powers  or  properties  as  real  existences  appears  to  be  warranted 
by  a  sound  philosophy. 

*4th,  and  last.  The  Successions  and  Co-existences,  the 
Likenesses  and  Unlikenesses,  between  feelings  or  states  of 
consciousness.  Those  relations,  when  considered  as  sub- 
sisting between  other  things,  exist  in  reality  only  between  the 
states  of  consciousness  which  those  things,  if  bodies,  excite,  if 
minds,  either  excite  or  experience. 

*  This,  until  a  better  can  be  suggested,  may  serve  as  a  sub- 
stitute for  the  abortive  Classification  of  Existences,  termed 
the  Categories  of  Aristotle.  The  practical  application  of  it 
will  appear  when  we  commence  the  inquiry  into  the  Import  of 
Propositions ;  in  other  words,  when  we  inquire  what  it  is 
which  the  mind  actually  believes,  when  it  gives  what  is  called 
its  assent  to  a  proposition. 

*  These  four  classes  comprising,  if  the  classification  bo  cor- 
rect, all  Nameable  Things,  these  or  some  of  them  must  of 
course  compose  the  signification  of  all  names ;  and  of  these, 
or  some  of  them,  is  made  up  whatever  we  call  a  fact.'  (Logic 
Book  I.,  Chap.  III). 

The  Categories  of  Aristotle, 

We  owe  the  Categories  to  the  opposition  made  by  Aristotle 
to  Plato's  Realism  of  Universals.  Plato  viewed  Ens  or  Real 
Being  as  belonging  only  to  Universals  separated  from  their 
particulars  ;  they  only  being  permanent  as  contrasted  with 
the  Generated  and  Perishable.  Aristotle  held,  on  the  contrary, 
that  Real  Being  attached  only  to  the  Particulars  ;  that  certain 
varieties  of  Being  might  be  predicated  of  an  individual — Hoc 
aliquid.  That  man,  This  horse,  &c. — but  that  no  Being  had 


662 


ENUMERATION   OF  THINGS. 


HAMILTON   ON  THE  CATEGORIEa 


t 
I 


any  reality  apart  from  the  individual.  The  varieties  of  Being 
that  might  thus  be  predicated  of  a  particular  iadividual,  he 
enumerated  in  a  scheme  known  as  the  Categories  (icaTj/7o/)tai, 
Predicamerda).     They  are  as  follows  : — 

1 .  O vaia — Su hstajitia — S  ubstance. 

2.  Il'xroi/ — Quantum — Quantity. 

3.  flofoV — Quale — Quality. 

4.  Il/jo'?  Tt — Ad  aliquid — Relation. 
6.  Uov — Ubi — Location. 

6.  Tlorc — Quando—'Period  of  Time. 

7.  Ke7ff Oat — Jacere — Attitude,  Posture. 

8.  "Exeip — flaiera— Equipment,  Appurtenance,  Property. 

9.  rio/eti/ — Facere — Active  Occupation. 
10.  lla<T;^6fi/ — Pati — Passive  Occupation. 

Mr.  Mill  points  out  the  more  obvious  defects  of  the  Cate- 
gories considered  as  an  enumeration  of  Things. 

*  The  imperfections  of  this  classification  are  too  obvious  to 
require,  and  its  merits  are  not  sufficient  to  reward  a  minute 
examination.  It  is  a  mere  catalogue  of  the  distintions 
rudely  marked  out  by  the  language  of  familiar  life,  with 
little  or  no  attempt  to  penetrate,  by  philosophical  analysis,  to 
the  rationale  even  of  those  common  distinctions.  Such  an 
analysis,  however  superficially  conducted,  would  have  shown 
the  enumeration  to  be  both  redundant  and  defective.  Some 
objects  are  omitted,  and  others  repeated  several  times  under 
different  heads.  It  is  like  a  division  of  animals  into  men, 
quadrupeds,  horses,  asses,  and  ponies.' 

Hamilton  endeavours  to  obviate  this  last  objection,  by  cast- 
ing it  into  a  scheme  of  successive  grades  of  subordination.  His 
elucidation  is  as  follows  : — *  Being  (to  ot^,  ens)  is  primarily 
divided  into  Being  hij  itself,  {ens  per  se),  and  Being  by  accident, 
(ens  per  accidens).  Being  by  itself  corresponds  to  the  first 
Category  of  Aristotle,  equivalent  to  Substance:  Being  hi 
accident  comprehends  the  other  nine,  but  is,  I  think,  more 
properly  divided  in  the  following  manner  i^Being  by  accident 
is  viewed  either  as  absolute  or  as  relative.  As  absolute,  it 
flows  either  from  the  matter,  or  from  the  form  of  things  :  if 
from  the  matter, — it  is  Quantity,  Aristotle's  second  category. 
If  from  the  form,  it  is  Quality,  Aristotle's  third  category.  Aa 
relative,  it  corresponds  to  Aristotle's  fourth  category  Eelatimi 
and  to  Relation  all  the  other  six  may  be  reduced. 

The  arrangement  would  stand  thus  : — 


663 


L  Substance  (1) 

(  Quantity  (2) 
n.  Attribute  ■<  Quality  (3) 

(  Relation  (4)      /Place  (5) 

Time  (6) 
Posture  (7) 
Appurtenance  (8) 
Activity  (9) 

(Passivity  (10) 
There  is  no  evidence  that  Aristotle  saw  the  division  in  this 
light ;  if  be  had  done  so,  he  might  have  adverted  to  the  mis- 
placement of  *  Relation,'  which,  if  it  includes  any  of  the  others, 
equally  includes  them  all ;  Substance  and  Attribute,  Quan- 
tity Quality— are  all  relationships.  Still,  the  arrangement  is 
useful  as  showing  how  some  of  the  worst  defects  may  be 
remedied,  and  as  an  aid  to  remembering  the  list.  The  four 
first  are  easily  remembered;  the  remaining  six  (under  Relation) 
may  be  cast  into  three  couples— Place  and  Time,  Activity  and 
Passivity,  Posture  and  Possession  or  Appurtenance. 

The  Categories  do  not  seem  to  have  been  intended  as  a 
classification  of  nameable  things,  in  the  sense  of  "  an  enumera- 
tion of  all  kinds  of  Things  which  are  capable  of  beincr  made 
predicates,  or  of  having  anything  predicated  of  them."*^   They 
seem  to  have  been  rather  intended  as  a  generalization  of  vrL 
dicates  an  analysis  of  the  final  import  of  predication,  including 
Verbal  as  well  as  Real  predication.     Viewed  in  this  light  they 
are  not  open  to  the  objections  offered  by  Mr.  Mill.     The  pro- 
per question  to  ask  is  not— In  what  Category  are  we  to  place 
sensations,  or  any  other  feelings  or  states  of  miad,  but— Under 
what  categories  can  we  predicate  regarding  states  of  mind  ? 
lake,  for  example,  Hope.     When  we  say  that  it  is  a  state  of 
mmd,  we  predicate  *  substance :'  we  may  also  describe  how 
great  it  is  ('Quantity'),  what  is  the  quality  of  it,  pleasurable 
urpamfiil  (*  Quality'),  what  it  has  reference  to  ('Relation') 
Aristotle  seems  to  have  framed  the  Categories  on  the  plan- 
Here  IS  an  individual :  what  is  the  final  analysis  of  all  that  we 
can  predicate  about  him  ? 

The  proper  comparison  of  the  Categories  is  to  the  Predi- 
cables,  and  to  the  Import  of  Propositions,  or  the  Universal 
Predicates.  Comparing  the  Categories  with  the  Predicables 
we  see  that  through  both  runs  the  distinction  between  Funda- 
mental and  Concomitant,  Essential  and  Accidental.  The  four 
predicables,  genus,  species,  differentia,  proprium,  are  predications 
of  substance  :'  accidens,— co^icomiiance  {mj^/Se^nKo^)  embraces 
29 


66^ 


THE  UNIVEESAL  POSTULATE. 


TESTIMONY  OF  CONSCIOUSNESS. 


665 


all  the  categories  except  substance.  Other  categories  than 
substance  might  be  jpropria,  or  predications  deduced  from  the 
f;ssence  of  the  subject ;  but  it  is  probable  that  Aristotle,  in 
speaking  of  '  fundamental '  and  *  concomitant  *  in  connection 
with  the  categories,  meant  to  include  j?ropna  in  the  category 
of  substance.  Probably  Aristotle's  list  of  propria  had  been 
smaller  than  the  list  that  could  be  made  out  now.  Secondly, 
if  we  compare  the  Categories  with  the  Universal  Predicates 
{Co-existence^  Succession y  Quantity) ,  we  see  that  the  Categories 
are  more  superficial  and  less  ultimate  than  the  later  analysis. 
The  category  of  *  substance  *  (if  we  do  not  include  propria) 
belongs  to  the  department  of  Verbal  predication  :  the  remain- 
ing Categories  are  Real  predicates,  corresponding  to  the  final 
analysis  of  propositions.  As  such  an  analysis,  they  are  open 
to  the  objection  of  not  being  ultimate  ;  for  example,  the  predi- 
cations concerning  *  space  '  and  *  time  *  may  regard  *  co-exist- 
ence '  or  they  may  regard  'succession.'  More  than  this,  they 
are  not  adapted  to  any  logical  purpose  ;  they  cannot  be  made 
the  basis  of  logical  departments. 

While  these  comparisons  show  the  bearings  of  the  cate- 
gories as  regards  Logic,  it  should  be  kept  in  mind  that  their 
original  purpose  was  simply  to  exhaust  the  possible  predicates 
regarding  an  individual,  and  not  either  to  exhibit  a  classification 
of  nameable  things,  or  to  analyze  the  import  of  propositions 
with  a  view  to  the  arrangement  of  logical  departments. 

D. — THE   UNIVERSAL   POSTULATE. 

The  theory  of  Demonstration  supposes  that  we  come  at  last 
to  something  that  cannot  be  demonstrated.  Demonstration  is 
the  referring  of  a  fact  to  a  higher  generality,  already  esta- 
blished ;  to  demonstrate  such  higher  generality  would  be  to 
find  some  principle  still  more  general ;  a  few  steps  must  lead 
us  to  something  that  is  absolutely  final,  something  whose  evi- 
dence is  not  demonstrative,  something  believed  in  without 
extraneous  support. 

The  edifice  of  demonstration  is  not  complete  until  we  clear 
out  these  ultimate  foundations,  and  state  distinctly  the  nature 
of  the  certainty  attaching  to  them.  Let  us  then  ask  what  are 
the  facts  to  be  received  without  proof,  as  underivable,  unde- 
ducible,  undemonstrable  ? 

In  probing  to  the  deepest  foundations  of  knowledge  and 
certainty,  there  has  often  been  a  confusion  of  two  classes  of 
primary  facts— the  Logical  and  the  Psychological.  By  the 
Xjogicsi primordia  are  meant  the  indemonstrable  assumption^ 


%t  the  foundation  of  all  demonstrable  truth ;  by  the  Psvcho- 
logical,   are   meant  the  elementary  sensibilities  of  the  iind 
whence   our   complex   intellectual   products  are  evolved   by 
growth,  ag:  r  gation,  or  association.     What  the  logical  founda- 
tions  are,  will  be  stated  fully  in  this  note ;  the  Psychological 
toundations   are   the    primary  sensibilities  arrived   at   in  an 
ultimate  analysis  of  the  mind-such  as  Resistance,  Motion, 
Colour,  Sound,  &c.     There  may  be  a  partial  coincidence  of  the 
two  classes  of  ultimate  data;  but  the  coincidence  is  not  neces- 
sarily total ;  and  each  must  stand  on  its  own  grounds      The 
propriety  of  an  Analysis  of  the  mind  needs  to  be  established 
by  evidence;  hence  it  must  appeal  to  some  first  principles 
different  from  itself ;  so  that  the  priority  belongs  to  the  Logical 
toundations  of  our  knowledge. 

The  phrase  *  Universal  Postulate,'  proposed  by  Mr.  Herbert 
bpencer,  to  express  the  ultimate  foundations  of  certain tv,  is 
adopted  from  Euclid.    While  the  subject-matter  is  quite  differ- 
ent m  the  two  applications,  there  is  this  common  feature,  that 
m  both  something  has  to  be  begged  on  one  side  and  granted 
on  the  other  ;  one  person  cannot  force  another  person  into  the 
admission      The  basis  of  all  reasoning  is  something  mutually 
conceded  between  the  different  reasoners.    When  an  opponent 
accepts  a  certain  first  principle,  and   declares   that   he   will 
abide  by  all  its  consequences,  we  may  compel  him  to  accept 
whatever  we  can  show  to  be  a  consequence ;  but  we  have  not 
the  same  fulcrum  with  the  first  principle  itself. 

In  reviewing  the  modes  of  stating  the  primary  assumptions, 
we  may  commence  with  the  so-called  Laws  of  Thouc^ht-- 
Identity,  Contradiction,  and  Excluded  Middle.  These, ^how- 
ever, are  too  limited  for  our  purpose.  As  explained  in  this 
work,  they  are  laws  of  Consistency  and  Equivalence  ;  the 
Jb  ormal  Logicians  suppose  them  to  include  also  Syllogism,  or 
Mediate  Consistency ;  by  no  one  are  they  Jield  as  furnishincr  a 
criterion  of  material  truth. 

Hamilton  has  put  forward  *  the  testimony  of  Consciousness  ' 
as  the  ultimate  and  infallible  criterion  of  certainty.  He  ex- 
presses the  reference  to  consciousness  in  these  three  maxims 
or  precautions  ; — 

*  (1)  That  we  admit  nothing,  not  either  an  original  datum  of 
consciousness,  or  the  legitimate  consequence  of  such  a  datum. 

*  (2)  That  we  embrace  all  the  original  data  of  consciousness, 
and  all  their  legitimate  consequences  ;  and— 


«M 


666 


THE  UNIVERSAL  POSTULA.TE. 


INCONCEIVABILITY   OF  THE  OPPOSITE. 


667 


*  (3)  That  we  exhibit  each  of  these  in  its  individual  integrity, 
neither  distorted  nor  mutilated,  and  in  its  relative  place, 
whether  of  pre-eminence  or  subordination.'  (Reid's  Works,  p. 

Stated  in  general  terms,  this  criterion  seems  unimpeachable. 
But  when  we  come  to  specific  enquiries,  we  are  aware  of  its 
vagueness  and  uncertainty.  Our  present  consciousness  must 
be  admitted  to  be  our  present  consciousness ;  when  we  fuel 
hungry,  we  have  the  fullest  certainty  that  we  are  hungry. 
The  question,  however,  arises — what  does  consciousness  say  to 
facts  in  the  past,  and  to  facts  in  the  future.  And  strange  as 
the  thing  may  appear,  people  may  differ  as  to  what  things  we 
are  actually  conscious  of,  as  will  be  seen  presently, 

Mr.  Spencer  expresses  the  Universal  Postulate  under  the 
form  of  the  Inconceivability  of  the  Opposite.  The  only  reason 
assignable,  he  says,  for  our  primary  beliefs,  is  the  fact  of  *  in- 
variable existence  tested  by  an  abortive  effort  to  cause  non- 
existence.' When  the  opposite  of  an  assertion  is  utterly 
unthinkable  by  us,  we  can  do  nothing  but  receive  that  assertion 
as  true. 

Thtj  difficulties  attending  the  employment  of  this  test  are 
these  : 

First.  The  examples  that  are  most  in  its  favour  are  cases 
where  the  opposite  is  a  self-contradiction.  I  cannot  think  that 
I  do  not  at  present  exist,  because  the  two  suppositions  are  in- 
compatible ;  the  attempt  is  a  violation  of  the  law  of  consistency. 
So, — *  Motion  cannot  be  thought  of  without  an  object  that 
moves  being  at  the  same  time  thought  of*  is  an  instance  where 
the  two  statements  give  the  very  same  fact ;  *  motion  *  and 
*a  thing  moving,'  are  two  slightly  different  phrases  for  an 
identical  conception.     The  opposite  is  pure  self-contradiction. 

Now,  for  all  such  instances,  a  postulate  of  self-consistency 
would  answer  the  same  end  as  a  postulate  of  unthinkableness 
of  the  negation. 

Secondly.  In  assertions  where  there  is  not  mutual  implica- 
tion but  difference  in  things  conjoined,  the  inconceivableness 
of  the  disjunction  has  arisen  from  unremitted  experience,  op 
indissoluble  association.  This  is  the  case  with  extension  and 
colour ;  we  cannot  think  of  an  object  as  extended  without 
thinking  it  as  of  some  colour ;  the  visible  form,  although  a 
different  fact  from  colour,  has  always  been  embodied  in  an 
optical  impression  of  colour.  Again,  ice  cannot,  without  great 
difficulty,  be  thought  of  but  as  cold ;  the  visible  appearance 


of  ice  and  the  sensation  of  warmth  are  repugnant  because  of 
the  strong  opposing  association. 

The  same  remark  applies  to  the  (proper)  Axioms  of  Mathe- 
matics. The  iteration  of  them  in  experience  creates  an  almost 
indissoluble  link  of  thought  in  their  favour.  We  are  practi- 
cally unable  to  think  their  opposites.  So  with  the  Loc^ical 
Axiom  of  Mediate  Consistency.  ° 

Now,  with  regard  to  this  class  of  beliefs,  it  is  an  open  ques- 
tion,  whether  the  stress  should  be  laid  upon  the  acquired 
inconceivableness  of  the  negations,  or  upon  the  circumstance 
that  has  brought  about  the  inconceivableness,  namely,  the 
unbroken  iteration  of  the  facts.  Whether  are  we  to  lay  hold 
of  the  primary  condition,  or  of  its  consequence  or  concomitant  ? 
1  here  seems  to  be  a  presumption  in  favour  of  the  primary 
condition,  namely,  the  unbroken  experience. 

Mr.  Spencer  himself  attributes  our  inability  to  conceive  the 
opposites  of  axioms  and  other  strong  beliefs  to  the  experience 
ot  the  race  accumulated  and  transmitted  to  us.  *  Objective 
facts  are  ever  impressing  themselves  upon  us  ;  our  experience 
18  a  register  of  these  objective  facts  ;  and  the  inconceivableness 
ot  a  thmg  implies  that  it  is  wholly  at  variance  with  the  re- 
gister. 

Thirdly.  There  are  propositions  admitted  by  us  to  be  uni- 
versally  true,  but  whose  opposites  we  can  well  conceive, 
buch  is  the  law  of  gravity.  We  can  easily  suppose  that  law 
to  be  suspended.  The  reason  in  this  case  is,  that  althoucrh  the 
greater  number  of  unsupported  bodies  fall  to  the  groundtsome 
do  not ;  smoke  and  dust  may  be  seen  ascending.  We  learn  to 
regard  these  as  exceptions,  but  they  prevent  us  from  having 
an  overpowering  strength  of  association  between  the  absence 
ot  solid  support  and  the  descent  of  a  body  to  the  ground. 

Fourthly.  Some  examples  given  as  unquestionable  applica- 
tions of  the  principle  of  Inconceivableness  are  denied  bv  a 
whole  school  of  thinkei-s.      Both  Sir  W.  Hamilton   and  Mr. 
bpencer  maintain  that  we  are  under  the  necessity  of  believing 
the   Persistence   of  Force ;    that   we  cannot  conceive  either 
fatter  or  Force  as  absolutely  created  or  absolutely  destroyed 
It  IS   under  the  first  kind  of  inconceivableness  (where  the 
opposite  is  a  self-contradiction)  that  this  case  is  brought;  there 
is  no  attempt   to   affirm    it   on    unbroken   experience.      The 
Belf-contradiction,  however,  is  by  no  means  apparent ;  Force  is 
one  thing,  and  its  commencement  or  termination  is  seemindv 
a  different  thing.     That  aspect  of  Force  whereby,  in  communi- 
eating  itself,  it  loses  the   numerical  equivalent  of  what  ia 


\ 


668 


THE  UNIVERSAL  POSTULATE. 


SOURCES  OF  BELIEF. 


669 


communicated,  becomes  familiar  to  us  after  we  are  educated  in 
mechanical  facts ;  and  we  are  then  prepared  to  receive  the 
doctrine  of  Persistence.  Bat  prior  to  this  experience,  which, 
to  be  sure,  is  requisite  to  a  clear  and  precise  coguition  of 
Force,  we  can  form  a  conception  of  force  bcp^inning  we  know 
not  how,  and  ending  we  know  not  how.  We  are  not  at  first 
struck  with  any  self-contradiction  in  force  arising  out  of  no 
prior  force  ;  the  contradiction  that  we  discover  at  last  is  a 
contradiction  of  our  experieuce. 

A  still  more  doubtful  example  is  furnished  by  the  question 
of  questions — Material  Perception,  which  Mr.  Spencer  upholds 
in  its  popularly  received  form,  on  the  authority  of  the  test  of 
inconceivableness  of  the  negative.  Mysterious  as  is  the  con- 
sciousness of  something  out  of  consciousness,  we  are,  he  says, 
obliged  to  think  it.  *  The  current  belief  iu  objects  as  external 
inde^iendent  entities,  has  a  higher  guarantee  than  any  other 
belief  whatever.'  Yet  this  is  the  belief  that  would  have  re- 
mained undisturbed  to  this  hour,  but  for  its  glaring  self-contra- 
diction, first  exposed  by  Berkeley,  and  since  by  others.  (See, 
in  particular,  Ferrier's  Review  of  Berkeley).  Any  t^st  of 
belief  that  guarantees  this  assumption  must  needs  be  repudi- 
ated by  the  numerous  believers  in  its  self-contradictory 
character.  There  is  an  evident  incongruity  in  laying  down, 
as  a  universal  postulate,  what  begs  the  very  point  in  dispute, 
in  a  leading  controversy. 

Fifthly.  Mr.  Spencer's  view,  that  inconceivableness  (where 
there  is  no  self-contradiction)  represents  *  the  net  result  of  our 
experience  up  to  the  present  time,'  supposes  a  theory  of  the 
sources  of  belief  which  is  liable  to  great  objections.  He 
considers  that  our  habitual  contact  with  actual  things  has 
engi  aiued  in  our  minds  an  intensity  of  connexion  between  the 
ideas  of  those  things  proportioned  to  the  frequency  of  their 
recurrence.  For  example.  Space  relations  are  the  most  iterated 
of  any,  and,  consequently,  our  minds  are  moulded  to  these  with 
the  highest  possible  tenacity.  Next  are  Matter  and  Force 
relations.  In  this  way,  as  already  remarked,  our  repugnance 
to  form  ev(  n  an  idea  of  the  opposites  is  a  proof  of  the  persist- 
ence of  tlie  corresponding  facts.  So  that,  experience  and 
inconceivability  of  the  opposite  are  convertible  statements. 

Now,  it  may  be  granted  that  the  contact  with  actual  things 
is  o/ieof  the  sources  of  belief;  but  it  is  not  the  only  nor  the 
greatest  source.  Indeed,  so  considerable  are  the  other  sources 
as  to  reduce  this  seemingly  prepondemting  consideration  to 
comparative    insignificance.       The   competing    elements   are 


briefly  the  following  : — (1)  The  innate  impetuosity  of  believ- 
ing that  what  is  will  continue ;  and  (2)  The  influence  of  our 
strong  emotions  and  predilections.  Both  influences  will  be 
illustrated  afterwards  as  prevailing  causes  of  error  or  Fallacy 
(Book  Yl).  There  should  also  be  taken  into  account  the 
circumstance  that  our  strength  of  association  does  not  represent 
the  comparative  recurrence  of  the  fact,  unless  our  position  is 
such  as  to  encounter  the  facts  in  proportion  to  their  exact 
frequency.  What  is  most  familiar  to  nature,  may  not  be  the 
most  familiar  to  us.  We  may  not  see  the  world  from  a 
central  or  commanding  point  of  view.  The  best  example  of 
this  is  our  excessive  familiarity  with  one  type  of  causation — 
the  human  will ;  in  consequence  of  which,  we  represent  that 
as  the  proper  and  natural  type  ;  whereas,  it  is  an  exceptional 
and  narrow  instance  of  causal  agency. 

There  still  remains  the  eSect  of  society  in  propagating  and 
iterating  certain  propositions  in  language ;  by  which  iteration, 
no  less  than  by  confronting  the  facts  in  our  own  person,  we 
are  moulded  to  belief  in  certain  doctrines.  On  the  whole, 
therefore,  when  the  various  agencies  operating  to  form  our 
convictions  are  taken  together,  the  one  circumstance  assigned 
by  Mr.  Spencer  is  so  overborne  as  to  render  our  strength  of 
belief  no  just  criterion  of  the  facts  believed. 

Sixthly.  Nothing  is  gained  by  putting  under  one  head,  and 
subjecting  to  a  common  test,  two  classes  of  beliefs  so  distinct, 
as  Self-Consistency  and  Consistency  with  Facts.     Hitherto,  in 
philosophy,  these  two  departments,  under  various  names,  have 
been  kept  distinct.      The   one  is  known   as   Formal    Truth, 
Necessary  Truth,  the  Laws  of  Thought ;  the  other  is  Material 
Truth,  Contingent  Truth,  Inductive  Certainty.     Although  the 
most  strongly  iterated  of  the  laws  inductively  arrived  at  tend 
to  indissoluble  associations,  and  to  a  difficulty  of  thinking  their 
opposites — in  that  way  approximating  to  the  truths  of  consist- 
ency, this  is  a  mere  incident  belonging  unequally  to  things 
that  are  alike   true.      When    the   inconceivability  occurs,  a 
reason  can  be  given  for  it ;    and  the  reason  not  being  always 
the  same,  there  is  no  propriety  in  disguising  the  deeper  dif- 
ferences by  the  superficial  agreement.     We  are  not  obliged  to 
have  only  one  Universal  Postulate.      Should  there  occur  two 
very  different  kinds  of  certainty,  neither  reposing  on  the  other, 
our  proper  course  is  to  assign  different  postulates. 

On  these  various  grounds,  we  demur  to  the  test  of  the 
*  Inconceivableness  of  the  Opposite '  as  the  basis  of  all  cer- 
tainty, or  as  the  matter  that  cannot  be  proved,  but  must  be 


.1- 


670 


THE  UNIVEKSAL  POSTULATE. 


THE  LEAP  TO  THE  FUTURE. 


on 


asked  and  granted,  before  demonstration  can  begin.  We  should 
propose,  instead  of  that  test,  at  least  two  Postulates,  accord- 
ing to  the  distinction  last  noted ;  perhaps  more  may  be  re- 
quisite. 

First  and  foremost,  we  should  place  the  Postulate  of  Consis- 
tency, or  Self- Consistency — the  absence  of  self-contradiction. 
This  is  the  basis  of  Immediate  Inferences,  or  Equivalent  Forms. 
It  must  be  conceded  as  a  prime  condition  of  all  reasoning, 
discussion,  and  intelligent  communication.  Enough  has  been 
said  in  regard  to  it. 

Secondly,  there  must  be  some  assumption  or  assumptions  at 
the  foundation  of  all  inferences  or  conclusions  from  Experience 
— some  grounds  of  Material  or  Inductive  certainty.  There  is 
much  more  difficulty  in  deciding  what  the  postulate  should  be 
for  the  department  of  real  inference,  or  whether  a  single 
postulate  is  enougL  Wo  here  enter  upon  a  totally  new 
sphere. 

In  order  to  guarantee  the  conclusions  of  our  experience, 
or  to  support  us  in  such  allegations  as — *  water  quenches  thirst,* 
*  unsupported  bodies  fall' — there  is  clearly  demanded,  in  the 
first  instance,  a  trust  in  present  consciousness.  We  must  assume 
that  what  we  feel,  we  do  feel ;  that  our  sensations  and  feelings 
occur  as  they  are  felt.  Whether  or  not  we  call  this  an  irresisti- 
ble belief,  an  assertion  whose  opposite  is  inconceivable  or 
unthinkable,  we  assume  it  and  proceed  upon  it,  in  all  that  we 
do.  The  calling  the  negation  unthinkable  does  not  constitute 
any  reason  for  assuming  it ;  we  can  give  no  reason  better  than 
that  we  do  assume  it. 

The  importance  of  stating  this  primary  assumption  is  not 
apparent,  till  we  proceed  beyond  it.  We  are  carried  a  very 
little  way  into  knowledge  by  the  admission  taken  by  itself; 
we  must  make  some  steps  in  advance,  and  assume  things 
seemingly  precarious  in  their  character  when  compared  with 
the  decisive  certainty  of  immediate  consciousness. 

It  is  requisite,  in  the  second  place,  that  we  should  believe 
in  past  consciousnesSy  or  vicmonj.  Unless  we  trust  our  recol- 
lection, our  knowledge  is  limited  to  what  is  now  present ;  and 
we  cannot  compare  two  successive  experiences,  or  declare  two 
facts  to  succeed  one  another.  We  have,  one  moment,  the 
consciousness  of  thirst ;  the  next  moment,  we  have  the  con- 
sciousness of  a  certain  act  called  drinking ;  the  next  follow- 
ing moment,  we  have  the  farther  consciousnees  of  relief  from 
thirst.  The  succession  of  the  three  steps  is  a  fact  or  experi- 
ence;   but  we  cannot   believe   it,  unless  we  believe   in   tho 


recent  fact,  given  in  memory,  as  well  as  the  present,  given  in 
consciousness. 

The  belief  in  memory  must  therefore  be  postulated.  It 
may  be  asked,  however,  are  we  to  believe  our  memory  without 
limits,  or,  if  not,  what  are  the  limits  to  our  belief?  If  there 
be  any  circumstance  qualifying  or  defining  the  belief,  that 
circumstance  should  be  produced  as  something  more  funda- 
*  mental,  and  therefore  proper  to  take  the  place  of  the  assump- 
tion that  it  limits  and  qualifies.  In  short,  memory  must  be 
believed  in ;  yet  the  postulate  of  the  belief  is  not  wholly 
independent  and  isolated,  but  leans  to  some  extent  on  another 
and  a  different  postulate. 

Granting,  however,  that  the  belief  in  memory,  as  well  as 
the  belief  in  present  consciousness,  is  a  primary  assumption, 
we  next  remark  that  it  comes  short  of  our  needs.  TLe  most 
authentic  recollection  gives  only  what  has  been;  something 
that  has  ceased,  and  can  concern  us  no  longer.  A  far  more 
perilous  leap  remains  ;  the  leap  to  the  future.  All  our  interest 
is  concentrated  on  what  has  yet  to  be ;  the  present  and  the 
past  are  of  value  only  as  a  clue  to  the  events  that  are  to 
come.  Now,  it  is  far  easier  to  satisfy  us  of  what  has  been, 
than  of  what  is  still  to  be. 

The  postulate  that  we  are  in  quest  of  must  carry  us  across 
the  gulph,  from  the  experienced  known,  «ither  present  or 
remembered,  to  the  unexperienced  and  unknown — must  per- 
form the  leap  of  real  inference.  '  Water  has  quenched  oui 
thirst  in  the  past ;'  by  what  assumption  do  we  atfirm  that  the 
same  will  happen  in  the  future  ?  Experience  does  not  teach 
us  this;  experience  is  only  what  has  actually  been;  and, 
after  never  so  many  repetitions  of  a  thing,  there  still  remains 
the  peril  of  venturing  upon  the  unrrodden  land  of  future 
possibility. 

The  fact,  generally  expressed  as  Nature's  Uniformity,  is  the 
guarantee,  the  ultimate  major  premise,  of  all  Induction. 
*  What  has  been,  will  be,'  justifies  the  inference  that  water 
will  assuage  thrist  in  after  times.  We  can  give  no  reason,  or 
evidence,  for  this  uniformity ;  and,  therefore,  the  course  seems 
to  be  to  adopt  this  as  the  finishing  postulate.  And,  undoubtedly, 
there  is  no  other  issue  possible.  We  have  a  choice  of  modes  of 
expressing  the  assumption,  but  whatever  be  the  expression,  the 
substance  is  what  is  conveyed  by  the  fact  of  Uniformity. 

As  nature  is  not  uniform  in  everything,  we  have  to  apply 
a  test  to  discriminate  the  uniformities  from  the  varieties. 
There  is  a  uniformity  in  the  manner  of  animal  generation,  but 


n 


f 


672 


THE   UNIVERS.VL  POSTULATE 


not  an  absolute  sameness  in  the  individuals  born  even  of  the 
Bame  pair.  Now  experience  will  not  establish  uniformity,  but 
it  will  establish  exceptions  to  uniformity ;  it  will  sift  the  natural 
sequences  and  enable  us  to  reject  all  that  are  not  uuiform.  It 
does  not  prove  that  anything  will  always  be  in  the  future 
■what  it  has  been  in  the  past,  but  it  will  prove  that  some  things 
have  been  uniform  in  the  past,  and  others  not  uniform.  It 
has  at  least  a  destructive  certainty. 

Let  us  word  the  postulate  thus  : — What  has  uniformly  been 
in  the  past  ivill  he  in  the  future.  Otherwise,  *  what  has  never 
been  contradicted  in  any  known  instance  (there  being  ample 
means  and  opportunities  of  search)  will  always  be  true.*  In 
the  course  of  our  experience,  we  have  seen  a  great  many  pro- 
mising uniformities  break  down.  Again,  we  have  found  in- 
stances that  have  never  failed  ;  on  such  cases,  we  venture, 
and  it  is  a  mere  venture,  to  predict  the  future  continuance  of 
the  same  state  of  things.  We  go  forward  in  blind  faith,  until 
we  receive  a  check ;  our  confidence  grows  with  experience ; 
yet  experience  has  only  a  negative  force,  it  shows  us  what  has 
never  been  contradicted  ;  and  on  that  we  run  the  risk  of  go- 
ing forward  in  the  same  course. 

This  assumption  is  an  ample  justification  of  the  inductive 
operation,  as  a  process  of  real  inference.  Without  it,  we  can 
do  nothing;  witl\,it,  we  can  do  anything.  Our  only  error  is 
in  proposing  to  give  any  reason  or  justification  of  it,  to  treat 
it  other  wise  than  as  legged  at  the  very  outset.  If  there  be  a 
reason,  it  is  not  theoretical,  but  practical.  Without  the  as- 
sumption, we  could  not  take  the  smallest  steps  in  practical 
matters  ;  we  could  not  pursue  any  object  or  end  in  life.  Un- 
less the  future  is  to  reproduce  the  past,  it  is  an  enigma,  a 
labyrinth.  Our  natural  prompting  is  to  assume  such  identity, 
to  believe  it  first,  and  prove  it  afterwards. 

This  third  Postulate  is,  properly  speaking,  the  Postulate  of 
Experience.  Not  only  does  it  involve  a  hazard  peculiar  to 
itself,  making  a  broad  line  between  it  and  the  postulates  of 
present  conscionsness  and  of  memory,  but  it  seems  to  remove 
all  the  doubts  and  ambiguities  connected  with  these  appar- 
ently more  facile  assumptions.  Nothing  can  be  better  evidence 
than  present  reality,  provided  we  do  not  mistake  an  actual 
consciousness  for  an  inference,  or  a  recollection.  This  diffi- 
culty is  got  over  by  comparison  of  instances,  and  by  the  appli- 
cation of  general  principles,  which  repose  ultimately  upon  the 
Great  Postulate. 

So  with  Memory.      We  trust  in-plicitly  a  recent  recollcc- 


FALLACIES  IN  LANGUAGE. 


673 


tion  ;  but  as  the  interval  of  time  enlarges,  our  trust  diminishes. 
A  limit  has  thus  to  be  prescribed,  through  a  comparison  of 
experiences,  followed  by  an  inference  from  the  past  to  the 
future,  which  brings  us  round  again  to  the  assumption  of  the 
future  from  the  past.  Hence,  whichever  way  we  turn,  we 
find  this  to  be  the  one  resting  place  for  the  soL^  of  our  foot. 

E. — ARISTOTELIAN   AND   SCHOLASTIC   FALLACIES. 

The  Aristotelian  is  the  basis  of  all  subsequent  classifications. 
It  proceeds  upon  the  distinction  between  fallacies  in  Language, 
and  fallacies  in  Thought. 

L  Fallacies  arising  in  Language  (In  Dldione,  ol  Trapa  rrji^ 
Xe^it/).  1.  Aequivocatio,  Homonymia,  ojuLtvuv^ia ;  ambiguity 
in  a  single  term.  This  is  a  very  comprehensive  class  of  fal- 
lacy. One  of  the  examples  given  by  Aristotle  illustrates  an 
ambiguity  in  the  word  *  necessary.'  *  Evil  is  good,  for  what  is 
necessary  (ra  ^eoVra)  is  good,  and  evil  is  necessary.'  What  is 
necessary  as  a  means  to  a  desired  end  is  good;  but  what 
necessarily  results  from  antecedent  conditions  may  be  eviL 
Whately  gives,  in  his  Logic,  an  enumeration  of  words  often 
used  ambiguously  in  discussion.  This  task  belongs  as  much 
at  least  to  the  lexicographer  as  to  the  logician.  Thus :  *  Ex- 
pect '  is  either  what  is  possible,  as  that  the  sun  will  rise  to- 
morrow, or  what  is  right,  as  *  England  expects  every  man  to 
do  his  duty. '  *  Old '  means  either  length  of  duration,  or  dis- 
tance of  time.  As  age  gives  experience,  and  experience  often 
teaches  wisdom,  there  is  a  disposition  to  regard  the  ancients 
as  wiser  than  ourselves.  To  this  Bacon  replied,  *  we  are  the 
ancients ;'  we  inherit  the  wisdom  of  the  old,  and  can  add  to  it 
more  experience. 

A  chief  cause  of  ambiguity  is  that  the  signification  of  words 
is  constantly  shifting.     The  word  *  publish '  formerly  meant 

*  communicate '  or  *  show,' — *  The  unwearied  sun  publishes  to 
every  land.*  This  is  now  the  legal  meaning  of  publish :  to 
publish  a  libel  is  not  necessarily  to  print  it,  any  communica- 
tion of  written  libellous  matter  to  another  is  sufficient.  The 
law  still  speaks  of  *  uttering '  coin. 

*  Some  '  is  of  interest  to  the  logician,  in  its  two  chief  senses 

*  some  at  least,'  and  *  some  at  most,'  or  some  =  not  none,  and 
some  =  not  all. 

The  remedy  for  ambiguity  is  Definition. 

2.  Amphibolyy  amphiholiay  a/i(/)i^o\ta.  A  sentence  may  have 
two  grammatical  renderings,  but  by  preference  suggest  the  one 
intended  to  mislead.      This  was  an  occasional  trick  of  the 


674         ARISTOTELIAN  AND  SCHOLASTIC  FALLACIES. 

ancient  oracles.  *  Aio  te,  -^acida,  Romanos  vincere  posse,' 
reads  as  well  whether  the  Romans  are  victors  or  vanquished. 
*I  hope  that  you  the  enemy  may  slay.' 

3.  Fallacia  composiiionis  et  divisionis.  Whately  defines  this 
fallacy  as  the  use  of  a  term  collectively  in  one  premise,  and 
distributive] y  in  another.  If  the  term  is  collective  in  the 
major  premise,  and  distributive  in  the  minor,  it  is  a  fallacy  of 
division  ;  if  the  collective  is  in  the  minor,  and  the  distributive 
in  the  major,  it  is  a  fallacy  of  composition. 


I 


Five  is  one  number. 

Three  and  two  are  five, 

Three  and  two  are  one  number,      y 

Three  and  two  are  two  numbers, 

Three  and  two  are  five, 

Five  is  two  numbers. 


Fallacy  of  Division. 


Fallacy  of  Composition. 


Aristotle  gives  a  similar  division, — avvOeai^,  or  the  possibility 
of  wrong  disjunction,  and  hialpeai^  or  the  possibility  of  wrong 
conjunction.     His  example  of  Biaipeat^  is : — 

Five  is  two  and  three  ; 

Two  and  three  are  even  and  odd ; 

Five  is  even  and  odd. 
This  would  be  a  fallacy  of  composition,  according  to  Whately; 
and  Mr.  Foste  observes  that  it  is  not  easy  to  understand  exactly 
Aristotle's  distinction,  and  not  worth  the  trouble. 

4.  Fallacia  Frosodiae  or  Accenius,  TrpoawSia.  This  is  of 
very  trifling  consequence,  and  chiefly  noticeable  because  of 
the  diflerent  meanings  that  may  be  given  to  a  sentence  by 
varying  the  emphasis.  Mr.  De  Morgan  remarks  that  the 
commandment,  *  Thou  shalt  not  bear  false  witness  against  thy 
neighbour,'  is  often  read  with  the  emphasis  so  placed  as  "  to 
suggest  that  subornation  is  not  forbidden,  or  that  anything 
false  except  evidence  is  permitted,  or  that  it  may  be  given  for 
him,  or  that  it  is  only  against  neiyhhours  that  false  witness 
may  not  be  borne.'  Most  of  the  old  examples  are  mere  puns. 
*  Tu  es  qui  es  ;  quies  est  requies  ;  ergo,  tu  es  requies.' 

5.  Fallacia  fiijurae  dictionis,  a^ijixa  Xt'^fWK,  According  to 
Aristotle's  view,  this  fallacy  is  a  species  of  grammatical 
mistake,  arising  from  the  circumstance  that  unlike  things 
have  names  with  a  like  inflexion.  Thus,  RiUng  and  cutting 
have  the  same  termination,  but  one  applies  to  a  state  or 
quality,  the  other  to  an  action. 

II.  Fallacies  in  Thought  {Extra  Dictiovcm,  ol  tfo?  ttJ*  Xf'^eo)*?). 
1.    Fallacia   accidentia,  or    a  dicto    simj^ticiler    ad  dictum 


FALLACIES  IN  THOUGHT. 


675 


ieeundum  quid,  •mipd  ro  avp^eprjKOf,  A  fallacy  assuming  that 
subject  and  predicate  have  all  their  attributes  in  common.  It 
is  taking  a  predicate  as  co-extensive  with  a  subject,  when  it 
is  not. 

2.  Fallacia  a  dicto  secundum  quid  ad  dictum  simpliciter, 
TO  av\w9  tf  fj.Tj  a7r\uj9  aWa  Try  rj  Trod  y  vore  y  irpo^  ri  Xef^eadatf 
confusion  of  an  absolute  statement  with  a  statement  limited  in 
manner,  place,  time,  or  relation. 

What  you  bought  yesterday,  you  eat  to-day ; 

You  bought  raw  meat  yesterday ; 

You  eat  raw  meat  to-day. 
This  is  the  converse  of  the  fallacia  accidentis ;   many  of  the 
examples  of  both  are  instances  of  erroneous  conversion  of  an 
universal  affirmative. 

3.  Ignoratio  §lenchi^    ro   Trapa    ryu     ruv   eXe^/xov   ur^fvoinv,     an 

inadequate  notion  of  confutation.  A  debater  undertakes  to 
contradict  and  overthrow  a  thesis,  and  proceeds  to  destroy 
some  different  position.  It  is  the  common  error  of  arguing 
beside  the  point,  of  proving  what  has  only  a  superficial 
resemblance  to  the  conclusion,  or  of  simply  trying  to  distract 
attention  from  the  point  at  issue.  Mr.  de  Morgan  classifies, 
along  with  this,  any  attempt  to  transfer  the  onws  prohandi  to 
the  wrong  side. 

4.  Fallacia  consequentisy  nan  sequitur,  to  Trapii  to  iTro/nepov, 
To  mistake  gall  for  honey,  because  it  is  yellow,  is  a  nan 
sequitur.  Rain  wets  the  ground,  therefore  wet  ground  implies 
that  it  has  rained.  Every  one  in  a  fever  is  hot,  but  every 
one  that  is  hot  is  not  in  a  fever.  In  this  case  also,  the  ex- 
amples are  generally  instances  of  wrong  conversion  of  an 
universal  affirmative*. 

6.  Felitio  Pri7icipii,  to  Trapa  to  eV  apxy  \au^aveiv  Aristotle 
describes  five  forms  of  this  fallacy.  (I)  When  one  begs  the 
very  thing  that  ought  to  be  demonstrated.  (2)  When  one 
begs  universally,  what  ought  to  be  demonstrated  particularly, 
(o)  When  one  begs  the  particular  to  help  to  prove  the  uni- 
versal. (4)  When  one  begs  all  the  particulars  that  compose 
the  universal.  (5)  When  one  begs  something  necessarily  con- 
nected with  the  conclusion. 

Logicians  discuss  the  question  whether  the  syllogism  itself 
is  a  petitio  principii. 

6.  Non  causa  pro  causa,  to  fiy  ainou  oj?  ainov  Ti64uat,  an 
inductive  fallacy,  for  which  another  name  is,  post  lioc,  ergo 
proper  hoc,  which  is  the  vice  of  the  delusive  induction  called 
per  simplicem  enumerationem.     Whitfield  attributed  his  being 


676 


ARISTOTELIAN  AND   SCHOLASTIC    FALLACIES. 


overtaken  by  a  hailstonn  on  a  certain  occasion  to  his  having 
not  preached  at  the  last  town. 

7.  Fallaciub  phirium  interrogaiionum^  to  ta  irXettv  cptoTyfiara 
61/  TToteiu,  is  the  fallacy  of  putting  more  questions  than  one  as 
one.  Why  did  you  strike  your  father  ?  It  is  an  easy  snare 
to  ask  a  reason  for  a  fact  that  has  no  existence.  The  first 
members  of  the  Royal  Society  were  in  this  predicament,  when 
they  tried  to  explain  why  a  dead  fish  weighed  more  than  a 
living  fish.     The  answer  was,  it  did  not. 

Hardly  any  addition  has  been  made  to  Aristotle's  list  of 
Fallacies  by  modern  writers  on  the  Syllogism.  Aristotle's 
principle  of  classification  has  been  pronounced  illogical,  and 
new  arrangements  have  been  proposed  j  but  his  enumeration 
has  not  been  materially  increased. 

The  arrangement  followed  in  most  Manuals  of  Syllogistic 
Logic,  is  that  adopted  by  Whately. 

Rejecting  as  indistinct  the  division  of  Fallacies  into  those 
in  the  words  (in  dictione)  and  those  not  in  the  words  (extra 
dictionem),  Whately  divides  them  into  Logical  and  NoN- 
LoGiCAL.  The  Logical  include  all  cases  of  insufficient  premises 
advanced  as  sufficient;  all  cases  *  where  the  conclusion  does 
not  follow  from  the  premises.*  Such  cases  only,  he  contends, 
are  logical  in  the  strict  sense :  logic  having  to  do  only  with 
the  sufficiency  of  the  premises  given  for  the  conclusion  based 
upon  them.  As  Non-Logical  he  reckons  all  cases  where  the 
premises  are  sufficient  for  the  conclusion,  '  where  the  conclu- 
Kion  dues  follow  from  the  premises,'  but  where  either  the 
premises  are  unduly  assumed,  or  the  conclusion  is  irrelevant 
to  the  point  in  dispute.  To  settle  whether  the  premises  are 
legitimate  or  whether  the  conclusion  is  in  point,  passes  beyond 
the  proper  sphere  of  Logic. 

Such  are  Whately's  main  divisions.  Tlie  grouping  of  the 
Aristotelian  fallacies  under  them  is  as  follows  : — I.  Ho  sub- 
divides Logical  fallacies  into  the  Purely  Logical  and  the  Semi- 
logical.  The  Purely  Logical  are  Undistributed  Middle,  and 
Illicit  Process  of  the  Major  and  of  the  Minor  :  two  errors  which 
Aristotle  did  not  enumerate  in  his  list  of  Fallacies  (sophismata), 
whether  because  he  considered  them  too  palpable  to  be  fraudu- 
lently used  by  a  sophist,  or  because  he  had  sufficiently  exposed 
them  in  treating  of  the  syllogism.  The  Semi-logical  embrace 
all  instances  of  ambiguous  middle  term.  The  ambiguity  may 
be  in  the  term  itself,  or  may  depend  upon  the  context.  The 
ambiguity  being  in  the  term  itself,  we  have  Fallacia  Eouivo- 


WHATELY'S  CLASSIFCATION. 


677 


tatiovis,  and  Fallacia  Antphiholiae.  Our  author  takes  an 
opportunity  of  remarking  that  a  term  may  have  two  meanings 
from  accident  (as  the  term  *  light  *)  ;  or  from  some  connexion 
of  resemblance,  analogy,  cause  and  effisct,  &c.,  between  the 
different  senses.  The  ambiguity  arising  from  the  context,  we 
have  Fallacia  Compositionis  et  Divisionis,  and  Fallacia  Accidentis, 
and  a  dicto  secundum  quid  ad  dictum  simpliciter.  In  these 
cases  the  middle  term  is  not  ambiguous  in  itself,  but  is  used 
with  different  adjuncts  in  the  two  promises. 

IL  In  the  Non-logical  or  Material  group,  the  premises  may 
be  unduly  assumed,  and  the  conclusion  may  be  irrelevant.  A 
premise  may  be  altogether  false  and  unsupported.  The  only 
guarantee  against  this  is  a  knowledge  of  the  conditions  of  In- 
duction. The  major  premise  may  beg  the  conclusion  (petitio 
principiij ;  being  either  the  very  same  as  the  conclusion,  and 
differing  only  in  form,  or  not  quite  the  same  as  the  conclusion, 
but  unfairly  implying  it.  So  much  for  premises  unduly 
assumed.  Turning  now  to  the  other  sub-division  of  the  Non- 
logical  fallacies  (ignoratio  elejichi,  or  irrelevant  conclusion),  sve 
find  various  modes  of  shirking  the  question  particularized. 
One  way  is  to  lay  great  stress  upon  the  objections,  taking  no 
notice  of  what  may  be  said  in  favour.  Another  way  is  to  shift 
ground,  either  to  something  wholly  irrelevant,  or  from  one 
premise  to  another.  A  third  way  is  to  escape  under  cover  of 
complex  and  general  terms.  And  a  fourth  way  consists  in 
appeals  to  the  passions  and  sentiments,  ignoring  altogether  the 
rational  grounds  of  the  point  in  question.     (See  Book  YI). 


THE  AXIOM   OF  THE   SYLLOGISM. 
(Supplementary  Note  to  the  Second  Edition.) 

In  pp.  18,  15t5,  226,  237,  247,  209,  the  Logical  Axiom  of 
the  Syllogism  has  been  placed  under  the  head  of  Inductive 
truth.  This  has  not  been  done  without  misgivings,  as  the 
following  remarks  will  show. 

The  drawing  of  a  broad  line  between  Immediate  and 
Mediate  or  Syllogistic  Inference,  and  the  laying  down  of  a 
Deductive  Axiom  founded  on  experience  as  the  basis  of  the 
Syllogism,  will  be  seen  to  be  attended  with  difficulties. 

The  first  is  the  anomalous  middle  position  of  the  Hypo« 


678 


SUPPLEMENTARY  NOTE. 


tbetical  Syllogism.  If  we  are  bound  to  bring  hypotbetlcal 
inference  under  one  or  other  of  the  two  forms,  we  feel  that 
our  decision  is  not  satisfactory ;  the  case  passes  somewhat 
beyond  Immediate  Inference,  and  yet  does  not  reach  to 
Syllogism. 

There  is  the  same  unpleasant  doubt  about  the  cases  dis- 
cussed in  p.  109,  and  p.  157,  where  a  singular  proposition 
has  to  be  treated  as  a  Universal,  We  cannot,  without  con- 
siderable straining,  make  these  out  either  Equivalent  proposi- 
tions or  Syllogisms. 

The  second  difficulty  is  still  greater.  The  question  has  to 
be  raised,  whether  syllogistic  inference  is  or  is  not  Self- 
consistency.  Is  the  conclusion  the  mere  equivalent  of  the 
premises,  so  that  to  deny  it,  while  admitting  the  premises, 
would  be  self-contradictory  ? 

That  the  conclusion  of  the  Syllogism  flows  necessarily  from 
the  premises,  is  generally  insisted  on.  To  refuse  the  con- 
clusion would  be  to  contradict  the  premises.  Indeed,  the 
self-contradiction  would  be  as  unequivocal  as  in  the  denial  of 
an  immediate  inference — all  A  is  B,  some  A  is  B.  In  what 
then  consists  the  distinction,  as  regards  the  logical  foundation, 
or  the  kind  of  certainty,  between  Mediate  and  Immediate 
inference  ? 

In  the  Syllogism,  the  bond  of  necessary  equivalence  lies 
between  one  proposition  and  two  others  ;  in  the  immediate 
inference,  it  lies  between  one  proposition  and  one  other. 
This  makes  the  case  a  degree  more  complicated,  without 
apparently  altering  the  generic  character  of  the  inference  ; 
it  is  an  inference  contained  in  the  premises  j  it  cannot  be 
refused  without  contradiction  in  terras. 

This  circumstance  of  necessary,  or  self-consistent  relation- 
ship should  appear  in  the  axiom  of  the  Syllogism.  It  does  so 
in  the  dichun  de  omni  et  nullo.  That  axiom  seems  to  be  a 
necessary  truth  ;  we  feel  that  to  deny  it  would  be  not  merely 
to  deny  a  fact,  but  to  deny  in  one  form  of  words  what  we 
have  already  affirmed  in  another  ;  which  expresses  what  is 
meant  by  '  contradiction  in  terms,'  and  by  the  denial  of  a 
*  necessary '  truth. 

The  other  form  of  the  axiom — Nota  notm — *  whatever  has  a 
mark  has  whatever  that  mark  is  a  mark  of,'  must  also  be 
necessary,  if  it  is  an  exact  equivalent.  We  cannot  suppose 
that  the  Syllogism  under  one  form  of  axiom  is  an  implicated 
or  necessary  inference — an  analytic  judgment  ;  and,  under 
another  form,  an  inductive  or  contingent  inference — a  syn- 


i 


THE  AXIOM   OF  THE   SYLLOGISM. 


679 


tLetic  judgment ;  such  a  supposition  could  arise  only  from 
Borae  great  confusion  of  ideas. 

If,  under  the  guise  of  nota  noiw^  the  axiom  is  exactly  equiva- 
lent in  substance,  as  it  is  in  appearance,  to  the  mathematical 
axiom  of  mediate  equality — equals  of  the  same  are  equal — 
it  would  not  be  an  axiom  of  self-consistency,  or  an  analytic 
judgment.  That  axiom  may  be  very  evident,  may  be  styled 
by  courtesy  self  evident,  bub  it  is  a  synthetic  judgment ;  the 
subject  and  the  predicate  are  not  mutually  implicated ;  its 
denial  is  not  a  contradiction  in  terms.  The  subject  is  *  equals 
of  the  same* — things  severally  compared  to  a  common  stan- 
dard or  measure ;  the  predicate  is — equal  by  *  coincidence,*  or 
by  being  compared  immediately — a  totally  distinct  mode  of 
comparison.  These  two  modes  are  said  to  concur ;  the  trial 
by  the  one  mode  is  a  test  or  mark  of  what  would  happen  in  a 
trial  by  the  other  mode.  We  have  an  opportunity  of  comparing 
two  things  with  the  same  third ;  we  have  no  opportunity  of 
applying  the  two  things  to  each  other ;  we  are  assured  by  the 
axiom  that  the  coincidence  of  the  two  with  the  common  third 
is  proof  that  they  would  coincide  if  we  could  apply  them  to 
each  other.  There  would  not  be  a  contradiction  in  terms, 
theie  would  only  be  a  contradiction  of  experienced  facts,  if  we 
denied  that  mediate  coincidence  infers  immediate  coinci- 
dence. 

Mr.  Mill,  in  the  new  edition  of  his  Logic,  p.  208,  states  that 
he  regards  Formal  Logic  as  the  logic  of  mere  consistency,  and 
the  dictum  de  omni  as  its  axiom  ;  he  does  not  insist  on  apply- 
ing to  it  the  nota  notce^  although  he  regards  that  form  as  the 
proper  axiom  for  the  logic  of  the  pursuit  of  truth  by  way  of 
Deduction ;  the  recognition  of  which  can  alone  show  how  it 
is  possible  that  deductive  reasoning  can  be  a  road  to  truth. 
So  viewed  it  is,  not  self-consistency,  but  an  inductive,  con- 
tingent, or  synthetic  proposition,  like  the  mathematical  axiom 
of  mediate  equals. 

The  difference  between  formal  deduction  and  real  deduction 
is  the  difference  between  syllogism  and  inductive  or  experi- 
mental truth.  Keal  deduction  is  the  following  out  of  an 
induction,  and  assumes  the  uniformity  of  nature.  That  the 
men  living  and  unborn  will  die  is  a  necessary  inference  from 
*  all  men  are  mortal,'  but  not  a  necessary  inference  from  the 
actual  premise,  which  is  confined  to  the  men  that  have 
actually  died.  The  real  deduction  contains  three  steps : — 
certain  individuals  possess  the  attributes  called  humanity,  and 
also  the  attribute  mortality  ;  these  two  attributes  have  been 


■■■  t 


i  v\ 


I 

i 


680 


SUPPLEMENTARY  NOTE. 


f 


conjoined  tlirongli  all  our  past  experience  ;  hence  tlie  presence 
of  the  one  marks  the  presence  of  the  other.  Now,  John  Brown 
and  William  Smith  possesses  the  first  fact,  humanity,  therefore 
they  possess  what  it  marks,  that  is  the  second  fact,  mortality. 
This  is  the  application  of  the  nota  noiw  in  its  purity  and  sim- 
plicity ;  the  uniformity  of  nature  being  supposed  in  addition. 

For  greater  clearness,  take  another  instance.  *  All  inert 
substances  gravitate ;  *  throughout  all  our  experience,  the 
j)roperty  *  inertness'  is  a  mark  of  the  property  *  gravity.' 
Now,  the  etherial  medium  in  space  has  the  mark  inertia  (by 
resisting  the  comets) ;  it  therefore  gravitates. 

But  still  the  question  recurs,  might  not  the  inference  in 
both  these  instances  be  given  under  the  dictum  de  omni  / 
For,  basing  on  the  uniformity  of  nature,  we  at  once  convert 
the  special  observations  into  a  general  law  ;  men  in  the  past 
have  died,  men  in  the  future  will  die  ;  whence  all  men  are 
mortal.  Caius  has  the  marks  of  man,  is  a  man  ;  Cains  is 
mortal.  Inert  matter  gravitates ;  the  ether  is  inert ;  the 
ether  gravitates. 

It  would  thus  seem  that  the  attainment  of  new  truth  by 
the  way  of  deduction,  does  not  imperatively  demand  any 
change  of  axiom.  The  dictum  and  the  nota  7iotcB  are  equally 
suitable.  If  so,  the  inference  must  still  be  a  case  of  necessary, 
implied,  or  self-consistent  truth.  Of  the  dictum  and  the  nota 
notce  alike,  we  must  declare  that  their  denial  is  a  self-contra- 
diction. 

Necessary  or  self-consistent  inference,  instead  of  being  con- 
fined to  the  manipulation  of  the  equivalent  forms  of  pro- 
positions, takes  a  wider  sweep  and  embraces  the  Syllogism, 
which  we  should  have  to  characterise  as  *  mediate  self-con- 
sistency,' *  mediate  necessity,'  *  complex  implication.'  The 
forms  lying  between  immediate  inference  or  propositional 
equivalence,  and  mediate  inference  or  syllogistic  equivalence, 
would  be  regarded  as  incidental  varieties  of  Self-consistency  ; 
they  need  not  be  forced  under  either  of  the  two  principal 
genera. 

When  we  sny  *  Socrates  was  wise,'  *  Socrates  was  poor ; ' 
therefore  *  one  man  was  wise  and  poor,'  we  draw  a  necessary 
or  self-consistent  conclusion,  but  not  by  the  way  of  the 
Syllogism,      as     representing     deductive     reasoning.      From 

*  Socrates  is  wise,'   and   *  Socrates  is  poor,'  we  can  conclude 

*  Socrates  is  wise  and  poor;*  *  wisdom  and  poverty  are  con- 
joined in  Socrates  ; '  the  axiom  or  assumption  here  is — when 
properties  can  be  afiirmed  of  a  subject  separately,  or  in  separate 


■^ 


THE  AXIOM  OF  THE  SYLLOGISM. 


681 


5 
ll 


propositions,  they  may  be  affirmed  conjunctly,  or  in  a  com 
pound  proposition.  Again,  to  proceed  to  the  farther  variation 
— one  man  was  wise  and  poor — we  perform  the  process  of  sub- 
Btituting  for  *  Socrates '  the  designation  *  one  man,'  which  prop- 
erly applies  to  him.  This  is  the  mode  of  equivalence  con- 
stantly assumed  in  working  algebraic  equations ;  where,  for  any 
expression,  we  insert  at  pleasure  another  equal  to  it.  Neither 
of  these  modes  is  the  same  as  the  dictum  de  omni,  and,  there- 
fore, they  need  not  be  forced  under  the  syllogism,  although  they 
amount  to  something  more  than  stating  an  equivalent  form  of  a 
single  proposition. 

F.— ANALYSIS  AND   SYNTHESIS. 

The  common  idea — Analysis  and  Synthesis — is  difficult  to 
express  adequately,  owing  to  the  variety  of  its  applications. 
Chemical  Analysis,  Mathematical  Analysis,  Logical  Analysis, 
with  the  corresponding  Syntheses,  have  a  basis  of  agreement,  but 
with  points  of  difference. 

The  general  idea  of  Analysis  is  separation;  of  Synthesis, 
composition  or  combination.  Yet  the  contrast  does  not  alto- 
gether correspond  to  the  distinction  of  Abstract  and  Concrete. 
Analysis  is  Abstraction,  but  Synthesis  is  not  the  negative  or 
the  absence  of  Abstraction ;  it  is  not  the  un-abstracted  Concrete. 
While  the  scientific  man  is,  by  the  law  of  his  beini^,  an  analyst, 
the  poet  or  artist,  who  does  not  analyze  but  combines,  is  not  a 
sjTithesist.  Synthesis  in  contrast  with  analysis,  is  combining 
after  analyzinsf. 

The  simplest  exemplification  of  the  two  correlated  processes 
is  seen  in  Chemical  Analysis.  The  Chemist  operates  upon  an 
unknown  mixture  or  combination  of  substances,  as  a  strange  pro- 
duct from  a  furnace,  or  the  stomach  of  a  poisoned  man.  He 
separates  and  identifies  the  various  ingredients  of  the  compound. 

The  obverse  Synthesis  would  consist  in  making  up  the  given 
compounds  by  means  of  the  several  elements  in  their  proper 
proportions.  Thus,  having  ascertained  the  precise  constituents 
of  a  mineral  water,  it  is  then  possible  to  form  the  water  artifi- 
cially. If  the  artificial  water  is  exactly  identical  with  the  natural 
water,  both  the  analysis  and  the  synthesis  are  successful  and 
complete.  It  is  by  the  analysis,  however,  that  the  synthesis 
has  been  possible.  The  analysis  is  the  foundation  of  a  new 
nrieans  of  production;  it  enables  us  not  merely  to  imitate  and 
rival  the   spontaneous  products  of  nature,  but  also,  if  need 


I  1 


N  '1 


CS2 


ANALYSIS  AND   SYNTHESIS. 


be,  to  vary  those  products  on  a  definite  plun  or  purpose.  Wo 
may  introduce  beneticiiil  vai-iatious  into  the  syntheses  of 
mineral  waters.  So,  having  analyzed  some  crude  substance 
medicinally  valuable,  we  may  artificially  compound  it,  first, 
literally  (which  proves  the  sufficiency  of  the  analysis),  and 
next  with  improved  adaptations  lor  the  end. 

The  most  notable  application  of  Chemical  synthesis  is  to 
the  formation  of  organic  compounds  in  tho  laboratory.  ^  By  a 
foregone  analysis,  the  chemist  has  discovered  the  constituent 
elements  of  these  compounds,  and  the  peculiarities  of  their 
union  ;  he  then  uses  his  knowledge  to  re-produce  by  laboratory 
processes  what  has  been  produced  in  the  course  of  living 
growth.  In  this  way,  urea,  acetic  acid,  and  many  other  or- 
ganic products  have  been  obtained  by  laboratory  synthesis. 
Such  syntbetic  efforts  are  the  trophies  of  analysis. 

Our  next  example  may  be  termed  Logical  Analysis  ;  it  is 
the  ordinary  Scientific  Analysis,  the  peculiar  case  of  Mathe- 
matics being  resei  ved.  Here,  Analysis  is  substantially  iden- 
tical with  generalization,  whether  of  the  notion  or  of  the  pro- 
position.    What  Synthesis  is  will  appear  presently. 

The  processes  of  assimilating,  identifying,  classing,  general- 
izing, absti'acting,  defining,  are  the  various  sides,  aspects  or 
stages,  of  one  fundamental  operation.  Now  Analysis  is  merely 
a  farther  aspect,  another  side,  of  the  same  proteaa.  To  identify, 
classify,  and  abstract,  is  to  separate  or  imalyse,  so  far  as  the 
case  admits ;  the  separation  being  no  longer  actual,  as  in 
Chemistry,  but  mental  or  ideal.  To  identify  and  classify 
transparent  bodies,  is  to  make  abstractive  separation,  or  ana- 
lysis, of  the  property  called  transparency  ;  or  to  view  its  func- 
tions, powers,  or  agencies  alone  and  apart  from  all  the  other 
powers  possessed  by  the  individual  transparent  bodies.  Water 
is  liquid,  but  this  aspect  is  disregarded  ;  diamond  has  extra- 
ordinary refractive  power  but  no  notice  is  taken  of  it ;  the 
two  substances  are  studied  merely  in  their  agreement  in  what 
we  call  transparency. 

Now  the  investigation  of  nature  turns  exclusively  on  this 
abstractive  separation.  Bodies  are  constituted  with  a  cluster 
of  powers  or  properties  iiiseparably  combinated,  yet  each 
pursuing  its  independent  course  without  any  disturbance  from 
the  others.  Water,  as  transparent,  has  a  power  exactly  iden- 
tical with  diamond  and  rock  crystal,  as  transparent ;  the  other 
peculiarities  wherein  the  two  bodies  stand  widely  contrasted 
have  no  relevance,  exercise  no  interference,  as  regards  the 
transparency.     Hence,  the  mind,  having  very  limited  powers 


ANALYSIS   MEANS  ABSTRACTION   AND   INDUCTION.     683 

of  attention,  and  being  easily  impeded  and  thwarted  by  dis« 
tracting  circumstances,  finds  the  advantage  of  neglecting  all 
allied  properties,  and  concentrating  its  powers  on  the  one 
subject  of  study  at  the  time. 

Thus,  Abstraction  and  Analysis,  if  not  identical,  are  the 
same  fact  viewed  with  a  slight  difference.  Abstraction  means 
separately  viewing  one  point  of  agreement,  and  leaving  all 
other  accompaniments  in  the  shade  ;  the  transparency  is 
studied  by  itself,  the  specific  gravity  and  all  other  incorpo- 
rated properties  being  left  out  of  sight.  Analysis  means  the 
very  same  thing  ;  only,  proceeding  a  little  farther,  it  supposes 
that  every  one  of  the  powers  of  a  given  concrete,  as  water, 
may  be  abstracted  by  turns, — tiansparency,  liquidity,  specific 
gravity ;  so  that  water  as  a  whole  may  be  analyzed,  or  sepa- 
rated (mentally)  into  a  number  of  different  powers,  whose 
enumeration  is  a  full  account  of  the  agency  of  water. 

The  farther  we  push  abstraction  and  generalization,  the 
farther  we  push  Analysis.  When,  after  generalizing  all 
mechanical  movements,  and  forming  an  abstract  idea,  or 
analytic  separation  of  molar  or  mechanical  force,  we  proceed 
to  identify  mechanical  momentum  with  molecular  forces,  we 
make  a  new  analysis  ;  we  separate  the  property  of  force  from 
its  exclusive  connexion  with  the  movements  of  masses,  and 
view  it  as  the  movement  of  matter,  whether  in  larger  or  in 
smaller  aggregates. 

It  is  now  requisite  to  assign  a  correlative  meaning  of  Syn- 
thesis. As  Analysis  is  the  ideal  separation  and  separate  exhi- 
bition of  all  the  functions  of  a  concrete  thing,  as  water,  iron, 
blood,  Synthesis  is  the  re-statement  of  the  whole  in  their 
aggregate.  Its  efficacy  would  be  shown  in  supposing  a  new 
^gg^^gO'te*  as  a  liquid  diamond,  a  metal  with  all  the  properties 
of  lead  except  its  corrosion.  It  would  also  be  exemplified  in 
the  act  of  communicating,  by  description,  the  knowledge  of  a 
mineral,  apart  from  a  concrete  specimen. 

Another  step  is  inevitable.  As  these  abstractive  properties, 
or  notions,  are  what  enter  into  the  Inductive  generalizations  of 
nature,  each  inductive  law  being  two  or  more  coupled  together, 
Analysis  becomes  applied  to  Inductive  discovery.  There  can 
be  no  wide  induction  without  a  correspondingly  wide  genera- 
lization of  at  least  two  notions,  that  is,  without  an  equivalent 
analytic  sepai'ation.  The  summit  of  generalization,  in  the 
notions  Quantity,  Inertia,  Gravity,  Persistence,  is  the  summit 
of  Analysis.  The  highest  generalities  of  Mind  are  attained 
through  the  most  thorough  Analysis  of  Mind. 


\h 


684 


ANALYSIS  AND  SYNTHESIS. 


The  employment  of  Analysis  to  signify  Indiiction  appears  in 
Aristotle,  and  pervades  the  logicians  after  him.  (See  Hansel's 
Aldrich,  App.  G,  Hamilton's  Logic,  II.,  2).  By  an  easy 
transition,  Synthesis  would  be  applied  to  Deduction.  The 
deductive  operation  of  following  out  the  law  of  gravity  to 
lunar  perturbations,  to  the  tides,  to  precession,  &c.,  would  be 
called  synthetical,  as  reuniting  abstract  elements  into  new 
combinations.  Having  mastered  the  laws  of  central  force, 
and  the  composition  of  forces,  Newton  deduced  or  inferred  the 
orbits  of  bodies  governed  by  other  forces  than  gravity. 

Synthesis,  however,  scarcely  applies  to  simjjle  Deduction, 
the  following  out  an  induction  to  a  new  case,  as  when  we  infer 
the  death  of  the  reigning  pope  from  the  mortality  of  the  men 
that  have  died.  There  is  no  element  of  combination  in  such 
cases,  there  is  but  the  filling  up  of  the  Induction,  which  is 
only  formally  complete  so  long  as  any  particulars  are  still 
outstanding.  The  synthetic  operation  is  best  realized  by  the 
complex  deductions,  or  the  union  of  several  deductive  laws  to 
a  composite  or  concrete  case — a  secondary  law. 

There  is  nothing  gained  by  using  the  terms  Analysis  and 
Synthesis  to  the  Inductive  and  Deductive  processes  respec- 
tively. We  may  show  in  what  wny  the  application  is  proper 
or  admissible,  and  that  is  all. 

The  use  of  the  Syllogism  may  be  expressed  ns  analyzing  or 
separating,  out  of  regard  to  our  mental  infirmity,  the  three 
parts  of  a  step  of  reasoning,  so  that  they  may  be  studied  in 
separation.  The  premises,  instead  of  being  confused  together, 
can  be  looked  at  apart,  and  each  judged  on  its  merits  in  its 
isolated  condition.  This  is  an  advantage  belonging  to  Method, 
or  Discovery,  Wherever  a  separation  of  this  kind  can  take 
place,  a  great  relief  is  given  to  the  understanding,  with  a 
corresponding  enlargement  of  its  powers. 

An  accountant  separates  his  columns  of  debit  and  of  credit, 
and  classifies  under  different  heads  payments  that  relate  to 
different  subjects  and  follow  different  rules. 

Grammatical  Analysis  may  be  followed  by  Grammatical 
Synthesis,  as  in  constructing  sentences  upon  new  types  sug- 
gested by  putting  together  the  component  elements  in  various 
ways. 

Criticism  is  a  species  of  analysis ;  and  the  composition  of 
an  Oration  or  a  Poem,  by  the  guidance  of  critical  and  rheto- 
rical rules,  is  a  strictly  synthetic  operation ;  the  previous 
analysis  is  the  foundation  of  the  method.  Composition,  with- 
out any  rules,  is  not  synthesis 


MATHEMATICAL  ANALYSIS. 


685 


It  is  a  weakness  of  the  unscientific  man  to  suppose  that  a 
concrete  thing,  as,  for  example,  a  political  institution,  can  be 
viewed  only  as  a  whole — that  its  operations  are  an  indivisible 
totality.  Thus,  the  obtaining  of  justice  by  the  procedure  in  a 
court  of  law  is  through  a  series  of  steps  and  processes — raisino* 
the  action,  appearing  by  counsel,  summoning  a  jury,  and  so 
on.  The  effect  of  the  whole  being  good,  the  un-analyzing  mind 
distributes  the  merit  equally  over  all  the  parts,  and  is  shocked 
when  a  doubt  is  raised  as  to  the  utility  of  any  one  constituent, 
as,  for  example,  the  jury. 

To  advert  finally,  to  the  special  instance  of  Mathematical 
Analysis  and  Synthesis.  A  new  step  in  geometry  may  be 
taken  either  by  analysis  or  by  synthesis.  The  various  Geo- 
metrical properties  are  said  to  have  been  first  discovered,  by 
analysis,  while  in  exposition  they  are  in  the  form  of  synthesis  ; 
which  is  not  strictly  the  fact ;  we  may  proceed  from  the  known 
to  the  unknown  in  both  ways  ;  discovering  new  properties  by 
synthesis  no  less  than  by  analysis. 

Let  us  take  Synthesis  first,  as  suiting  the  case  of  a  science 
whose  onward  march  is  by  the  way  of  Deduction.  Let  us 
assume  that  a  certain  proposition  has  been  arrived  at,  *no 
matter  how,  say,  *  Parallelograms  on  the  some  base,  and  be- 
tween the  same  parallels,  are  equal.'  Now  any  one  consider- 
ing this  proposition  might  readily  see,  that  the  axiom  of 
mediate  equality  applied  to  it,  would  show  that  the  same 
thing  might  be  predicated  of  equal  bases ;  such  an  inference 
would  be  an  effort  of  pure  deduction^  or  the  skilful  combin- 
ing of  two  already  established  propositions  to  yield  a  new 
third  proposition.  So,  by  a  repetition  of  the  same  apposite 
union  of  truths  possessed,  one  might  also  infer  that  '  Tri- 
angles on  the  same  base,  or  on  equal  bases,  and  between  the 
same  parallels,  are  equal.*  By  farther  combinations,  the  rea^ 
soner  might  go  on  to  deduce  or  infer  the  47th,  and  so  forth. 
All  which  is  a  purely  synthetic  operation ;  and  geometrical 
truths  may  be  evolved  to  any  extent  in  this  way.  Corollaries 
are  usually  deductive  inferences,  of  short  leap,  from  the  main 
proposition.  The  operation  is  seldom  one  of  simple  deduc- 
*tion,  there  is  usually  a  certain  concurrence  of  two  or  more 
propositions  to  the  new  result ;  and  the  mental  effort  lies  in 
bringing  these  together.  Geometrical  synthesis  and  deduc- 
tion are  thus  the  same  thing. 

What  then  is  Geometrical  Analysis  ?  Is  it  Induction  ?  We 
are  told  that  it  proceeds  from  the  unknown  to  the  known.  If 
one  were  to  suspect  or  gurmise  (without  being  sure)  that  the 


\ 


\ 


686 


ANA.LYSIS  AND   SYNTHESIS. 


square  of  the  hjpothenuse  of  a  triangle  is  eqnal  to  the  snm  of 
the  squares  of  the  sides,  and  assuming  it,  were  to  endeavour 
to  connect  it  by  a  thread  of  geometrical  reasoning  with  the 
established  propositions  of  geometry,  the  operation  would  be 
called  analytic  or  regressive,  as  compared  with  the  synthetic 
or  progressive  course  above  described.  Yet  in  reahty,  the 
mental  operation  is  substantially  the  same  in  both ;  the  two 
differ  only  in  superficial  appearance,  like  the  enquiry  from 
cause  to  effect,  and  from  effect  to  cause.  Assuming  the  truth 
of  the  surmise  first,  we  have  to  consider  what  prior  proposi- 
tions would  be  requisite  to  support  it ;  and,  again,  what  other 
propositions  would  support  these;  until  we  come  at  last 
upon  admitted  theorems.  The  real  operation  at  each  step  is 
a  deductive  one ;  we  feign  a  proposition  and  try  its  conse- 
quences ;  if  these  coincide  with  the  case,  such  proposition  or 
propositions  are  what  we  need  ;  and  if  they  are  found  among 
the  true  propositions  of  geometry,  we  have  made  good^  our 
point;  wo  have  proved  our  surmise,  and  put  it  in  the  triiin  of 
geometrical  deductions. 

The  facilities  for  this  inverted  deduction  are  so  greatly  mul- 
tiplied  by  Algebra  as  to  give  to  the  algebraic  processes  the 
designation  *  analytical'  by  pre-eminence.  In  an  Algebraic 
equation,  we  work  backward  from  the  known  to  the  unknown ; 
yet  it  is  by  a  series  of  properly  deductive  operations — the 
application  of  axioms  and  theorems  already  established. 
Algebraic  Geometry  is  called  *  Analytical ;  *  the  more  recon- 
dite processes  of  Algebra  are  called  the  Higher  Analysis. 

Thus,  while  Synthesis  has  throughout  a  reference  to  the 
deductive  and  combining  processes  of  science,  Analysis  relates 
to  generalization  or  induction,  everywhere  except  in  Mathe- 
matics, in  which  it  is  merely  the  mode  of  deductive  synthesis 
adapted  to  the  solution  of  special  problems.  The  geometer, 
when  he  has  no  special  end  in  view,  evolves  new  pnipositions 
by  direct  or  progressive  synthesis  ;  when  he  has  a  problem  to 
work  out,  he  confines  his  deductions  to  those  that  lie  in  the 
approaches  to  the  desired  solution.  The  course  of  discovery 
in  a  Deductive  science  can  be  only  Deductive;  it  consists  in 
following  out  generalities  in  hand  to  new  appliciitions ;  usually' 
by  combining  several  in  one  application.  The  art,  the  labour, 
lies  in  the  union  of  several  propositions  to  a  result.  The 
operation  must  be  tentative  ;  it  cannot  be  foretold  ;  yet  it  is 
amenable  to  a  certain  general  method,  which  practice  instils, 
and  which  is  not  altogether  beyond  the  reach  of  precept. 


BACON  ON  THE  NECESSITY  OF  FACTS. 


O. — GROWTH  OF  THE  LOGIC  OF  INDUCTION. 


687 


Previous  to  Mr.  Mill,  the  principal  contributors  to  the  Logic 
of  Induction  were  Bacon,  Newton,  Herschel,  and  Whewell. 

Bacon. — The  essential  part  of  the  service  rendered  by  Bacon 
to  Science  was  his  protest  in  favour  of  basing  generalities  on  a 
patient  collection  and  accurate  comparison  of  facts.  It  was 
too  much  the  custom,  he  complained,  to  *  just  glance  at  experi- 
ments and  particulars  in  passing  ;*  in  place  of  this,  he  proposed 
to  *  dwell  duly  and  orderly  among  them.'  With  the  whole 
force  of  his  eloquence  he  discouraged  flighty  speculation  and 
rash  conjecture,  and  urged  that  generalities  must  be  founded 
upon  a  wide  comparison  of  particulars. 

Following  np  his  emphatic  enunciation  that  men  must  have 
done  with  rash  speculations  and  rashly  abstracted  notions,  if 
they  desire  to  make  progress  in  their  knowledge  of  Nature,  he 
devised    modes   of  elucidating   truth    by  the   comparison  of 
instances  on  a  methodical  plan.     He  directs  the  arrangement 
of  facts  m  three  different  tables.     The  first  table  is  to  contain 
instances  agreeing  in  the  presence  of  the  phenomenon  to  be 
investigated ;  this  he  calls  a  Table  of  Essence  and  Presence 
{Tabula  Essentiae  et  Praesentiae),     The  second  table  is  to  con- 
*^|P  instances  wanting   in   the   phenomenon,   but   otherwise 
allied  to  the  instances  where  the  phenomenon  occurs,  each 
instance  corresponding  as  far  as  possible  to  some  one  instance 
in  the  first  table ;  this  he  calls  the  Table  of  Deviation,  or  of 
Absence  in  Allied  Instances  (Tabula  DecUnationis,  sive  Absen- 
tiae  m  Proximo).    The  third  table  contains  the  phenomenon  in 
different  degrees,  and  is  called  the  Table  of  Degrees  or  Table 
of  Comparison   (Tabula  Graduum,  sive  Tabula  Gomparitiva), 
The  constitution  of  the  three  Tables  is  exemplified  upon  an 
enquiry  into  the  phenomenon  of  Heat ;   for  the  prosecution  of 
which  are  assembled  no  less  than  27  instances  agreeing  in  the 
presence  of  heat,  32  allied  instances  agreeing  in  its  absence, 
and  41  instances  of  heat  manifested  in  different  degrees. 
^  The  three  Tables  seem  designed  for  the  convenient  applica* 
tion  of  the  three  leading  methods  of  Inductive  elimination- 
Agreement,  Difference,  and  Concomitant  Variations ;   but  we 
must   not   suppose   that   Bacon    realized   anything   like   the 
precision  of  those  methods.     He  did  not  conceive  the  idea  of 
choosing  his  instances  so  that  they  should  differ  in  every  point 
but  the  phenomenon  under  investigation,  agreeing  only  in  that 
—the  fundamental  idea  of  the  method  of  Agreement.    Nor  did 
he  conceive  the  idea  of  the  decisive  method  of  Difference,  the 


688 


GROWTH   OF  THE   LOGIC   OF  INDUCTION. 


choice  of  two  instances  agreeing  in  every  point  save  the  given 
phenomenon.  Having  collected  his  Tables  of  Instances,  he 
went  to  work  by  excluding  according  to  certain  canons  the 
irrelevant  instances,  then  making  a  hypothesis  or  guess  at  the 
troth,  and  finally  verifying  this  b}  farther  enquiry. 

Bacon  takes  especial  credit  for  his  process  of  Exclusion  or 
Rejection.  He  contrasts  it  with  the  popular  method  of  pro- 
ceeding by  Simple  Enumeration,  that  is,  by  counting  only  the 
favourable  instances,  overlooking  the  unfavourable;  and  he 
claims  to  be  the  first  to  make  it  prominent.  The  problem  of 
Induction  being  to  *  find  such  a  quality  as  is  always  present  or 
absent  with  the  given  quality,  and  always  increases  or 
decreases  with  it,*  *  the  first  work  of  true  induction  is  the 
rejection  or  exclusion  of  the  several  qualities  which  are  not 
found  in  some  instance  where  the  given  quality  is  present,  or 
are  found  in  some  instance  where  the  given  quality  is  absent, 
or  are  found  to  increase  in  some  instance  where  the  given 
quality  decreases,    or  to  decrease  whoa    the  given   quality 

increases.' 

It  will  be  observed  that  this  process  of  exclusion,  although 
a  great  advance  upon  generalizing  without  regard  to  contra- 
dictory instances,  is  very  rudimentary.  Bacon  does  not  dis- 
tinguish between  laws  "of  simple  Co-existence  and  laws  of 
Causation.  The  first  of  his  principles  of  Rejection  is  suited 
only  to  the  establishment  of  co  existences,  and  amounts  to  this, 
that  we  are  not  to  declare  two  qualities  universally  concomi- 
tant, if  in  certain  instances  we  find  one  absent  when  the  other 
is  present.  His  other  principle  of  rejection  is  the  reverse  of 
the  method  of  Concomitant  variations,  a  disproving  of  causal 
connexion  on  account  of  independent  variation ;   and  applies 

to  causation  alone.  ^ 

As  to  the  modes  of  certifying  the  hypothesis  allowed  after 
this  process  of  collecting  and  sifting  instances— the  Logic  of 
Proof,  Bacon  has  left  us  but  a  fragment.  Of  his  nine  divi- 
sions of  aids  to  Induction,  he  completed  only  the  first,  Prero- 
gatwe  Instanoea,  Under  this  head,  he  dictates  a  farther 
enquiry  into  particulars,  and  dwells  upon  instances  of  special 
value  to  the  inquirer,  calling  them  Prerogative  from  that  cir- 
cumstance. To  call  this  division  of  his  subject  an  aid  to 
induction  is  misleading;  we  expect  to  find  an  account  of 
instances  particularly  suitable  for  founding  inductions  upon, 
and  find  instead  illustrations  of  various  maxims  applicable  to 
Definition,  Observation,  and  even  Experiment,  as  well  as  som« 
specially  adapted  for  Inductive  EUmiuation. 


bacon's  inductive   METHODS. 


689 


It  is  among  the  Prerogative  Instances,  if  anywhere,  that  we 
are  to  look  whether  Bacon  had  conceived  any  practical  device 
for  bringing  the  process   of  Exclusion  or  Elimination  to  a  po- 
sitive result,  as  is  done  in  the  modern  methods  of  Agreement 
and  DiSerence.     Under  the  heading  of  Solitary  Instances,  we 
do  find  a  crude  approach  to  the  selection  of  instances  implied 
in  these  methods.      Solitary  Instances  are  either   instances 
that  exhibit  a  phenomenon  without  any  of  its   usual  accom- 
paniments, as  colour  produced  by  the  passage  of  light  through 
a  prism ;    or  instances  agreeing  in  everything  except  some 
particular  phenomenon,   as  different  colours  in  the  same  piece 
of  marble.      He   says  in  a  vague  way  that   such  instances 
shorten  very  much  the  process  of  Exclusion,     They  contain 
really  all  that  is  demanded  for  the  methods  of  Agreement  and 
Difierence.      Yet  in  Bacon's  hands  they  are  comparatively 
useless,  and,  as  part  of  his  method,  could  not  even  furnish  a 
suggestion  for  more  perfect  contrivances.     The  reasons  are  to 
be  found  in  his  vague  conception  of  the  problem  of  Induction. 
His  methods  of  Exclusion  are  of  avail  only  for  problems  of 
Cause  and  Effect ;  they  are  superfluous  for  problems  of  simple 
concomitance,  a  single  instance  of  disunion  being  sufficient  to 
disprove  such  a  connexion ;    yet  he  speaks  throughout  as  if 
his  elaborate  comparison  of  instances  were  designed  only  to 
prove  two  properties  co-existent.     To  this  confusion  he  was 
inevitably  led  by  the  subjects  he  proposed  to  investigate.     He 
seems  to  have  thought  principally  of  investigating  abstract 
qualities  of  bodies,  such  as   density,  weight,  colour,  volatility, 
porosity,  heat ;  his  purpose  being  to  establish  their  Form,  by 
which  he  seems  to  have  vaguely  understood  something  inva- 
riably present  with  these  qualities  and  endowing  them  with 
their  peculiar  nature.      Such  an  investigation   gave   ample 
scope  for  numerous  assemblages  of  instances  ;  but  the  methods 
of  sound  knowledge  were  not  likely  to  be  perfected  in  a  region 
that  can  be  approached  only  by  hypothesis. 

Under  Migratory  Instances,  keeping  still  in  view  the  same 
class  of  subjects,  he  recommends  attention  to  cases  where 
qualities  are  produced  in  bodies  ;  giving,  as  examples  the  pro- 
duction of  whiteness  by  pounding  glass  and  by  agitating  water 
into  froth.  From  this  we  gather  that  he  was  sensible  in  a 
measure  of  the  advantage  of  studying  the  introduction  of  a 
cause  into  known  circumstances,  although  in  his  narrow  field 
of  investigation  it  could  lead  to  no  result. 

In  these  two  first  instances  we  see  how  far  he  anticipated 
the  Methods  of  Agreement  and  of  Difference.     Few  of  the  other 


690 


GROWTH   OF  THE  LOGIC  OF  INDUCTION. 


twenty-five  instances  bear  strictly  on  the  Indnctive  ProcesB. 
With  Migratmy  Instances,  he  comipaires  Listances  of  CompaniorU' 
ship  or  Enmity,  such  as  the  nniversal  concurrence  of  heat  with 
flame,  and  the  nniversal  absence  of  consistency  in  air  ;  just  as 
when  a  change  is  produced,  we  must  seek  the  cause  in  some 
added  influence,  so  when  a  quality  is  always  present  in  a  sub- 
stance, we  must  seek  the  cause  in  some  property  of  that  sub- 
stance. In  StriJdng  or  Shining  Instances,  and  Clandestine 
Instances,  he  urges  the  importance  of  the  two  extremes  in  a 
variable  phenomenon.  His  seventh  and  eighth  Instances, 
Singular  Instances  (as  the  magnet  among  stones,  quicksilver 
among  metals),  and  Deviating  Instances  (individual  monstro- 
sities), are  important  for  alike  reason  ;  their  novelty  sharpens 
investigation.  His  twelfth  case.  Instances  of  Ultimity  or  Limits 
is  of  the  same  nature.  The  five  last  go  together  ;  the  stimu- 
lating efficacy  ascribed  to  them  is  a  favourite  topic  with 
Bacon,  and  is  the  real  characteristic  of  several  other  Instances. 
Instances  of  Alliance  or  Union  and  Instances  of  Divorce,  the 
thirteenth  and  fourteenth,  form  a  natural  couple.  The  one 
constitute  instances  reconciling  apparent  contradictions  ;  the 
heat  of  the  Sun  cherishes,  the  heat  of  Fire  destroys ;  a  con- 
ciliatory instance  is  found  in  the  growth  of  grapes  in  a  house 
heated  by  fire.  The  second  constitute  instances  disproving 
an  alleged  universal  connection ;  it  is  asserted  that  Heat, 
Brightness,  Rarity,  Mobility  are  always  found  together ;  we 
point  to  air,  which  is  rare  and  mobile  but  neither  hot  nor  bright. 

In  exemplifying  Instances  Conformable  or  of  Analogy,  he 
breaks  clean  away  from  Inductive  caution  ;  he  gives  as  ana- 
logous cases  the  gums  of  trees  and  most  rock  gems,  and  refers 
the  splendour  and  clearness  of  both  products  to  the  same 
cause,  fine  and  delicate  filtering.  Such  fancies  show  how  little 
Bacon  was  removed  from  the  rash  speculation  he  condemned 
in  the  works  of  his  predecessors. 

His  fourteenth  case,  the  famous  Instantia  Crucis  (Fingerpost 
Instance),  is  mentioned  in  the  Chapter  on  Hypotheses,  §  7, 
(p.  135),  and  is  there  placed  in  its  true  light  as  an  instance 
decisive  of  rival  hypotheses.  Such  instances  are  otherwise 
called  Decisive  and  Judicial  or  Oracular  and  Commanding. 

These  are  all  the  instances  that  have  a  direct  bearing  on 
Induction.  Of  the  remainder,  two  are  of  importance  for  Defi- 
nition, the  fifth  and  the  ninth,  Constit%Uive  Instances,  and 
Bordering  Instances.  Constitutive  instances  give  the  constitu- 
ents of  a  complex  notion ;  Bordering  instances  make  the 
baffling  transition  border  between  two  classes. 


PREROGATIVE  INSTANCES   OF  BACON. 


691 


Five  instances  are  classed  together  as  Instances  of  the  Lamp^ 
or  of  First  Information;  and  relate  to  Observation,     Under 
Instances  of  the  Door  or  Gate  he  comments  on  artificial  aids  to 
the  Senses — the  Microscope,  the  Telescope,    and   measuring 
rods.     By  Summoning  or  FJvoking  Instances,  he  means  indica- 
tions of  things  not  directly  accessible  to  observation  ;  such 
are  the  pulse  and  the  urine,  as  symptoms  of  the  condition  of 
the  human   body.      Instances  of  the  Road,  otherwise   called 
Travelling  and  Articulate  Instances,  display  stages  of  growth 
and  of  other  gradual  changes  ; — the  study  of  these  is  strongly 
recommended.     Supplementary  histances  or  Instances  of  Refuge 
are  said  to  supply  us  with  information  when  the  senses  entirely 
fail  us  ;  when  we  cannot  remove  an  agent  altogether  we  may 
vary  its  influence,  and  when  a  phenomenon  defies  observation 
we  may  study  analogous  phenomena.     Dissecting  or  Awakening 
Instances  are  such  as  great  efiects  produced  by  small  causes  j 
they  appeal  to  our  wonder,  and  stimulate  enquiry. 
^  The  seven  concluding  instances  embody  advice  on  the  prac- 
tical conduct  of  investigations.     The  four  first  of  the  seven 
instruct  us  how  to  attain  precision  by  definite  determination 
and  measurement  [Mathematical  or  Measuring  Instances) ;  the 
three  last  how  to  economize  our  resouces  {Propitious  or  Bene^ 
volent  Instances),     The  Mathematical  Instances  are  Instances 
of  the  Rod  or  Ride,  otherwise  called  of  Range  or  of  Limitation 
(where  measurement  of  Space  is  required)  ;  Instances  of  the 
Course  (measurement  of  Time) ;  Instances  of  Quantity,  or  Doses 
of  Nature  (where  attention  is  called  to  the  quantity  of  an 
agent) ;  and  distances  of  Strife  or  Predominance,  under  which 
title  he  gives  a  confused  enumeration  of  various  *  Motions,'  or 
tendencies  to  motion,  and  represents  the  movements  of  bodies 
as  determined  by  the  victory  of  one  or  other  of  these  conflict- 
ing tendencies — for  example,  when  water  runs  out  of  a  crack, 
the  motion  of  Continuity  is  overcome  by  the  motion  of  Greater 
Congregation  (the  tendency  of  bodies  to  the  ground).    Nothing 
could  be  more  fanciful  and  illogical  than  this  enumeration  of 
'  Motions.'      The   Propitious    Instances   are — Intimating  In- 
stances, which  point  out  what  is  most  useful  to  mankind ; 
Polychrest  histances  or  Instances  of  General  Use,  (contrivances 
useful  for  a  variety  of  purposes,  as  various  modes  of  excluding 
air  from  bodies  to  prevent  decomposition) ;    finally,  Instances 
of  Magic,  the  use  of  small  causes  to  produce  great  effects. 

We  have  given  no  account  of  the  tenth  division.  Instances 
of  Power,  oihQvw'xBQ  Instances  of  the  Wit  or  Hands  of  Man.  It 
is  partly  identical  with  awakening  Instances :  we  have  singled 


fel 


692 


GROWTH   OF  THE   LOGIC   OF  INDUCTIOJf. 


it  out  here  as  containing  a  homily  against  being  led  away  by 
admiration  of  skilful  contrivances  from  better  ways  of  accom- 
plishing the  same  end. 

In  concluding  this  brief  account  of  the  Baconian  method 
we  may  reiterate  that  the  merit  of  Bacon  lay  neither  in  the 
machinery  he  provided  nor  in  the  example  he  set,  but  in  the 
grand  impulse  he  gave  to  the  study  of  facts. 

Newton.  Newton  cannot  be  said,  any  more  than  Bacon, 
to  have  made  a  direct  contribution  to  the  methods  either  of 
Discovery  or  of  Proof;  but  he  set  an  example  of  rigorously 
cautious  enquiry  that  did  more  than  all  the  precepts  of  Bacon 
to  raise  the  standard  of  Proof,  and  to  purify  science  of  fanciful 
hypotheses.  He  even  went  to  an  extreme  and  was  over- 
rigorous  in  his  requirements  of  proof ;  such  was  his  dislike  to 
making  hypotheses  (in  the  sense  of  assuming  causes  not 
known  to  exist),  that  ho  wished  to  banish  them  from  science 
altogether. 

The  Rules  of  Philosophizing  (Regulce  Philosophandl)  pre- 
fixed to  his  Principia  were  long  quoted  t»,s  authoritative. 
Although  worded  with  an  express  view  to  the  establishment 
of  Gravitation,  they  are  necessarily  applicable  to  other  induc- 
tive generalizations. 

The  Frst  rule  is  twofold,  and  may  be  thus  explicated. 
(1)  "  Only  real  causes"  {veroe  causoe,  actually  existing  causes) 
*'  are  to  be  admitted  in  explanation  of  phenomena.'*  We  have 
stated  the  limits  to  this  under  Hypotheses  (p.  131).  (2)  "No 
more  causes  are  to  be  admitted  than  such  as  suffice  to  explain 
the  phenomena."  This  is  an  echo  of  the  maxim  known  as 
*  Occam's  razor  *  (*  Entia  non  sunt  multiplicanda  praDter  neces- 
sitatem  *),  and  means  that  when  one  cause  is  proved  to  be 
present  in  sufficient  amount  for  the  efFdct,  we  are  not  at 
liberty  to  suppose  the  presence  of  other  causes.  From  a  few 
words  of  explanation  affixed  to  the  rule,  we  should  gather  that 
he  meant  also  to  suggest  that  there  was  a  presumption  in 
favour  of  an  explanation  accounting  for  the  phenomena  by  the 
fewest  agencies — a  special  pleading  for  his  theory  of  gravita- 
tion :  *  Nature  does  nothing  in  vain,  and  a  thing  is  done  in 
vain  by  several  agents  when  it  can  be  done  by  a  smaller 
number.* 

The  Second  rule  is — **  In  as  far  as  possible,  the  same  causes 
are  to  be  assigned  for  the  same  kind  of  natural  effiicts."  For 
example,  respiration  in  man  and  in  beasts ;  the  fall  of  stones 
in  Europe  and  in  America.  An  aspect  of  the  Uniformity  of 
Nature  designed  to  favour  his  view  of  Solar  attraction  as  the 


NEWTON'S  RULES  OF  PHILOSOPHIZING. 


693 


etime  kind  of  effect  with  the  attraction  of  the  Earth  for  the 
Moon  or  for  terrestrial  bodies. 

The  Third — *' Qualities  of  bodies  that  can  neither  be  increased 
nor  diminished  in  intensity,  and  that  obtain  in  all  bodies 
accessible  to  experiment,  must  be  considered  qualities  of  all 
bodies  whatsoever."  Another  aspect  of  the  Uniformity  of 
Nature,  also  specially  adapted  to  his  extension  of  Gravity  to 
the  heavenly  bodies. 

The  Fourth — *  In  philosophical  experiment,  propositions 
collected  from  phenomena  by  induction,  are  to  be  held,  not- 
withstanding contrary  hypotheses,  as  either  exactly  or  ap- 
proximately true,  until  other  phenomena  occur  whereby  they 
are  either  rendered  more  exact  or  are  proved  liable  to  excep- 
tions.* This  is  indirectly  aimed  at  the  Cartesian  explanation  of 
the  celestial  movements  by  Vortices,  the  word  hypothesis  being 
used  in  an  opprobrious  sense,  as  involving  an  element  of  fancy 
operating  upon  imperfectly  known  materials.  The  rule  may 
be  held  to  imply  that  the  test  of  a  theory  is  its  accordance 
with  facts,  which  is  not  altogether  correct. 

Herschel.  Sir  John  Herschel  devotes  a  considerable  por- 
tion of  his  Discourse  on  the  Study  of  Natural  Philosophy  to  an 
account  of  *  the  principles  on  which  Physical  Science  relies 
for  its  successful  prosecution,  and  the  rules  by  which  a  syste- 
matic examination  of  Nature  should  be  conducted,  with  illus- 
trations of  their  influence  as  exemplified  in  the  history  of  its 
progress.*  His  introductory  chapters  on  this  head  reiterate 
with  greater  clearness  the  admonitions  of  Bacon ;  enforcing 
recourse  to  experience  as  the  sole  fountain  of  knowledge, 
illustrating  the  dangers  of  prejudice,  and  urging  the  import- 
ance of  recording  observations  with  numerical  precision. 
Farther,  he  dwells  upon  the  value  of  Classification  and 
Nomenclature ;  although  he  suggests  no  leadmg  principles  for 
either  process.  In  these  preliminary  remarks  we  recognize 
the  sagacity  of  the  practised  experimenter ;  but  it  is  when  he 
comes  to  analyze  what  is  involved  in  the  notion  of  Cause,  and 
to  state  his  rules  of  philosophizing,  that  we  become  fully  aware 
of  the  advance  made  in  the  investigation  of  Nature  since 
Bacon  and  Newtoo,  and  of  the  advantage  possessed  by  the 
expounder  of  scientific  method  in  having  a  large  body  of 
successful  observations  and  experiments  to  generalize  from. 

From  the  characters  implied  in  the  connexion  between 
cause  and  effect,  he  derives  nine  *  propositions  readily  appli- 
cable to  particulfir  cases,  or  rules  of  philosophizing.'  Four  of 
them,  the  second,  seventh,  eighth,  and  ninth,  are  the  four 


i 


III 


694 


GROWTH   OF  THE   LOGIC   OF  INDUCTION. 


Experimental  Methods  ;  which  are  stated  with  sufficient  pre- 
cision, although  not  exalted  into  the  prominence  given  them  by- 
Mr.  Mill  as  the  sufficing  and  only  methods  of  Proof.  By 
Herschel  in  fact,  the  four  rules  are  regarded  solely  as  aids  to 
Discovery  ;  the  idea  of  Proof  does  not  seem  to  have  crossed 
his  mind.  His  other  rules  are  more  purely  suited  for  Dis- 
covery. The  first  is  a  more  precise  statement  of  Bacon's  main 
principle  of  Exclusion,  the  foundation  of  the  methods  of  Agree- 
ment and  of  Difference  : — *  that  if  in  our  group  of  facts  there 
be  one  in  which  any  assigned  peculiarity  or  attendant  circum- 
stance is  wanting  or  opposite,  such  peculiarity  cannot  be  the 
cause  we  seek.*  The  third  is  *  we  are  not  to  deny  the  exist- 
ence of  a  cause  in  favour  of  which  we  have  a  unanimous 
agreement  of  strong  analogies,  though  it  may  not  be  apparent 
how  such  a  cause  can  produce  the  effect,  or  even  though  it 
may  be  difficult  to  conceive  its  existence  under  the  circum- 
stances of  the  case  ': — a  maxim  identical  with  the  principle  of 
analogy,  that  we  may  sometimes  infer  the  presence  of  one 
phenomenon  from  the  presence  of  another,  although  no  causal 
connection  has  been  established  between  them.  As  an  example 
he  states  that  though  we  do  not  know  how  heat  can  produce 
light,  we  yet  conclude  that  the  sun  is  intensely  hot  because  it 
is  vividly  luminous.  The  fourth  rule  is  that  *  contrary  or 
opposing  facts  are  equally  instructive  for  the  discovery  of 
causes  with  favourable  ones.*  The  fifth  recommends  the 
tabulation  of  facts  *  in  the  order  of  intensity  in  which  some 
peculiar  quality  subsists,* — perhaps  the  most  valuable  art  of 
Discovery.  To  this  precept  Herschel  very  properly  appends 
that  the  value  of  the  device  may  be  frustrated  by  the  interfer- 
ence of  counteracting  or  modifying  causes.  The  sixth  rule 
reminds  the  enquirer  *  that  sucFi  counteracting  or  modifying 
causes  may  subsist  unperceived,'  and  urges  atiention  to  them 
as  a  means  of  explaining  exceptions. 

In  some  general  remarks  following  the  enunications  of  his 
rules,  he  illustrates  the  necessity  of  combining  Deduction  with 
Induction  in  complicated  enquiries,  and  explains  the  nature 
of  Empirical  Laws,  glancing  at  the  fact  that  they  are  limited 
in  their  application  to  new  cases,  without  stating  more  pre- 
cisely what  their  limits  are. 

The  concluding  chapter  treats  *  of  the  higher  degrees  of 
Inductive  Generalization,  and  of  the  formation  and  verification 
of  theories.*  He  insists  that  the  assumed  agents  must  be 
verce  causoi^  *  such  as  we  have  good  inductive  grounds  to 
believe  do  exist  in  nature.*     The  value  and  the  test  of  a  hypo- 


WHEWELL*S   FACTS   AND   IDEAS. 


695 


thesis  he  places  in  its  accordance  with  the  facts,  and  its  enabling 
ns  '  to  predict  facts  before  trial.' 

Whewell.  The  echeme  of  the  late  Dr.  WhewelFs  Novum 
Organum  Renovatum  commends  itself  as  strikingly  thorough 
and  exhaustive.  It  professes  to  be  *  a  revision  and  improve- 
ment of  the  methods  by  which  Science  must  rise  and  grow,* 
founded  upon  a  comprehensive  History  of  Scientific  Discovery 
and  a  History  of  Scientific  Ideas.  Now,  theoretically,  there 
could  be  no  more  perfect  way  of  elaborating  a  body  of  maxims 
for  the  aid  of  the  discoverer,  than  to  pass  in  review,  chronolo- 
gically or  otherwise,  the  great  physical  discoveries  that  have 
been  made,  and  to  study  the  essentials  of  the  process  in  each 
case. 

tj  The  distinguishing  feature  of  Whe well's  scientific  writings 
is  his  persistent  driving  at  an  antithesis  that  he  conceives  to 
be  fundamental,  between  Ideas  or  Conceptions   and  Facts, 

This  antithesis  is  the  shaping  principle  of  his  system  and 
meets  us  at  every  point.  It  regulates  the  division  of  his 
history  into  two  parts  :  the  Histori/  of  Scientific  Ideas  tracing 
the  gradual  development  of  the  so-called  ideas,  such  as  Cause 
Affinity,  Life,  that  form  the  subject-matter  of  various  depart- 
ments of  science  ;  and  the  History  of  Scientific  Discovery,  illus- 
trating how  by  the  instrumentality  of  Ideas  (the  highest 
generalities),  and  of  Conceptions  (the  lower  generalities),  the 
particular  facts  of  Nature  are  united  and  bound  together. 
The  same  antithesis  divides  scientific  method  into  two  pro- 
cesses. Generalization  consisting  not  in  evolving  notions  from 
a  comparison  of  facts,  but  in  superinducing  upon  facts  con- 
ceptions supplied  by  the  mind.  There  are  two  requisites  to 
satisfy  before  this  operation  can  be  perfected,  namely,  that  the 
Conceptions  be  clear  and  distinct,  and  that  they  be  *  appro- 
priate *  to  the  Facts,  capable  of  being  *  applied  to  them  so  as 
to  produce  an  exact  and  universal  accordance : '  whence  there 
are  two  scientific  processes,  the  Exj^lication  of  Conceptions  and 
the  Colligation  of  Facts, 

The  grand  problem  of  Science  is  to  superinduce  Ideas  op 
Conceptions  upon  Facts.  The  business  of  the  discoverer  after 
familiarizing  himself  with  facts,  is  to  compare  them  with  con- 
ception after  conception,  in  the  view  of  finding  out  after  a 
longer  or  shorter  process  of  trial  and  rejection,  what  concep- 
tion is  exactly  *  appropriate  '  to  the  facts  under  his  consider- 
ation. When  the  investigator  has  at  length,  by  a  happy  guess, 
hit  upon  the  appropriate  conception,  he  is  said  to  *  colligate' 
the  facts,  to  *  bind   them  into  a  unity.*      No  distinction  is 


696 


GROWTH   OF  THE  LOGIC   OF   INDUCTION. 


m^* 


drawn  in  this  operation  between  the  generalization  of  Notions 
and  the  generalization  of  Propositions  ;  the  difference  between 
them  is  merged  in  the  one  grand  purpose  of  procuring  for 
facts  clear  and  appropriate  conceptions. 

It  is  difficult  to  understand  what  he  supposes  to  have  been 
the  origin  of  the  conceptions  thus  superinduced  upon  facts. 
He  speaks  of  them  as  being  struck  out  in  the  gradual  march 
of  Science  by  the  discussions  and  reflections  of  successive 
thinkers,  a  view  not  inconsistent  with  their  derivation  from 
the  comparison  of  particulars  and  the  gradual  evolution  of 
deep  and  pervading  agreements.  But  he  says  also  that  they 
are  supplied  by  the  mind,  while  facts  are  supplied  by  sense ; 
and  the  language  he  holds  regarding  the  suiting  of  facts  with 
their  *  appropriate '  conceptions,  is  consistent  only  with  the 
assumption  that  the  mind  is  a  repository  of  conceptions  accu- 
mulated there  independently  of  the  experience  of  particulars. 

By  this  initial  severance  of  generalities  from  the  particulars 
they  repose  upon,  he  excluded  from  his  method  definitions 
formed  by  the  comparison  of  facts  and  the  precise  statement 
of  common  features.  He  rather  decries  the  value  of  Definition, 
and  allows  it  no  place  of  honour  in  his  Explication  of  Conceptiovs. 
The  meaning  of  a  conception  is,  he  thinks,  oftoner  apprehended 
from  an  axiom  than  a  definition — another  instance  of  his  total 
neglect  of  the  distinction  between  notions  and  propositions. 

His  *  methods  employed  in  the  formation  of  Science,'  the 
title  of  the  third  Book  of  the  Novum  Organon,  are  three  in 
number.  Methods  of  Observation,  Methods  of  obtaining  clear 
Ideas,  and  Methods  of  Induction.  As  a  preliminary  to  Obser- 
vation, he  recognises  an  Analysis  or  Decomposition  of  Facts. 
Under  Observation,  he  discusses  chiefly  the  modes  of  obtaining 
precise  measurement ;  he  speaks  also  of  the  education  of  the 
senses,  but  does  not  attempt  to  lay  down  any  definite  precepts 
farther  than  recommending  the  study  of  Natural  Histoiy  and 
the  pi*actice  of  Experimental  manipulation.  His  Methods  of  ac- 
quiring clear  scientific  ideas,  are  neither  more  nor  less  than 
the  study  of  the  various  departments  of  science  where  the 
ideas  occur  ;  the  very  method  that  would  be  recommended  by 
a  preceptor  believing  in  the  evolution  of  general  notions  from 
particulars.  An  aid  to  the  acquisition  of  clear  ideas  is  Discus- 
sion. 

We  find  no  trace  of  the  three  leading  Experimental  Methods 
in  his  Methods  of  Induction,  nor  indeed  of  any  methods  of 
Proof.  He  conceived  that  his  province  was  to  furnish  arts  of 
Discovery,  in  so  far  as  anything  was  of  avail  beyond  natural 


WH swell's   methods   OF  INDUCTION. 


697 


iagacity ;  and  he  seems  to  have  thought  slightingly  of  the 
efficacy  of  the  Three  Methods  as  a  means  to  the  attainment  of 
new  laws.  His  principal  arts  of  Discovery  are  given  under 
the  title  of  *  Special  Methods  of  Induction  applicable  to  Quan- 
tity." The  Method  of  Curves  is  a  device  for  making  apparent 
to  the  eye  the  result  of  observations  on  the  concomitant  varia- 
tion of  two  phenomena.  It  *  consists  in  drawing  a  curve  of 
which  the  observed  quantities  are  the  Ordinates,  the  qnaut-ity 
on  which  the  change  of  these  quantities  depends  being  the 
Abcissa.*  The  Method  of  Means  is  the  familiar  device  of 
eliminating  the  effects  of  a  constant  cause  from  the  conjoined 
effects  of  accidental  accompaniments  by  striking  an  average  of 
several  observations.  The  Method  of  Least  Squares  is  a  some- 
what complicated  supplement  to  the  Method  of  Means.  When 
more  than  one  mean  is  proposed,  they  are  each  compared  with 
the  series  of  actual  observations;  the  deviations  from  each 
case  in  the  series  are  squared,  and  the  mean  is  affirmed  to  be 
most  probable,  the  sum  of  whose  squares  is  lowest  in  amount. 
The  MctJiod  of  Residues  is  the  method  we  described  under  that 
name. 

Under  the  title  of  *  Methods  of  Induction  depending  on 
Resemblance,*  he  illustrates  the  Law  of  Continuity  (*  that  a 
quantity  cannot  pass  from  one  amount  to  another  by  any 
change  of  conditions,  without  passing  through  all  intermediate 
magnitudes  according  to  the  intermediate  conditions ') ;  the 
Method  of  Gradation,  a  name  given  to  the  process  of  proving 
that  things  differ  not  in  kind  but  in  degree)  ;  and,  in  the 
Method  of  Natural  Classification,  enforces  the  importance  of 
grouping  objects  according  to  their  most  important  resem- 
blances. 

Perhaps  the  most  valuable  part  of  the  Organon  is  the  con- 
cluding Book  on  the  Language  of  Science.  Of  this  subject 
Whewell  had  made  a  special  study ;  his  aphorisms  on  the 
requisites  of  philosophical  language  contain  nearly  all  the 
important  points. 

H. — ART   OF  DISCOVERY. 

It  was  the  distinction  of  Mr.  Mill's  handling  of  Logic  to 
draw  a  clear  and  broad  line  between  the  Art  and  Science  of 
Proof  and  the  Art  of  Discovery.  The  main  business  of  Logic, 
according  to  him,  is  the  proving  of  propositions ;  only  in  an 
incidental  way  does  it  aid  in  suggesting  them. 

There  is,  in  the  laws  of  evidence  well  understood,  a  power- 
ful indirect  incitement   to  original   discovery.     A  thorough 


■»* 


•«i 


4 


i 


I  X-l. 


698 


ART   OF  DISCOVERT. 


means  of  testing  whatever  is  propounded  for  acceptance  leads 
to  the  rejection  of  the  false,  and,  consequently  to  a  renewed 
Bearch,  ending  at  last  in  the  true.  For  this  reason  alone 
would  discovery  be  more  rapid  in  the  Mathematical  and 
Physical  sciences,  where  verification  is  easy,  than  in  the 
Mental,  Moral,  and  Political  sciences,  where  the  facts  are 
wanting  in  the  requisite  precision.  Kepler  was  not  left  in  any 
doubts  as  to  whether  he  had  arrived  at  the  true  law  of  the 
periodic  times  of  the  planets ;  psychologists  could  not  so 
easily  satisfy  themselves  as  to  the  thorough-going  concomitance 
of  mind  and  body. 

The  Arts  and  methods  of  Discovery  embrace  (1)  the  Facts, 
that  is,  Observation  ;  and  (2)  the  Reasonings  on  Facts,  namely, 
Deduction,  Induction,  and  Definition ;  which  are  all  compre- 
hended in  the  one  process,  generalization. 

As  regards  the  accumulation  of  Facts,  there  is  little  to  be 
said,  and  that  little  is  apparent  at  a  glance.  Facts  are  ob- 
tained by  active  search,  enquiry,  adventure,  exploration.  For 
some,  we  must  travel  far,  and  visit  many  countries  ;  for  others 
we  have  to  lie  in  wait  till  occasions  arise.  For  a  third  class, 
we  have  to  institute  experiments,  involving  contrivance  and 
devices,  and  the  creative  ingenuity  of  the  practical  mind  ;  all 
which  is  itself  a  department  of  discovery,  the  least  of  any 
amenable  to  rules. 

The  arts  of  Observing  were  remarked  on,  in  the  Introduc- 
tion, as  being  special  for  each  department,  and  not  a  fit  sub- 
ject for  general  logic.  The  precautions  common  to  all  kinds 
of  observation,  in  regard  to  accuracy  and  evidence,  would  be 
worthy  of  being  recited,  provided  there  could  be  given  a  suffi- 
ciency of  illustrative  instances  to  make  the  desired  impression. 

From  the  limitation  of  the  human  faculties,  the  highest 
powers  of  observation  are  not  usually  accompanied  with  high 
speculative  force.  Hence,  among  other  consequences,  a  not 
unusual  misdirection  of  the  energies  of  great  observers. 

Passing  from  the  region  of  fact,  we  come  to  the  region  of 
Generality.  A  number  of  mdividual  observations  being  sup- 
posed, the  next  thing  is  to  discover  agreements  among  them — 
to  strike  out  identities  wherever  there  are  points  to  be  identi- 
fied ;  these  identities  ending  either  in  Notions  or  in  General 
Principles.  It  may  seem  a  work  of  vast  labour  to  exhaust 
all  the  facts  of  the  material  and  of  the  mental  world  ;  it  is  not  a 
less  labour,  although  of  a  difierent  kind,  to  exhaust  all  the 
identities  among  the  facts. 

Although  the  main  condition  of  success,  in  bringing    about 


PSYCHOLOGICAL   AIDS   TO   DISCOVERY. 


699 


Identities,  is  a  peculiar  intellectual  aptitude,  belonging  to  some 
men  in  a  pre-eminent  degree ;  yet  there  are  aids,  methods, 
and  precautions,  for  increasing  the  power.  Some  of  these 
aids  are  suggested  by  intellectual  psychology,  others  grow  out 
of  the  methods  unfolded  in  logic. 

The  methods  growing  out  of  the  psychology  of  the  intellec- 
tual powers  are  briefly  these  : — to  possess  the  mind  of  a  large 
store  of  the  related  facts  ;  often  to  refresh  the  recollection  of 
them  ;  to  come  into  frequent  contact  with  subjects  that  seem 
likely  to  afford  comparisons  and  analogies ;  not  to  stand  too 
near  any  one  set  of  facts  so  as  to  be  overpowered  by  their 
specialities ;  not  to  be  engrossed  with  the  work  of  observing 
the  facts  ;  and  in  general,  as  to  matters  of  great  difficulty,  to 
keep  the  mind  free  from  attitudes  and  pursuits  antagomstio 
to  the  end  in  view. 

Newton  alternately  devoted  himself  to  mathematics  and  to 
the  observation  and  collection  of  facts  in  the  various  subjects 
of  natural  philosophy ;  and  this  alternation  doubtless  makes 
the  perfect  physical  enquirer. 

Frequently  an  identification  has  to  be  embedded  in  some 
conception  apart  from  the  facts  ;  as  Kepler's  laws  in  numerical 
and  geometrical  statements,  the  law  of  sines,  &c.  In  such 
cases,  proximity  to  the  sources  of  the  conceptions  will  help  to 
bring  about  the  coalition.  If  mathematical  relations,  the 
mathematical  knowledge  should  be  kept  fresh,  and  so  with 
other  subjects.  These  constructing  instances  alone  give  any 
meaning  to  Whewell's  much  iterated  antithesis  of  Fact  and 
Idea.  The  identification  and  generalization  of  facts  often 
happens  without  any  *  idea,'  any  central  form,  or  representa- 
tive beyond  the  facts  themselves  ;  there  is  no  idea  for  a  circle 
but  round  things,  abstractedly  viewed  ;  and  no  idea  for  gravity, 
but  gravitating  bodies  compared  and  regarded  in  their  points 
of  agreement.  In  certgiin  other  cases,  a  conception  is  obtained 
(not  from  any  intuitive  source,  but)  from  some  already  existing 
generalization,  either  in  the  same  department,  or  in  another 
department.  The  *  idea '  for  embracing  water  waves,  and 
sound  vibrations,  was  found  by  Newton  in  the  *  Pendulum ;' 
and  apart  from  the  facts  themselves,  no  better  *  idea  *  has  yet 
been  given. 

The  connexion  of  Body  and  Mind  has  its  '  idea  *  yet  to  seek. 
There*  has  hitherto  prevailed  the  bad  idea  of  External  and  In- 
ternal. In  short,  the  most  suitable  comparison  wherein  to  em- 
brace the  relation  has  not  been  obtained  from  any  source,  intuitive 
or  other.     One  approximation  is  a  *  union  of  distinct  states,' 


i 


700 


ART  OF  DISCOVERY. 


The  arriving  at  difficult  identifications,  that  is,  the  tracing 
of  similarities  shrouded  in  diversity,  by  such  devices  as  have 
been  advanced  in  logic  with  a  more  special  eye  to  proof,  may 
be  viewed  in  the  first  place  with  regard  to  generalization  as 
such ;  not  distinguishing  the  notion  from  the  principle  or 
proposition.  What  pertains  specially  to  the  induction  of  the 
general  proposition,  namely,  the  concomitance  of  distinct  pro- 
perties, is  best  considered  apart. 

Under  the  Deductive  Method  (p.  96)  attention  was  called 
to  three  helps  to  the  discovery  of  generalities — multiplication 
of  inst-ances,  close  individual  scrutiny  of  instances,  and  selec- 
tion of  the  least  complicated  instances.  A  wider  view  of  the 
available  resources  must  now  be  taken.  We  have  to  see  how 
far  the  thorough  explication  of  the  reasoning  processes,  and  of 
all  the  adjuncts  to  reasoning,  called  forth  by  the  comprehen- 
sive Logic  of  Proof,  can  be  brought  to  bear  also  in  the  striking 
out  of  suggestions  to  be  submitted  to  proof  or  disproof. 

The  first  great  practical  lesson  derivable  from  Logic,  and 
applicable  in  a  much  wider  sphere  than  proof,  is  to  impress  us 
with  Generality  as  the  central  fact  of  science  and  of  all  know- 
ledge transcending  individuals.  After  we  have  gained  posses- 
sion of  a  certain  range  of  facts,  the  next  great  aim  is  to 
generalize  them  to  the  uttermost.  This  is  not  all.  In  pro- 
portion to  the  compass  of  any  agreement,  ought  to  be  the 
pains  taken  with  it,  and  the  prominence  given  to  it.  Wo 
have  urged,  under  the  Logic  of  Medicine,  the  prime  import- 
ance of  generalizing  the  Diseased  Processes  and  General  Thera- 
peutics, because  of  the  wider  compass  of  their  application.  In 
everything  else,  the  rule  holds.  The  biologist  should  take  no 
rest  until  he  has  exhaustively  accumalated  instances  of  the 
great  fact  of  Assimilation,  under  every  possible  variation  of 
circumstances.  In  like  manner,  the  physical  concomitants  of 
mental  processes  need  to  be  searched  o«t  in  all  their  innumer- 
able modes,  in  order  to  rise  to  the  generalities  of  the  connexion. 

The  severest  etiquette  of  the  most  punctilious  system  of 
ranks  and  dignities  in  society  is  as  nothing  compared  with  the 
graduation  of  estimate  and  of  respect  to  be  shown  to  generali- 
ties of  different  grades.  It  is  a  grave  logical  misdemeanour 
ever  to  give  an  inferior  generality  precedence  over  a  superior, 
or  to  treat  the  two  as  of  equal  consequence,  or  even  ^or  a 
moment  to  be  unaware  of  their  relative  standing.  We  may 
give  all  due  consideration  to  the  phenomenon  of  falling  bodies 
as  a  wide  fact  co-extensive  with  the  surface  of  the  earth  ;  but 
in  presence  of  the  superior  sway  of  the  law  of  gravity  througb- 


VALUE  OF  ORDER  AND  METHOD, 


701 


ont  the  solar  system,  the  terrestrial  fact  must  sink  into  a 
second  place  in  our  esteem. 

The  next  great  application  of  Method,  as  an  aid  to  discovery, 
consists  in  the  use  of  the  various  Forms  or  Formalities,  ela- 
borated with  a  view  to  proof.  This  is  the  largest  part  of  the 
present  subject. 

Logicians  have  always  striven  to  set  forth  the  value  of  Order, 
method,  and  explicitness,  in  complicated  statements.  Hamil- 
ton's dictum— making  explicit  in  the  statement  what  is  implicit 
in  the  thought — has  been  received  as  a  happy  enunciation  of 
one  function  of  logic.  Mr.  Mill  remarks,—*  One  of  the  great 
uses  of  a  discipline  in  Formal  Lggic,  is  to  make  us  aware  when 
something  that  claims  to  be  a  single  proj)Osition,  really  con- 
sists of  several,  which,  not  being  necessarily  involved  one  in 
another,  require  to  be  separated,  and  to  be  considered  each  by 
itself,  before  we  admit  the  compound  assertion.*  This  is  the 
disentangling  or  analyzing  function  of  the  syllogism,  and  is 
deservedly  extolled  as  perhaps  its  highest  utility.  It  is  a 
direct  remedy  for  the  weakness  of  the  mind  formerly  adverted 
to  (p.398). 

We  may,  however,  go  farther  back  than  the  exposition  of 
Syllogism  for  valuable  aids  growing  out  of  the  logical  formali- 
ties. All  the  Equivalent  Prepositional  Forms  are  instrumental 
as  means  of  suggestion.  They  enlarge  the  compass  of  any 
given  proposition,  by  unfolding  all  its  implications  ;  many  of 
these  not  being  disposed  to  rise  to  view  of  themselves,  or 
without  the  stimulus  of  the  formal  enunciation.  Of  all  the 
modes  of  Equivalence,  probably  the  Obverse  is  the  most  fruit- 
ful and  suggestive  ;  this  has  become  apparent  on  many  occa- 
sions, in  the  course  of  the  present  work ;  we  may  instance 
especially  negative  defining.  Next  in  value  is  Conversion  ;  the 
converting  of  A  by  its  legitimate  form  is  a  check  to  the  blunder 
of  supposing  the  subject  and  predicate  co-extensive  in  uni- 
versal affirmations  ;  and  the  arresting  of  the  mind  on  the  road 
to  impending  error  seldom  ends  there,  but  is  also  a  start  in 
the  search  for  truth.  Even  the  immediate  inference  from  the 
Universal  to  the  Particular  is  suggestive  of  facts  not  previously 
in  the  view. 

Much  could  be  said  as  to  the  unsystematic  but  wide-ranging 
mode  of  Equivalence  by  Synomyous  terms,  or  by  varying  the 
ways  of  expressing  the  same  proposition.  Although  some- 
what ensnaring,  this  is  a  fruitful  and  suggestive  operation. 
Its  power  consists  in  resuscitating  from  the  stores  of  the  past 
all  the  various  known  examples  of  the  proposition  ;  to  which 


702 


ART  OF  DISCOVEKY. 


\ 


■«'   '!■■ 


also  may  be  added  even  illustrations  and  analogies.  We  know 
from  many  celebrated  instances,  how  mere  opulence  of  phrase- 
ology gives  the  semblance,  and  occasionally  the  reality,  of 
superior  insight.  The  Shakespearian  wisdom,  the  stirriog 
apothegms  of  Pope,  have  their  source,  not  in  the  scientific 
process  of  the  intellect,  but  in  the  suggest! veness  of  exuberant 
phraseology. 

The  Methods  of  Inductive  Elimination,  both  directly  and 
indirectly  assist  in  Discovery.  The  collection  and  comparison 
of  instances,  to  comply  with  the  method  of  Agreement  as  a 
method  of  proof,  will  in  many  cases  lead  to  new  and  improved 
generalizations.  A  man  can  scarcely  go  through  the  labour 
requisite  for  establishing  a  law  of  high  generality  upon  ade- 
quate evidence,  without  adding  to  his  knowledge  of  the  law. 
Especially  is  this  likely  to  happen  in  working  the  Method  of 
Agreement,  whose  exigencies  are  exactly  those  of  inductive 
discovery. 

The  same  remark  applies  to  the  union  of  Agreement  in 
Absence  with  Agreement  in  Presence  ;  and  there  is  the  addi- 
tional force  and  incisiveness  that  always  belongs  to  the  working 
of  the  negative  side. 

The  method  of  Residues,  to  which  Sir  John  Herschel  called 
special  attention,  was  by  him  expressly  commended  as  an  aid 
to  Discovery. 

The  importance  of  Concomitant  Variations  has  already  been 
signalized,  and  will  be  again  referred  to. 

Without  dwelling  farther  on  the  specific  virtues  of  the 
several  methods,  we  would  call  attention  to  the  value  of  a 
complete  scheme  of  Inductive  Proof,  in  urging  a  search  for 
instances  to  fill  up  all  its  requirements.  He  that  has  thoroughly 
mastered  the  experimental  methods,  desires  to  bring  np  in 
favour  of  every  important  principle  a  series  of  particulars 
nnder  each  one  of  them  separately  ;  an  operation  as  fertile  for 
discovery  as  it  is  thorough-going  for  proof  or  disproof. 

The  remark  is  not  confined  to  the  methods  of  experimental 
elimination.  The  greater  number  of  propositions  or  laws  may 
derive  evidence  through  the  Deductive  Method,  and  through 
Chance  and  Probability  also.  The  wish  to  satisfy  all  possible 
methods  of  establishing  a  law  is  a  wholesome  stimulus  to 
enquire  after  the  very  facts  that  improve  the  character  and 
extend  the  application  of  the  law.  The  consilience  of  Induc- 
tion and  Deduction  is  the  very  highest  art  that  the  human 
intellect  can  command,  not  merely  for  proving  difficult  propo- 
gitions,  but  for  getting  hold  of  propositions  to  be  proved. 


INDUCTIVE  ELIMINATION. 


703 


All  this  is  to  repeat  in  another  shape,  and  in  a  grander 
sphere,  the  function  of  the  Syllogism  in  insisting  that  there 
should  be  produced  an  explicit  major  and  an  explicit  minor 
premise  in  any  pretended  ratiocination.  Every  inductive  in- 
stance should  be  viewed  in  its  proper  character,  by  reference 
to  the  method  that  it  subserves.  An  instance  of  Agreement 
should  be  given  as  such  j  a  Deductive  proof  should  be  quoted 
nnder  that  description.  If  the  Logical  rules  are  not  arbitrary, 
but  founded  on  a  correct  analysis  of  the  scientific  processes, 
the  conscious  reference  to  them,  on  all  different  occasions, 
must  be  a  relief  and  a  comfort  to  the  perplexed  enquirer. 

The  Deductive  operation,  understood  not  formally  as  in  the 
syllogism,  but  really  and  materially,  as  in  finding  new  appli- 
cations and  extensions  of  inductions,  is  a  pure  generalizing 
process.  It  consists  in  identifying  particulars  with  other  par- 
ticulars, exactly  as  in  the  properly  inductive  operation.  It  is 
the  same  march  of  mind  continued  and  prolonged.  An  induc- 
tion so  called  is  merely  a  certain  collection  of  particulars,  with 
a  generalized  expression  superadded  ;  deduction  is  the  bring- 
ing in  of  new  particulars.  The  difference  of  the  two  is  not  in 
the  mental  operation  ;  it  is  in  the  end  that  is  served.  The 
inductive  particulars  are  those  necessary  for  giving  the  gen- 
eralized expression,  and  for  proving  it  as  a  law  of  nature  ;  the 
subsequent  deduced  particulars,  not  being  required  for  esta- 
blishing the  generality,  receive  illumination  from  the  other 
class.  In  both  cases  the  effort  of  discovery  is  identical ;  it  is 
the  bringing  together  in  the  mind  by  the  force  of  resemblance 
a  host  of  particular  facts  from  all  times,  places,  and  subjects. 
Before  the  induction  is  gained,  the  particulars  contribute  to 
its  establishment ;  after  it  is  gained,  the  new  particulars  are 
receivers  and  not  givers  of  benefit. 

The  processes  included  under  Definition — the  canons  for 
Defining,  General  Naming,  and  Classification — are  processes 
of  Discovery  directly,  and  of  Proof  indirectly.  Mr.  Mill  calls 
them  subsidiary  to  Induction,  meaning  Inductive  Proof. 
Every  step  indicated  under  those  several  heads  has  an  imme- 
diate efficacy  either  in  suggesting  generalities,  or  in  purifying 
them  from  ambiguity,  perplexity,  and  confusion.  It  is  impos- 
sible to  make  a  single  well  concerted  move  in  any  of  the  paths 
marked  out  in  these  several  departments  without  gaining  an 
enlargement  of  views,  or  the  means  of  some  future  enlarge- 
ment. 

Everything  of  the  nature  of  an  antidote  to  inadvertent  and 
confused  thinking,  everything  that  reduces  information  to  the 


!■ 


704 


AUT  OF  DISCOVERY. 


sbape  best  suited  for  recollection  and  reference,  everything 
that  facilitates  the  comparison  of  resembling  facts — must  be 
enrolled  among  the  means  of  Discovery.  These  various  ends 
are  explicitly  aimed  at  by  the  prescriptions  contained  under 
Definition,  Naming,  and  Classification.  To  substantiate  the 
allegation  would  be  to  rehearse  the  methods  explained 
nnder  those  heads.  The  amassing  of  particulars,  positive  and 
negative,  with  a  view  to  Definition,  is  the  express  act  of  gen- 
eralization, and  brings  with  it  discoveries  of  concomitance,  as 
well  as  generalizes  notions.  All  the  devices  of  Naming  are 
intended  primarily  to  ease  and  assist  the  understanding  in 
arriving  at  new  truths.  The  machinery  of  Classification  is  still 
more  strikingly  the  economizing  of  the  faculties  in  amassing 
and  in  manipulating  knowledge. 

When  the  generalizing  process  has  expressly  in  view  the 
discovery  of  laws,  or  concwning  properties,  a  most  material 
help  (as  formerly  seen)  is  afforded  by  Tabulation,  espe- 
cially according  to  a  scale  of  degree.  Failing  this,  great  stress 
is  always  laid  upon  extreme  instances.  These  are  the  glaring 
and  striking  instances  of  Bacon  and  Herschel  (see  the  Re- 
search on  Dew,  p.  68).  The  method  of  exhibiting  gradation 
by  Curves  is  considered  one  of  the  best  ways  of  suggesting 
numerical  laws. 

Mr.  Darwin  has  given  an  account  of  the  steps  that  led  him 
to  propound  the  doctrine  of  Development  under  Natural 
Selection.  It  affords  an  interesting  commentary  on  the  fore- 
going enumeration  of  the  causes  that  prompt  original  sugges- 
tions. 

*  When  I  visited,  during  the  voyage  of  H.M.S.  Beagle^  the 
Galapagos  Archipelago,  situated  in  the  Pacific  Ocean  about 
600  miles  from  the  shore  of  South  America,  I  found  myself 
surrounded  by  peculiar  species  of  birds,  reptiles,  and  plants, 
existing  nowhere  else  in  the  world.  Yet  they  nearly  all  bore 
an  American  stamp.  la  the  song  of  the  mo^king-thrush,  in 
the  harsh  cry  of  the  carrion-hawk,  in  the  great  candlestick- 
like opuntias,  I  clearly  perceived  the  neighbourhood  of 
Anoierica,  though  the  islands  were  separated  by  so  many  miles 
of  ocean  from  the  mainland,  and  differed  from  it  in  their 
geological  constitution  and  climate.  Still  more  surprising  was 
the  fact  that  most  of  the  inhabitants  of  each  separate  island 
in  this  small  archipelago  were  specifically  different,  though  most 
closely  related  to  each  other.  The  archipelago,  with  its  innu- 
merable craters  and  bare  streams  of  lava,  appeared  to  be  of 
recent  origin  ;  and  thus  I  fancied  myself  brought  near  to  the 


CONSTRUCTIVE  INVENTION. 


705 


very  act  of  creation.      I  often  asked  myself  how  these  many 
peculiar  animals  and  plants  have  been  produced  :  the  simplest 
answer  seemed  to  be  that  the  inhabitants  of  the  several  islands 
had  descended  from  each  ofeher,  undergoing  modification  in 
the  course  of  their  descent ;   and  that  all  the  inhabitants  of 
the  archipelago  had  descended  from  those  of  the  nearest  land, 
namely  America,  whence  colonists  would  naturally  have  been 
derived.     But  it  long  remained  to  me  an  inexplicable  problem 
how  the  necessary  degree  of  modification  could  have  been 
effected,  and  it  would  have  thus  remained  for  ever,  had  I  not 
studied  domestic  productions,  and  thus  acquired  a  just  idea 
of  the  power  of  Selection.     As  soon  as  I  had  fully  realized  this 
idea,  I  saw,  on  reading  Malthus  on  Population,  that  Natural 
Selection  was  the  inevitable  result  of  the  rapid  increase  of  all 
organic  beings  ;  for  I  was  prepared  to  appreciate  the  struggle 
for  existence  by  having  long  studied  the  habits  of  animals.  * 
(Domestication,  vol.  I.,  p.  9). 

Throughout  the  entire  logical  scheme,  the  analytic  separation 
already  insisted  on,  is  an  invaluable  help  to  the  faculties  under 
the  complications  of  natural  phenomena.  To  enable  us  to  view 
separately  whatever  can  be  separately  viewed  is  the  motive 
for  such  artificial  divisions  as  Structure  and  Function  in 
biology.  Physical  Side  and  Mental  Side  in  psychology.  Order 
and  Progress,  Theory  and  Practice  in  politics.  Conservation 
and  Collocations  in  cause  and  effect,  Description  and  Explana- 
tion everywhere. 

The  process  of  Invention  in  the  Arts  and  business  of  life,  is 
amenable  to  the  general  rule  of  kee})ing  the  mind  fresh  upon 
the  most  likely  sources.  The  mere  cogitating  process  in  prac- 
tical constructions  is  exactly  the  same  as  in  the  solving  of 
geometrical  or  other  problems.  Certain  data  are  given,  a 
certain  construction  is  required  ;  there  is  an  intervening  chasm 
that  has  to  be  bridged.  The  habit  of  analytical  separation  is 
of  avail  in  this  instance  also.  The  mind  should  steadily  view 
one  point  at  a  time,  drawing  out  connexions  with  each  by 
turns.  Thus,  to  t^ke  a  simple  geometrical  construction  :  given 
the  vertical  angle,  the  base,  and  the  altitude  of  a  triangle  to 
construct  it.  Now  the  base  is  given,  and  we  have  to  follow 
out  the  deductions  and  implications  of  the  two  other  data — 
altitude  and  vertical  angle — with  a  view  to  arrive  at  some 
known  process  that  will  construct  the  triangle.  Let  us  con- 
sider separately  what  the  altitude  will  suggest.  Now,  a 
certain  fixed  altitude  implies  that  the  apex  ot  the  triangle  will 
lie  somewhere  in  a  line  parallel  to  the  base ;  consequently,  if 


'II 


i* 


706 


ART  OF  DISCOVERY. 


we  draw  such  a  parallel,  we  limit  the  place  of  the  apex  to  that 
line.  Turn  next  to  the  given  angle.  Considering  how  to 
erect  upon  a  given  base  a  triangle  with  a  given  vertical  angle, 
we  are  reminded  that  upon  the  given  base  may  be  constructed 
an  arc  of  a  circle,  such  as  will  contain  that  angle.  The  next 
step  is  to  find  a  means  of  constructing  the  proper  arc ;  the 
operation  of  discovery  is  exactly  the  same ;  and  brings  us  at 
length  to  some  construction  that  we  can  perform.  We  then 
unite  our  two  threads  hitherto  followed  out  in  separation. 
The  parallel  line  first  suggested,  and  the  arc  next  found  out, 
give  by  their  intersection  an  apex  to  the  desired  triangle.  It 
is  our  previous  knowledge  that  must  forge  the  links  of  con- 
nexion between  what  is  given  and  what  is  required ;  but  the 
analytic  habit  concentrates  the  attention  by  turns  on  each 
datum,  and  each  outgoing  from  it ;  and  this  is  probably  the 
utmost  that  mere  art  or  method  can  do  for  us  in  constructive 
inventions. 

The  uncertainty  as  to  where  to  look,  for  the  next  opemng  m 
discovery,  brings  the  pain  of  conflict  and  the  debility  of 
indecision.  This  is  a  case  fit  to  be  met  by  the  collective 
wisdom  of  a  generation.  There  might  at  intervals  be  held  a 
congress  on  the  condition-of-science  question,  to  decide,  accord- 
ing to  all  the  appeai-ances,  what  problems  should  be  next 

taken  up.  ,, 

Lessons  may  be  drawn  from  the  history  of  ilirrors,  as  well 
as  of  Truths.  All  the  Fallacies  are  beacons  both  in  discovery 
and  in  proof.  Every  soarce  of  confusion  is  an  incubus  on  in- 
vention. More  particularly,  the  excessive  devotion  to  the  con- 
crete, and  to  the  artistic  interests  nourished  by  it,  may  amount 
to  a  total  disqualification  for  scientific  originality,  whose  very 
existence  is  in  the  domain  of  abstraction. 

Certain  widely  prevailing  tendencies  of  natural  phenomena 
have  been  indicated  as  of  value  in  prompting  discovery.  Such 
are  the  Law  of  Continuity,  and  the  maxim  that  Nature  works 
by  the  Simplest  Means.  Both  these  principles  are  uncertain 
in  their  scope ;  which,  however,  does  not  prevent  them  from 
being  used  to  give  suggestions  ;  it  only  disqualifies  them  from 
being  conclusive  evidence.  If  we  are  careful  to  verify  our 
hypotheses,  we  are  at  liberty  to  obtain  them  from  any  source. 
Still,  the  mind  that  has  become  largely  conversant  with  the 
ways  of  nature  will  find  many  more  fruitful  sources  of  suggeft- 
tion  than  either  of  those  principles. 


EECITAL  OF  FACTa 


I. — HISTORICAL   EVIDENCE. 


707 


Two  leading  branches  of  Evidence,  applied  in  practical  life, 
are  Legal  Evidence  and  Historical  Evidence.  The  two  depart- 
ments have  much  in  common.  The  evidence  both  in  courts  of 
law  and  in  matters  of  history  is  probable,  and  approaches  to 
certainty  by  the  summation  of  probabilities. 

The  following  abstract  of  Historical  Evidence  represents 
the  maxims  in  use  among  historians  at  the  present  day,  as 
summarized  by  Sir  G.  C.  Lewis. 

The  object  of  History  is  the  recital  of  facts— of  events  that 
have  actually  occurred. 

In  the  case  of  contemporary  history,  the  writer  may  be  able 
to  rely  upon  his  own  observations,  or  upon  original  documents 
obtained  from  authentic  sources.  Personal  knowledge  was 
the  basis  of  much  of  Xenophon's  Anabasis,  Polybius'  History, 
Caesar's  Gaelic  War,  and  Lord  Clarendon's  History  of  the 
Rebellion.  But  the  greater  part  even  of  contemporary  history 
must  repose  on  the  evidence  of  witnesses. 

To  a  historian,  not  himself  cognizant  of  the  events  he  nar- 
rates, the  sources  of  information  fall  under  one  or  other  of 
two  classes  : — (1)  Monuments,  ruins,  coins,  and  generally  all 
ancient  remains  ;  and  (2)  the  evidence  of  Witnesses.  From 
the  former  exclusively  is  derived  whatever  we  know  of  the 
pre-historic  age  ;  in  the  same  way  as  geology  is  built  on  in- 
ferences drawn  from  fossils  and  the  nature  and  position  of 
rocks.  It  is  only  with  regard  to  history  resting  upon  the  tes- 
timony of  witnesses  that  rules  of  historical  evidence  apply. 

Two  points  demand  the  notice  of  one  seeking  to  verify  any 
alleged  historical  fact.  (1)  Does  the  evidence  of  the  witness 
exist  in  an  authentic  shape  ?  and  (2)  Is  it  true  ?  The  first 
regards  the  accuracy  wherewith  the  evidence  has  been  trans- 
mitted to  us ;  the  second,  the  worth  of  the  evidence  itself. 
The  means  of  knowledge  of  the  witnesses,  the  goodness  of 
their  memory,  their  judgment,  their  general  veracity,  their 
special  interests, — are  all  to  be  considered.  This  the  historian 
has  in  common  with  a  jury  or  a  judge,  extiept  that  he  has  to 
deal  with  men  long  since  dead,  and  whose  character  there  is 
more  or  less  difficulty  in  ascertaining.  What  forms  the  pecu- 
liar subject-matter  of  rules  of  historical  evidence  is  not  there- 
fore the  worth  of  the  evidence,  but  the  accuracy  of  its  trans- 
mission. 

The  supreme  canon  of  historical  evidence  is  that  all  tasti* 


r 


H 


708 


HISTORICAL  EVIDENCE. 


mony  must  be  contemporary^  or  received  directly  or  through 
trustworthy  tradition,  from  contemporaries.  *  Whenever  any 
event  is  related  in  histories  written  after  the  time,  and  not 
avowedly  founded  on  contemporary  testimony,  the  proper 
mode  of  testing  its  historical  credibility  is  to  enquire  whether 
it  can  be  traced  up  to  a  contemporary  source.  If  this  cannot 
be  done,  we  must  be  able  to  raise  a  presumption  that  those 
who  transmitted  it  to  us  in  writing  received  it,  directly  or 
through  a  trustworthy  tradition,  from  contemporary  testi- 
mony? If  neither  of  these  conditions  can  be  fulfilled,  the 
event  must  be  considered  as  incurably  uncertain,  and  beyond 
the  reach  of  our  actual  knowledge.'  (Lewis's  Methods  of 
Politics,  I.  270.) 

This  rule  is  universally  recognized  as  inclusive ;  whatever 
is  established  by  such  testimony  is  credible.  There  is  not, 
however,  the  same  unanimity,  in  admitting  it  as  exclusive;  or  that 
whatever  is  not  authenticated  by  external  evidence  is  uncer- 
tain. A  stringent  application  of  the  rule  makes  such  havoc  of 
ancient  history,  that  many  learned  men  have  been  tempted  to 
exercise  their  ingenuity  in  trying  to  pick  out  of  the  mass  of 
tradition  some  certain  indications  of  the  true  course  of  events. 
The  same  impulse  that  first  led  to  the  invention  of  fabulous 
history — an  inability  to  rest  content  with  a  background  of 
historical  ignorance —now  misleads  critics  and  historians. 
They  expect  by  a  species  of  historical  divination  to  strip  ofi" 
the  false  additions  to  the  ancient  stories— to  sift  from  the 
fables  the  grains  of  genuine  fact.  Yet  it  would  seem  as  if  the 
utmost  that  could  be  gained  would  be  that  the  event  may  have 
happened  as  supposed.  To  prove  that  the  event  did  happen, 
nothing  can  make  up  for  the  want  of  external  attestation. 
Internal  improbability  may  enable  us  to  doubt  or  disbelieve 
an  alleged  fact ;  internal  probability  cannot  assure  us  that  the 
fact  was  as  alleged ;  ihe  only  decisive  evidence  is  the  testi- 
mony of  credible  witnesses. 

The  difference  between  the  internal  and  the  external  stand- 
ards of  evidence  appears  remarkably  in  the  results  of  their  ap- 
plication. Sir  G.  0.  Lewis,  refusing  to  admit  internal  con- 
sistency or  plausibility  as  a  warrant  for  belief,  rejects  the 
accepted  History  of  Kome  down  to  the  war  with  Pyrrhus. 
Niebuhr,  on  the  other  hand,  divides  this  period  into  three 
parts  that,  in  his  opinion,  differ  greatly  in  historical  value. 
The  era  of  Romulus  and  Numa  (80  years)  he  considers  wholly 
fabulus;  from  TuUus  Hostilius  to  the  first  Secession  of  the 
Plebs  (179  years)  is  mythico-historical,  a  twilight  of  fable 


■piiw-— 


TRAliSMISSION  OF  WRITTEN  EVIDENCE. 


709 


and  fact ;  from  the  Secession  of  the  Plebs  to  the  war  with 
Pyrrhus  (213  years)  is  solid  history.  It  would  perhaps  be 
too  much  to  condemn  Niebuhr's  efforts  on  a  priori  grounds. 
To  what  extent  a  license  of  guessing  may  be  permitted  will 
best  be  seen  when  it  has  been  tried  by  different  men.  If  the 
result  should  be  a  general  concordance  of  opinion,  we  might 
reasonably  infer  that  the  ancient  narratives,  although  they 
conceal,  nevertheless  betray  the  truth.  If,  however,  this 
method  lead  to  irreconcileable  and  endless  diversity  of  opinion, 
it  must  cease  to  be  regarded  as  valuable  or  trustworthy. 

Evidence  may  be  transmitted  in  two  ways,  by  writing  or  by 
oral  tradition.     These  may  be  considered  separately. 

The  value  of  a  written  memorial  consists  generally  in  this, 
that  its  credibility  is  not  impaired  by  the  mere  action  of  time. 
An  English  mathematician  named  Craig  held  that  all  testi- 
mony was  enfeebled  by  mere  lapse  of  time,  and  thus  the  evi- 
dence of  Christianity  would  at  length  be  reduced  to  zero. 
Assuming  that  that  event  would  coincide  with  the  end  of  the 
world,  he  calculated  when  the  end  would  come.  Laplace 
adopts  the  same  view,  and  says  that  even  in  spite  of  printing, 
the  events  that  are  now  most  certain,  will,  in  the  course  of 
ages,  become  doubtful.  But  this  must  be  regarded  as  an  error. 
The  only  deterioration  that  a  document  can  suffer  from  mere 
lapse  of  time  is  the  increased  difficulty  of  weighing  the  credi- 
bility of  the  writer.  A  written  memorial  has  none  of  the 
disadvantage  of  a  statement  handed  down  orally  from  one 
person  to  another,  and  losing  value  at  each  transmission. 

Yet  the  evils  of  transmission  are  not  wholly  overcome  even 
with  written  records.  Two  doubts  may  arise,  (1)  whether  the 
writing  is  ascribed  to  its  real  author,  and  (2)%vhether  it  is  free 
from  interpolation  and  mutilation. 

*  In  many  cases  the  original  memorial  is  preserved ;  as  in 
ancient  inscriptions  upon  stone,  brass,  or  other  durable  ma- 
terial. Such  are  the  inscriptions,  in  the  arrow-headed  cha- 
racter, on  the  Babylonian  bricks,  and  on  other  Assyrian 
monuments  ;  the  hieroglyphics  engraved  on  the  remains  of 
Egyptian  architecture  ;  and  the  numerous  Greek  and  Latin 
inscriptions  found  in  different  parts  of  Asia  Minor,  Africa,  and 
Europe,  and  belonging  to  different  ages.  Ancient  coins,  with 
their  legends,  are  another  original  record  of  the  same  kind,  as 
well  as  historical  sculptures  or  paintings,  such  as  the  bas-reliefs 
on  the  column  of  Trajan,  or  the  Bayeux  tapestry.  Ancient 
documents,  likewise,  containing  the  authentic  records  of  many 
important  events  and  public  acts,  are  preserved  in  the  original 


710 


HISTORICAL  EVIDENCE. 


ift'  ft 


in  national  archives.  Snch,  for  instance,  is  Domesday-book,  the 
rolls  of  Parliament,  court  records,  charters,  and  other  official 
registers  and  documents  kept  in  public  depositories.'  (Lewis, 
I.  201). 

In  authenticating  books  and  documents,  whose  safe-keeping 
is  not  specially  provided  for,  great  difficulty  is  often  experi- 
enced. A  mere  tradition  regarding  the  origin  of  a  document 
would  be  exposed  to  nearly  all  the  doubts  that  attach  to  oral 
tradition.  *  Hence  the  importance  of  archives,  chartularies, 
public  libraries,  and  other  safe  places  of  deposit,  which  are 
under  the  care  of  trustworthy  guardians,  appointed  and  con- 
trolled by  public  authority.*  The  law  of  England  requires 
that  written  documents,  before  they  can  be  tendered  as  evid- 
ence, be  produced  from  the  proper  place  of  custody. 

The  difficulty  of  ascertaining  the  genuineness  of  ancient 
books,  is  forcibly  illustrated  by  the  controversy  regarding  the 
Platonic  Dialogues.  Until  the  close  of  last  century,  thirty-six 
dialogues  were  attributed  to  Plato  on  the  authority  of  Thra- 
syllns,  whose  list  dates  from  about  the  commencement  of  the 
Christian  era.  As,  however,  Plato  died  more  than  three 
hundred  years  before,  the  canon  of  Thrasyllus  stands  in  need 
of  corroboration  and  suppoH.  Most  of  the  German  Critics 
allow  it  very  little  weight,  and  test  each  dialogue  upon 
own  evidence,  external  or  internal,  but  chiefly  internal.  This 
unavoidably  gives  rise  to  great  diversity  of  opinion,  and  there 
is  little  agreement  as  to  what  ought  to  be  rejected  or  retained. 
Ast,  the  least  sparing  critic,  leaves  only  fourteen  out  of  thirty- 
six.  Mr.  Grote,  on  the  other  hand,  discards  the  German 
criticism,  and  putting  little  stress  upon  the  indications  of 
authorship  contained  in  any  reputed  dialogue  of  Plato,  searches 
for  more  decisive  evidence,  so  far  as  it  can  be  got,  in  the 
history  of  the  books  mentioned  by  Thrasyllus. 

Plato  died  B.C.  347,  and  left  his  works  to  the  care  of  the  school 
continued  under  Xenophanes  and  Speusippus.  We  do  not 
possess  any  list  of  their  master's  works  resting  on  their  autho- 
rity, and  the  first  solid  ground  we  reach  (apart  from  the  few 
incidentally  mentioned  or  alluded  toby  Aristotle)  is  an  extract 
from  the  works  of  the  Grammaticus  Aristophanes,  who  lived 
at  Alexandria  from  B.C.  260  to  B.C.  184.  He  comes  thus  a 
century  after  Plato,  and  nearly  two  centuries  before  Thra- 
syllus. He  divided  the  dialogues  into  trilogies,  and  several 
of  these  are  mentioned  by  Diogenes  Laertius.  They  are  re- 
markable as  containing  the  names  of  some  of  the  compositions 
that  ai*e  least  acceptable  to  the  critics,  and  that  would  be  hard 


EXAMPLK  OF  PLATO's  DIALOGUES. 


711 


to  vindicate  on  internal  evidence.  These  are  Leges,  Epinomis, 
Minos,  Epistolae,  Sophistes,  Politicus.  It  would  be  interest- 
ing to  know  what  means  Aristophanes  had  of  distinguishing 
the  genuine  from  the  spurious  works,  if  any  such  then  existed. 
For  two  centuries  after  the  death  of  Plato,  the  Academy 
was  kept  up  as  a  philosophical  school,  with  an  unbroken  suc- 
cession of  presidents.  The  chief  treasure  of  the  school  was 
the  works  of  the  master.  It  cannot  be  too  much  to  assume 
that  there  was  provided  a  safe  custody  for  the  MSS.  of  Plato, 
and  a  ready  means  of  verifying  any  alleged  works.  Plato  is 
better  off  in  this  respect  than  any  of  his  great  contemporaries, 
Socrates,  Demosthenes,  Euripides,  or  Aristophanes. 

Aristophanes,  the  Grammaticus,  was  head  of  the  Alexan- 
drian Library.  He  was  taught  by  Callimachus,  who  preceded 
him  in  the  office  of  Chief  Librarian.  Callimachus  is  the  author 
of  the  *  Museum,'  a  general  description  of  the  Alexandrian 
Library  ;  and  less  important  authors  than  Plato,  as  e.g,  Demo- 
critus,  are  mentioned  by  him.  It  is  then  highly  probable  that 
such  a  library  as  that  of  Alexandria  would  contain  copies  of 
one  of  the  foremost  Greek  philosophers.  And,  considering 
the  ease  of  verification,  it  is  most  likely  that  the  Librarian 
would  assure  himself  that  his  copies  were  authentic. 

There  were,  in  the  time  of  Thrasyllus,  spurious  dialogues. 
Whence  came  these,  and  by  what  criterion  did  he  discard 
them  ?  If  Aristophanes  and  Thrasyllus  (who  appears  also  to 
have  been  connected  with  Alexandria)  depended  upon  the  lib- 
rary there,  they  must  be  allowed  to  speak  with  great  weight ; 
but  if  they  proceeded  wholly  or  partially  upon  internal  evidence, 
they  have  less  claims  on  our  attention  than  the  better-equipped 
modem  critics.  Mr.  Grote  supposes  that  the  spurious  works 
were  made  for  the  demand  in  Greece  and  Asia  Minor,  and 
for  the  library  started  by  the  Kings  of  Pergamus  as  a  rival  to 
the  Alexandrian. 

So  much  for  the  difficulty  of  settling  the  real  authorship. 
The  other  point  to  be  determined  is  the  freedom  of  existing 
copies  from  sparious  additions  or  omissions,  accidental  or 
intentional. 

In  the  first  place,  errors  will  accidentally  creep  in,  by  tho 
mere  act  of  copying.  It  is  impossible  to  guarantee  strict 
accuracy  in  ti^nscription.  This  is  recognised  in  jurisprudence^ 
and  the  English  law  refuses  to  admit  any  copy  where  the 
original  can  be  produced.  But  the  reason  of  the  law  does  not 
apply  with  the  same  force  in  history.  A  very  slight  alteration 
in  a  deed  might  sometimes  alter  the  meaning  of  it ;  and,  more- 

di 


I! 


712 


HISTORICAL  EVIDENCE, 


over,  tbere  is  often  an  exceedingly  powerful  temptation  to 
tamper  with  deeds.  Now,  the  value  of  a  copy  of  MS. 
depends  on  its  accnracy,  and  the  motives  for  falsifying  history 
are  far  weaker.  It  is  therefore  considered  that  tbe  works  of 
classical  authors  are  preserved  to  us  substantially  as  they  were 
when  published.  Such  variations  as  there  are  do  not  affect 
the  general  accuracy  of  the  copies  that  have  reached  us. 

In  the  second  place,  changes  may  be  made  intentionally,  to 
suit  a  purpose.  We  are  told  that  Solon  inserted  a  verse  in 
the  Iliad  with  a  view  to  confirm  the  title  of  the  Athenians  to 
the  possession  of  Salamis.  At  an  early  period,  authentic  lists 
or  canons  of  authors  and  their  works  were  prepared  to  guard 
against  deception.  Short  writings  are  most  easily  forged,  and 
hence  there  are  numberless  forgeries  of  letters ;  but  we  find 
examples  of  falsification  at  greater  length  in  the  poems  of 
Ossian.  Ecclesiastical  writings  contain  many  forgeries,  made  for 
the  purpose  of  propagating  or  confirming  opinion.  The  motive 
for  executing  forgeries  is  often  to  make  money  by  arousing 
curiosity ;  but  in  such  cases  as  Ossian,  it  is  merely  the  pleasure 
of  deceiving  the  world.  Literary  forgeries  are  generally 
detected  by  internal  evidence — by  inconsistencies,  anachron- 
isms, imitations  of  subsequent  writers,  and  other  marks  of 
recent  composition. 

When  we  have  sufficient  assurance  that  a  work  is  both 
authentic  and  genuine,  written  by  its  reputed  author,  and  not 
tampered  with  in  the  course  of  transmission,  we  have  still  to 
consider  the  worth  of  the  testimony.  Besides  examining  our 
author's  means  of  information — whether  he  writes  as  an  eye- 
witness or  at  second  hand,  or  at  what  other  remove  from  eye- 
witnesses— we  must  enquire  into  his  character  for  veracity  and 
bis  motives  to  depart  from  the  truth. 

There  is  often  iotentional  perversion  or  suppression  of  the 
truth,  especially  in  Autobiography,  as  Ccesar's  Gallic  Wars, 
and  Napoleon's  Memoirs  of  his  Campaigns.  Vanity,  a  love  of 
the  marvellous,  and  party  spirit,  operate  in  the  same  direction. 
There  are  Catholic  and  Protestant  histories  of  the  Reforma- 
tion ;  Whig  and  Tory  histories  of  England.  The  accounts  of 
modern  campaigns  and  military  operations  differ  very  much 
according  to  the  side  the  writer  belongs  to.  Many  inaccuracies 
arise  from  not  taking  the  trouble  to  investigate  the  truth. 
History  may  be  blended  with  fiction  for  a  didactic  or  moral 
purpose,  as  in  Xenophon's  Cyrope3dia. 

The  ancient  historians  departed  from  strict  truth,  by  intro- 
ducing into  their  works   speeches  composed  by  themselves. 


MYTHICAL  HISTORY. 


713 


One  fourth  of  the  history  of  Thucydides  is  composed  of  such 
speeches.  Lucian  thought  it  a  sufficient  excuse  for  introduc- 
ing fictitious  speeches,  that  they  were  suitable  to  the  charac- 
ter of  the  speaker,  and  appropriate  to  the  subject.  Polybius 
is  the  only  writer  of  antiquity  who  condemns  the  practice,  for, 
he  says,  the  object  of  the  historian  is  not  to  astonish  the  reader, 
but  to  record  what  was  actually  done  or  said.  This  opinion 
has  been  followed  by  modern  historians,  and  the  manufacture 
of  speeches  has  therefore  ceased.  The  same  thing,  however, 
in  substance,  is  still  done,  although  introduced  as  part  of  the 
history,  namely,  interpreting  acts  and  suggesting  motives. 
It  is  a  great,  though  perhaps  not  uncommon,  error,  to  treat  as 
history  what  thus  owes  its  origin  to  conjecture. 

Another  perversion  of  history  is  mytMcal  history.     «The 
original  author  of  such  a  legend  must,  no  doubt,  be  at  first 
conscious  that  it  is  the  spontaneous  product  of  his  own  inven- 
tion, unattested  by  any  external  evidence.     But  the  fiction  is 
suggested  by  prevailing  ideas  and  feelings;   it  interweaves 
existing  facts  and  customs  into  its  texture ;   it  furnishes  an 
apparent  support  to  institutions  or  practices  for  which   the 
popular  mind  seeks  an  explanation  ;   it  fills  a  void  which  is 
sensibly  felt,  and  supplies  food  for  an  appetite  whose  demands 
are  at  once  urgent  and  general.    The  inventor  of  such  a  legend, 
therefore,  differs  altogether  from  the   author  of  a  novel  or 
romance,  who  lays  before  the  public  a  tale  avowedly  fictitious, 
and  which  they  accept  as  such.*     Examples  may  be  found  in 
Greek  mythology,  in  the  fabulous  heroes  of  mediseval  chivalry, 
and  in  the  lives  of  mediaaval  saints.     Such  legends  have  a  use' 
not  as  describing  events,  but  as  throwing  a  reflected  light  on  the 
circumstances  and  character  of  those  who  invented,  believed,  and 
circulated  them.      The  most  difficult    case  to  the  historian 
is  not  pure  mythology,  but  the  blending  of  myth  and  history, 
which  lures  men  on  to  search  for  fiact,  but  leaves  them  un- 
able to  distinguish  it  from  fiction.      The  history  of  Greece 
from  the  first  Olympiad  to  the  Persian  war,  and  of  Rome| 
frona  TuUus  Hostilius  to  the  Punic  wars,  illustrates  this  inter- 
mediate period  of  twilight  and  uncertainty. 

The  second  mode  of  transmitting  evidence — Oral  Tradition 
loses  credit  very  rapidly  with  the  lapse  of  time.  An  account 
of  an  event,  diminishing  in  evidentiary  value  at  each  remove 
from  the  original  eye-witness,  very  soon  ceases  to  have  any 
value  at  all.  This  has  always  been  more  or  less  recognized. 
Polybius  confined  himself  to  what  he  learned  from  eye- 
witnesses  of  the  preceding  generation,  and  thus  begins  his 


I 


rl" 


714 


HISTOKICAL  EVIDENCE. 


consecutive  history  about  twenty  years  before  his  birthj 
Newton  thono^ht  that  oral  tradition  minrlit  be  trusted  for  80 
or  100  years  ;  and  Volney  remarks  that  the  Red  Indians  had 
no  accurate  tradition  of  facts  a  century  old. 

The  average  value  of  oral  tradition  may  be  enhanced  in 
various  ways.  During  the  panic  caused  by  the  mutilation  of 
the  Mercuries,  and  the  fear  of  treasonable  attempts  to  esta- 
blish a  despotism,  the  Athenians  recurred  to  the  government 
of  Pisistratus  and  his  sons,  which  had  begun  nearly  150  years 
and  ended  100  years  before  that  time.  Thucydides  describes 
the  Athenians  as  referring,  entirely  by  oral  tradition,  to  the 
attempt  by  Cylon — a  fact  at  the  time  180  years  old.  That 
event  had  however  created  a  hereditary  curse  in  the  powerful 
family  of  the  Alcmaeonidae,  and  the  memory  of  it  was  revived 
at  different  times  by  public  acts.  The  Dies  AUiensis,  the 
anniversary  of  the  fatal  battle  of  the  AUia,  was  doubtless  kept 
up  by  uninterrupted  usage  from  B.C.  390.  Festivals,  emblems, 
antiquated  offices,  serve  to  fix  tradition,  and  keep  alive  the 
recollection  of  events.  The  Interrex^  in  Rome,  who  continued  to 
be  appointed  during  the  Republic  in  the  vacancy  of  the  consul- 
ship, was  a  reminiscence  of  a  period  of  elective  kings.  The 
King  of  the  Sacrifices,  like  the  King  Archon  at  Athens,  is  also 
a  decided  indication  of  the  regal  period.  There  were,  more- 
over, many  buildings,  monuments,  and  public  places  in  Rome 
associated  with  the  names  of  kings.  The  existence  of  laws, 
like  the  Twelve  Tables,  inscribed  on  metal  or  stone,  may  serve 
to  perpetuate  a  correct  oral  tradition. 

Rubino,  the  author  of  a  work  on  the  early  Roman  Constitu- 
tion, has  laid  down  some  rules  on  this  subject.  He  divides 
oral  tradition  into  two  classes,  one  referring  to  the  constitution, 
and  the  religious  and  civil  institutions  connected  with  it,  the 
other  embracing  the  more  common  material  of  history,  wanj, 
negotiations,  and  the  striking  events  that  give  interest  to  the 
history  of  Rome.  This  last  alone  was  committed  to  the  ex- 
clusive keeping  of  oral  tradition,  and  was  much  more  liable 
to  error  and  uncertainty  than  the  traditions  relating  to  the 
constitution.  To  some  extent,  constitutional  usage  implies  a 
knowledge  of  precedents.  Such  information  in  all  probability 
existed  at  the  beginning  of  the  Second  Punic  war ;  but  it 
might  not  reach  far  back  without  the  help  of  documents. 
There  is  no  reason  to  suppose  that  accurate  knowledge  would 
have  gone  back  beyond  a  century.  It  is  not  possible  to  draw 
any  broad  line  between  constitutional  history,  and  the  common 
events  of  history  ;  we  could  not  discuss  the  changes  in  the 


■iTi'TTinnnsi- — ;■ 


ARGUMENT. — CATEGOEEMATIC. — DICTUM. 


715 


English  Constitution  during  the  seventeenth  century,  without 
a  knowledge  of  the  events  that  gave  birth  to  them. 

There  is  one  case  where  oral  transmission  makes  an  approach 
to  the  value  of  transmission  by  writing.  This  happens  when 
the  memory  is  assisted  and  checked  by  a  set  form  of  words, 
especially  if  the  form  be  metrical.  Caesar  tells  us  that  the 
secrets  of  the  Druidical  religion  were  contained  in  a  great 
number  of  verses,  in  committing  which  to  memory  a  druid 
would  spend  twenty  years  of  his  life.  In  like  manner,  the 
Iliad  and  Odyssey  were  perpetuated  by  a  race  of  professional 
reciters  and  rhapsodists. 

K. — EXPLANATION   OF  SOME  LOGICAL  TEKMS. 


The  following  terms,  not  being  deemed  essential  to  any  of 
the  important  doctrines  of  Logic,  may  not  have  been  made 
fully  understood  in  the  previous  exposition.  As  they  occasion- 
ally occur  in  logical  discussions,  short  explanations  of  them 
are  here  appended. 

Argument  is  used  in  several  different  senses.  Apart  from 
its  more  popular  significations,  a  disputation,  a  chain  of  rea- 
soning, and  even  a  chain  of  events  (the  argument  of  a  play), 
its  meaning  is  not  fixed  and  uniform  among  logicians.  Some 
apply  it  to  an  entire  syllogism,  premises  and  conclusion,  some 
to  the  premises  only  as  the  grounds  of  the  conclusion,  while 
Hamilton  maintains  that  its  proper  meaning  is  the  middle 
notion  in  a  reasoning, — *  what  is  assumed  to  argue  something.* 
So  Mansel  holds  that  the  word  should  be  .applied  only  to 
the  Middle  Term.  ' 

Categorematic. — A  distinction  is  drawn  between  words  that 
can  stand  alone  as  subject  or  predicate  of  a  proposition,  as 
man,  stone  (Categorematic) ;  and  words  that  can  stand  only 
in  company  with  other  words,  as  all,  none  (jSyncategorematic). 

Dictum  de  omni  et  nullo. — This  applies  directly  to  the  First 
Figure  alone.  It  is  usual  to  give  similar  principles  for  the 
other  Figures,  and  among  these  we  may  notice  the  d/c^a  given 
by  Mr.  Mansel  in  his  notes  on  Aldrich  (p.  86). 

*  Principle  of  second  figure.  Dictum  de  Viverso,  If  a  cer- 
tain attribute  can  be  predicated  (affirmatively  or  negatively) 
of  every  member  of  a  class,  any  subject  of  which  it  cannot  be 
BO  predicated,  does  not  belong  to  the  class. 

•  Principles  of  third  figure.  I.  Dictum  de  exemplo.  If  a 
certain  attribute  can  be  affirmed  ofany  portion  of  the  members 


I 


■Mwamp 


Mfir 


\f 


716 


EXPLANATION  ON  SOME  LOGICAL  TERMa 


of  a  class,  it  is  not  incompatible  with  the  distinctive  attributes 
of  that  class.  II.  Dictum  de  excepto.  If  a  certain  attribute 
can  be  denied  of  any  portion  of  the  members  of  a  class,  it  is 
not  inseparable  from  the  distinctive  attributes  of  that  class.' 

Enthymeme. — A  syllogism  with  one  of  its  premises  sup- 
pressed in  the  enunciation.  Hamilton  argues  against  the 
prominence  given  to  Enthymeme  as  a  division  of  syllogisms, 
on  the  ground  that  they  are  not  a  special  form  of  reasoning, 
but  only  an  elliptical  mode  of  expression.  He  also  shows 
(what  is  done  more  elaborately  by  Mr.  Mansel)  that  Aristotle 
understood  by  Enthymeme  not  an  elliptical  syllogism,  but 
'  a  syllogism  from  signs  and  likelihoods/  or  a  syllogism  with 
the  major  premise  only  probable. 

Ignava  Ratio  or  Sophisma  pigrum  is  the  master  fallacy  of 
Fatalism.  It  might  be  classed  with  fallacies  of  Non-observa- 
tion. The  Fatalist  argues  that,  if  a  thing  must  happen,  it 
will  happen  whether  he  interfere  or  no  ;  overlooking  that  his 
own  agency  is  one  of  the  co-operating  causes. 

Intuitive — Symbolical. — We  often  employ  words  and  sym- 
bols without  fully  realizing  their  meaning.  This  Leibnitz 
called  Symbolical  as  distinguished  from  Intuitive,  Knowledge, 
ideas  and  sensations  fully  realized  in  consciousness.  We  can 
conceive  a  yard,  a  mile,  or  even  ten  or  twenty  miles,  in 
the  full  reality  of  the  extent ;  but  of  the  distance  between  the 
earth  and  the  moon,  the  sun,  or  one  of  the  fixed  stars,  we  have 
no  proper  conception ;  we  may,  however,  express  such  diar 
tances  in  figures,  which  are  intelligible  as  such.  This  would 
be  a  symbolical  conception. 

MoDALS.--(See  Part  I.,  p.*  99).  The  opposition  of  Pro- 
positions has  been  applied  to  Modals,  in  the  following  state- 
ments. 

If  the  matter  be  necessary ,  all  affirmatives  must  be  true,  and 

all  negatives  false. 

If  the  matter  be  impossiUe,  all  negatives  must  be  true,  and 
all  affirmatives  must  be  false. 

If  the  matter  be  contingenfy  all  particulars  must  be  true,  and 
SkU  universals  false. 

Here  the  meaning  of  *  necesf  a^y  *  is  no  more  than  nniyerw 
sally  true,  as  all  men  are  mortal,  all  matter  gravitates.  '  Im- 
possible *  is  universally  false ;  all  men  are  gods.  '  Contin- 
gent' means  partly  true  and  partly  false ;  Some  men  are  wise. 

Porphyry's  Tree. — This  is  a  tabular  arrangement  showing 
different  grades  of  generality.  The  example  chosen  ranges 
from  the  summum  genus  Suhstance,  to  the  infima  species  Man, 


•v 


pbophyry's  teee. 


717 


ending  with  two  individuals.     It  may  be  exhibited  thus,  in  a 
form  better  described  by  the  Greek  name,  Porphyry's  Ladder 

Substance 
Corporeal  Incorporeal 

(Body) 
Animate        Inanimate 
(Living  Body) 
Sensitive  Insensitive 

(Animal) 
national         Irrational 
(Man) 
Socrates     Plato 

Predesignate  is  a  term  applied  by  Hamilton  to  propositions. 
Laving  their  quantity  expressed  by  one  of  the  signs  of  quan- 
tity, All,  None,  &c.  The  contrasting  term  is  l^reindesignate,. 
The  terms  commonly  used  in  logic  are  Definite^  Indefinite, 

Simple  Apprehension  is  defined  by  Whately  as  *  the  opera- 
tion of  the  mind  by  which  we  mentally  perceive  or  form  a 
notion  of  any  object.*  It  is  the  same  as  Perception,  whereby 
we  know  things  in  the  actual  or  concrete — a  house,  a  tree. 
By  another  faculty,  designated  Abstraction,  we  conceive  things 
in  the  general. 

Sufficient  Reason.— Under  this  title  Leibnitz  stated  the 
law  of  Causality.  Everything  that  exists  must  have  a  *  suffi- 
cient reason '  for  its  existence.  The  attempt  has  been  made  to 
prove  certain  truths,  such  as  the  law  of  perseverance  of  uni- 
form motion  in  a  straight  line,  on  the  ground  that  no  suffi- 
cient reason  can  be  given  why  a  body  should  either  lose  its 
velocity  or  deviate  to  one  side  or  the  other.  The  same  line  of 
jremark  has  been  used  with  the  principle  of  virtual  velocities. 

SoPHiSMA  Polyzetbseos  and  Sophisma  Heterozeteseos  are 
two  ingenious  Greek  Sophisms.  The  first  was  alluded  to 
under  Definition.  Choosing  a  word  having  a  doubtful  margin 
of  application,  the  sophist  asks  whether  it  applies  to  such  and 
such  a  case,  and  goes  on  putting  the  question  to  one  contiguous 
case  after  another,  until  he  has  drawn  the  respondent  palpably  , 
beyond  the  range  of  the  word,  when  he  demands  the  difierence 
between  the  last  case  admitted  and  the  first  refused.  Such 
words  as  heap,  calf  &c.,  are  suitable  :  the  sophist  asks — Was 
it  a  calf  to-day,  will  it  be  a  calf  to-morrow,  next  day,  and  so 
on  ;  the  respondent  cannot  say  on  what  day  it  ceases  to  be  a 
calf,  and  becomes  a  heifer.      The   Heterozeteseos  (Sophism  of 


1 


..II 


718 


EXPLANATION  ON  SOME  LOGICAL  TERMS. 


Irrelevant  Question)  decoys  a  person  into  committing  himself 
by  a  categorical  answer — *Have  you  cast  your  horns? — If 
you  answer,  I  have ;  it  is  rejoined,  Then  you  have  had  horns  : 
if  you  answer,  I  have  not,  it  is  rejoined,  Then  you  have  them 
BtilL' 


■■Mn 


Iljf  DEX. 


Abstraction,  allied  to  Analysis,  683. 
Abstract  Ideas,  dispute  regarding,  5. 
Abstract  name,  completion  of  gener- 
alizing process,  52. 
value  and  abuse  of,  63. 
Accidens^  76. 
Accidentia^  faUacia^  674. 
Activity,  a  source  of  fallacies,  607. 
Adjectives,  connotative,  being  gener- 
alized names,  49. 
./Equivocation  673. 
A  dido  secundum  quid  ad  dictum 

simptidter,  602,  624,  675. 
Esthetic  emotions,  a  source  of  fal- 
lacy, 613. 
A  dicto  simpliciier  ad  dictum  secun- 
dum quidy  674. 
Affinity,  chemical,  defined,  473. 
maximum  of,  417. 
in  Mineralogy,  624. 
in  Botany,  632. 
in  Zoology,  540. 
in  diseases,  596. 
A  fortioriy  164. 

Agreement,  intellectual  property  of, 
8. 
the  basis  of  Reasoning,  8. 
basis  of  Definition,  385. 
defines  the  limits  of  Explanation, 

861. 
stated  in  classification,  422. 
in  the  arrangement  of  chemical 

elements,  476. 
statement  of,  in  Mineralogy,  529. 
in  Botany,  636. 
in  Zoology,  643. 
in  diseases,  596. 
Method  of,  279. 
fundamental  maxim  of,  278. 
in  Biology,  600. 


Agreement,  Method  of,  in  Politics, 
565. 
in  Medicine,  590. 
frustrated  by  plurality  of  causes, 

308. 
protected  against  plurality  of 
causes,  309. 
an  aid  to  Discovery,  702. 
in  Absence,  basis  of,  279. 
Universal,  the  sole  evidence  for 

Inductive  truths,  237. 
the  test  of  uniform  co-existence, 

244. 
proof  of  concomitant  properties 

in  Natural  kinds,  245. 
the  sole  Inductive  Method,  277. 
fundamental  mode  of  Proof,  344. 
Algebra,  notions  of,  432. 
account  of,  443. 
highest  operation  of,  445. 
Algebraic  Geometry,  notions  of,  432. 

account  of,  448. 
All,  two  meanings  distinguished  by 

De  Morgan,  187. 
Ambiguity  of  terms,  602,  616. 
Amphiholia^  673. 
Analysis,  Chemical,  627. 
Logical,  628. 

allied  to  Abstraction,  39,  629. 
applied  to  Induction,  684. 
Grammatical,  684. 
Critical,  684. 
Mathematical,  685. 
preliminary  to  elimination,  272. 
in  Psychology,  511. 
in  Society,  570. 
conformed    to   rules  of  division, 

427. 
an  aid  to  Discovery,  706. 
Analytic  judgment,  76. 


; 


720 


INDEX 


Analogy,   as  a  form  of  Inference, 
373. 
does  not  amount  to  Proof,  873. 
examples  of,  376. 
Analogies,  false,  372,  624. 
Analogical  Hypotheses,  877. 
Animals  and  Plants  contrasted,  495. 
Antecedence,  invariable,  not  causa- 
tion, 268. 
causal  usually  complicated,  271. 
Apprehension,  simple,  717. 
Approximate  Generalizations,  365. 
probability  of,  stated  in  numbers, 

366. 
how  brought  nearer  certainty,  368. 
open  to  sophistry,  369. 
A  priori^  applied  to  knowledge,  10. 
Argument,  715. 

Aristotelian  contrasted  with  Bacon- 
ian logic,  642. 
Arithmetic,  definitions  of,  433. 
ultimate  notions  of,  434. 
account  of,  442. 
proof  in,  443. 
Associations,  a    source  of   fallacy, 

616. 
Astronomy,  its    place    among    the 

Sciences,  630,  636. 
Averages,  321. 

Axiom  of  Syllogism,  various  forms 
discussed,  166. 
proof  of,  in  experience,  169. 
Hamilton's  forms,  160. 
as  given  by  Thompson,  161. 
as  given  by  De  Morgan,  162. 
not  derivable  from  the  "  Laws  of 
Thought,"  162. 
Axioms,  nature  of,  224. 
requisites  of,  224. 
only  two  Mathematical,  224. 
of  Inductive  origin,  226. 

Bacon,   contributions    to   inductive 

methods,  687. 
Belief,  the  nature  of,  12. 

inherently  excessive,  607. 

law  of,  explains  intense  convic- 
tions, 226. 
Biology,  scope  of,  488. 

divisions  of,  492. 

notions  of,  494. 

propositions  of,  496. 


Biology,  conservation  of  Force  in, 
498. 

Empirical  laws  in,  498. 

logical  methods  of,  600. 

Hypotheses  of,  602. 

as  basis  of  Medicine,  677. 
Body,  substance  of,  660. 
Body  and  Mind,  357,  376,  605. 
Botany,  arrangement  of  characters 
in,  531. 

maximum  of  affinity  in,  632. 

grades  in,  634. 

agreement  and  difference  in,  536. 

peculiarity  in  exhibition  of  di£fer> 
ences,  536. 

index  in,  638. 

Calculus,  notions  of,  432. 

account  of,  448. 
Canons  of  Syllogism,  149. 

according  to  Hamilton,  161. 

special  for  each  Figure,  162. 
Canons,  special,  derived  from  Axiom, 

163. 
Categorematic,  716. 
Categories,  of  Aristotle,  661. 
Categorical  Imperative,  meaningless, 

376. 
Causation,  law  of,  20,  226. 

uniformities  of,  as  a  branch  of 
Logic,  239. 

law  of,  expressed,  246. 

obverse  denied,  246. 

three  aspects  of,  247. 

practically  viewed,  247. 

scientific,  249. 

fallacy  of,  260. 

as  Conservation  of  Force,  261. 

as  an  instrument  of  eliminatioiL 
276. 

unfolded  in  three  maxims  of  elimi- 
nation, 277. 

induction  of,  343. 

rests  on  Agreement  alone,  345. 

as  an  Empirical  law,  346. 

discriminated  from  Co-existence, 
381. 

not  distmguished  from  Co-exist 

ence,  688. 
propositions  of,  in  Biology,  497. 
in  Politics,  666,  664. 
contradiction  of,  incredible,  379. 


■H«9 


■^JF^- 


INDEX. 


721 


Cause,  an  alleged  intuition,  11. 

to  be  sought  among  the  antece- 
dent circumstances,  267. 

not  proved  by  invariable  antece- 
dence, 268. 

the  unconditional  invariable  ante- 
cedent, 268. 

material,   formal,   efficient,    finaL 
248. 
Causes,  composition  of,  268. 

combination  of,  327. 

real,  369. 
Chance,  computation  of,  a  resource 
under  Intermixture  of  Effects, 
813. 

coincidence  explained,  315. 

principle  of  computation,  316. 

applicable  where  other  methods 
fail,  316. 

combined  with  law,  319. 

submerging  a  small    uniformity, 
319. 

in  Biology,  601. 

in  Psychology,  616. 

in  Medicine,  692. 

elunination  of,  an  aid  to  Discov- 
ery, 702. 
Character,  Science  of,  based  on  Psy- 
chology, 516. 

elements  of,  618. 

as  affected  by  Conservation,  518. 

influences  on,  519. 

not  classified  like  Natural  History, 
520.  •^' 

peculiarities  of,  621. 

human,  in  Politics,  556. 

Characters,  descriptive,  sequence  of, 
414. 

in  Chemistry,  478. 
in  Mineralogy,  523. 
in  Botany,  531. 
in  Zoology,  538. 
Chemical  force,  conservation  of,  355. 
combination,  not  a  union  of  forces, 

870. 
defined  by  contrast,  393. 
Chemistry,  fundamental  fact  of,  472. 
propositions  of,  473. 
arrangement  and  methods  of,  474. 
elements  of,  classified,  474. 
descriptive  method  of,  478. 
agreement  and  difference  in,  483. 


Chemistry,  empirical  laws  in,  484. 
law  of  Conservation  in,  484. 
hypotheses  in,  486. 
nomenclature  of^  486. 
notation  of,  48V. 
Class,  two  meanings  of,  definite  and 

indefinite,  280. 
Classification,  golden  rule  of,  388, 
416. 
Methods  of,  414. 
descriptive  characters  in,  414. 
grades  of,  418. 

terminates  with  Species,  420. 
statement  of  agreements  and  dif- 
ferences in,  422. 
Index,  424. 
of  Characters,  620. 
Sciences  of,  522. 
an  aid  to  Discovery,  704. 
Co-existence  one  of  the  three  Uni- 
versal Predicates,  103. 
as  Order  in  Place,  103. 
as    Co-inherence    of   Attributes, 

104. 
uniformities  of,  as  a  branch  of 

Logic,  239,  243. 
induction  of,  241. 
proof  of,  by  Universal  Agreement, 

244. 
propositions  of,  in  Biology,  296. 

in  politics,  656. 
and  Succession,  common  to  sub- 
ject and    object  experience, 
656. 
Collective  nam^,  singular  or  gener 

al,  48.    ' 
Colligation  of  Facts,  696. 
Collocation  of  Circumstances,  261. 
degrees  of  complexity,  260. 
elliptically  spoken  of  as  the  Cause, 

262. 
as  Potential  Energy,  264. 
the  effect  of  expended  force,  265. 
in  Politics,  664. 
Colony,  example  of  positive  defini- 

tion,  388. 
Colour,  not  intrinsically  objective, 

667. 
Complex  Propositions,  how  far  mat- 
ter of  Logic,  86. 
Complications  of  Cause  and  EffccL 
271. 


4 


722 


INDEX. 


Compositionis  et  Division  iSy  fallaciaj 

674. 
Comprehension,  50. 
practically  more  important  than 

extension,  333. 
Hamilton's  syllogism  in,  criticized, 
180. 
Conceptualism,  6. 
Concept,  formation  of,  383. 
Conception,  formal,  473. 
Concomitance,  discovery  of  laws  of, 
419. 
in  Zoology,  639. 
Concomitant,  a  predicable,  76. 
separable  and  inseparable,  77. 
Variations,  292. 

fundamental  maxims  of,  278. 
interrupted  by  critical   points, 

294. 
as  a  means  of  suggestion,  294. 
tables  of,  for  Discovery,  295. 
under  Intermixture  of  effects, 

403. 
in  Biology,  500. 
in  Politics,  567. 
in  Medicine,  591. 
Concrete  names,  54. 
Conditional  Propositions,  85. 
Syllogism,  involves  no  inference, 
117. 
Confusion,  fallacies  of,  602,  616. 
Consciousness,  507. 
testimony  of,  665. 
Connotation,  of  General  Names,  49. 
Conservation  of  Force,  law  stated, 
251. 
proved  by  universal    agreement, 

237. 
explained,  250,  252. 
evidence  of,  344. 

has  same  proof  as  Causation,  266. 
not  an  a  priori  conception,  267. 
in  Chemistry,  484. 
in  Biology,  498. 
in  Medicine,  589. 
under  re-distribution,  460. 
in  Character,  518. 
Consistency,   Prmciple  of,  14,  108, 

645,  670. 
Contiguity,    extension     of     names 

through,  403. 
Oontinuity,  law  of,  empirical,  838. 


Continuit7,  a  help  to  Discovery,  697, 

706. 
Continuous  Comparison,  295. 
Contradiction,  principle  of,  16. 
Contradictory,  propositions,  93. 

misapplication  of  the  name,  94. 
Contraries,  expression  of,  made  pre- 
cise by  De  Morgan,  56. 
basis  of  De  Morgan's  additions  to 
syllogism,  184. 
Contrary  propositions,  92. 
Contrast,  in  defining,  385. 
animals  with  plants,  495. 
exhibition  of,  in  Chemistry,  483. 
Conversion,  Simple,  113. 
Fallacies  of,  114, 
by  Limitation,  per  aceidens,  1 14. 
obverted,  or  by  Negation,  or  Con- 
traposition, 116. 
Copula,  44. 

meanings  of,  182. 
Correlative  names,  55. 
Correlation  of  Forces,  see  Conserva- 
tion. 
Credibility,  consistency  with  proved 

inductions,  379. 
Crystallization,  an  example  of  Agree- 
ment, 284. 
explanation  of,  confirmed  by  Joint 
Method,  291. 
Curves,  method  of,  697,  704. 

Deduction,  first  principles  of,  17. 
explained,  40. 
why  placed  before  Induction  and 

Definition,  41. 
laws  of,  645. 

as  general  presumption,  284. 
involves    observation    of    facts, 

825. 
two  stages  of  complexity,  327. 
simple,  extension  of  a  law,  827. 
combination  of  causes,  329. 
fallacies  of,  625. 
Deductive  Method,  three  requisites 
of,  325. 
in  Psychology,  518. 
in  Politics,  567. 
in  Medicine,  592. 
alone,   insufficient  in    Politics, 
572. 
Sciences,  how  constituted,  216. 


INDEX. 


723 


Definition,  as  verbal  predication,  71. 
exhaustive  and  unexhaustive,  71, 

72. 
explained,  38,  384. 
fundamentals  of,  385. 
Positive  Method  of,  386. 
margin  of  transition,  390. 
Negative  Method  of,  392. 
deductive,  395. 
the  language  of,  395. 
by  synonyms,  396. 
per  genus  et  differ enUam^  74,  396. 
by  Analysis,  396. 
notions  not  susceptible  of,  398. 
mixed  with  Real  predication,  582, 

687. 
fallacies  of,  626. 
neglected  by  Whewell,  696. 
an  aid  to  Discovery,  706. 
De  Morgan,  divisions  of  Terms,  51. 
on  Positive  and  Negative  names, 

66. 
enumeration  of  Propositions,  90. 
additions  to  syllogism,  182. 
Demonstration,  based  on  Induction, 

219. 
Denotation,  of  General  Names,  49. 
Derivative  laws,  334. 

various  kinds  of,  334. 
limited  application  of,  336. 
of  wider  application  than  Em- 
pirical, 842. 
in  Pontics,  568. 
Description,  of  chemical  bodies,  478. 
not  to  be  mixed  with  explanation, 
483,  584. 
Descriptive  terminology,  407. 

characters,  sequence  of,  414. 
Development  hypothesis,  502. 
Dew,  research  on,  an  example  of 

elimination,  298. 
Dictum  de  omni  et  Nvllo,  166. 
Difference,  Method  of,  fundamental 
maxims  of,  278. 
explamed,  287. 
where  indecisive,  289. 
in  Politics,  566. 
in  Medicine,  591. 
exhibition  of,  in  Chemistry,  483. 
Differences,  statement  of,  in  Classi- 
fication, 422,  529. 
in  Botany,  535. 


Differences,  statement  of,  difficult  in 
Botany,  536. 
in  Zoology,  543. 
in  Diseases,  596. 
Differentia^  73. 

Dignity,  a  source  of  fallacies,  613. 
Dilemma,  121. 
Discovery,  Art  of,  697. 
distinguished  from  Proof  by  Mill. 

697. 
three  aids  to,  326. 
secondary  in  Logic,  327. 
Disease,  definition  of,  575. 
Disjunctive  Propositions,  85. 
Disjunctive  Syllogism,  involves  no 

inference,  119. 
Division,  an  aspect  of  classification, 
425. 
rules  of,  426. 
a  mode  of  grades,  427. 
fails  with  undefined  classes,  428. 
Documents,    invalidated     by    two 
doubts,  709. 

Efficient  Cause,  248. 
Electricity,  Conservation  of  Force  in, 
257. 
characters  and  branches  of,  468. 
EUmination,   of  Cause  and   Effect 
271. 
weapons  of,  276. 
is  Proof,  279. 
of  chance,  314. 
Empirical  laws,  explained,  833. 
various  kinds  of,  334. 
criteria  of,  386. 
limited  application  of,  336. 
established  by  Universal  Agree- 
ment, 237. 
more  precarious  than  derivative, 

842. 
in  Chemistry,  484. 
in  Biology,  498. 
in  Psychology,  514. 
in  Politics,  568. 
Enthymeme,  716. 
Equality,  uniformities  of,  as  a  branch 

of  Logic,  239. 
Equality  and  inequality,  one  of  the 
three    Universal    Predicates, 
103. 
Equivalence  of  propositions,  107. 


724 


INDEX 


Equivalent  terms,  as  an  aid  to  Dis- 
covery, 702. 
Essential  attributes,  74. 

predication,  in  Psychology,  609. 
Excluded  Middle,  principle  of,  17. 
Exclusion,  Bacon's  process  of,  688. 
Existence,  has  no  real  opposite,  69. 
propositions  of  elliptical,  107. 
means  Object  and  Subject  indis- 
criminately, 620. 
Experience,   the  source  of  knowl- 
edge, 9. 
the  proof  of  the  Axiom  of  the  Syl- 
logism, 159,  226. 
the  proof  of  Causation,  226. 
Experiment,  advantages  of,  273. 
in  Biology,  500. 
in  Politics,  563. 
Experimental  Methods,  apply  only  to 
Cause  and  Effect,  240. 
deductive,   in    character,    277, 

346. 
explained,  279. 
examples  of,  297. 
frustration  of,  306,  312,  313. 
"  in  Psychology,  612. 
in  Politics,  565,  572. 
in  Medicine,  690. 
how  far  anticipated  by  Bacon, 

687,  689. 
given  by  Herschel,  694. 
neglected  by  Whewell,  696. 
Experimentum  crucisy  866. 
Explanation  of  Nature,  a  joint  effect, 
847. 
intermediate  links,  848. 
subsumption  of  laws,  849. 
limits  of,  861. 
fallacious,  364. 
Extension,  60. 

fundamental  property  of  the  Ob- 
ject, 667. 
Evidence,  assertions  beyond  reach 
of,  incredible,  882. 
Historical,  423. 
supreme  canon  of,  707. 
internal  and  external,  708. 
two  modes  of  external,  709. 
transmitted  by  writing,  709. 
transmitted  orally,  718. 

Facts  ju^d  Ideas,  696,  699. 


Fallacies,  Aristotelian  and  Scholastic, 
673. 
Whately's  division,  676. 
Mill's  classification  of,  599. 
a  priori^  599. 
of  observation,  600. 
of  generalization,  601. 
of  ratiocination,  601. 
of  confusion,  602,  616. 
position  of,  603. 
extralogical,  605. 
tendencies  to,  606. 
logical,  624. 
knowledge    of,    aids    Discovery, 

707. 
in  Politics,  672. 
Fear,  a  source  of  fallacy,  612. 
Feeling,  two-sided,  2. 
Feelings,  a  source  of  fallacy,  609. 
Fever,  definition  of,  581. 
Figures,  136. 

relative  value  of,  146. 
reasons  for  different,  146. 
FigurcB  didionis,  faHacia^  674. 
Final  Cause,  248. 
Food,  an  example  of  positive  defini« 

tion,  888. 
Force,  definition  of,  251. 
chief  predicates  of,  261. 
Conservation  of,  21. 
Form  and  Matter,  639. 
Formal  Logic,  too  narrow,  646. 
Cause,  248. 

thinking  explained,  640. 
requires  inductive  verification, 
648. 
Freedom  of  the  will,  844,  621. 
Functions  of  living  bodies,  491. 

Function  and  Structure  viewed 
separately,  498. 

General  Name,  explained,  48. 
Generality,  Names  classed  according 
to,  47. 

higher  and  lower,  64. 

degrees  of,  in  Notions,  64. 

fixed  grades  of,  in  Botany,  and  in 
Zoology,  66. 

degrees  of,  in  Propositions,  78. 

of  Proposition  follows  Notion,  78. 

as  classifying  Propositions,  78. 

as  a  basis  of  Definition,  386. 


I 


INDEX. 


Generalization,  identical  with  Expla- 
nation, 446. 
the  highest  ambition  of  Science. 
456.  ' 

approximate,  465. 
fallacies  of,  601. 
excessive  tendency  to,  608. 
as  an  art  of  Discovery,  279,  698. 
Genus  and  species,  movable  names, 
except  in  Natural  History,  65. 
a  predicable,  73. 
Geometry,  notions  of,  432. 
definitions  of,  434. 
ultimate  notions  of,  436. 
axioms  of,  438. 
postulates  of,  439. 
order  of  topics  in,  446. 
proof  of  Euclid's  fourth  proposi 
tion  in,  447. 
Glaring  mstances,  690,  704. 
Government,  forms  of,  549,  663. 
definition  of,  651. 
functions  of,  662. 
local  and  central,  654. 
defines  Public  and  Private,  554. 
Gracfts  of  generality,  great  import- 
ance of,  700. 
in  classification,  418. 
Statement  of,  suited  to  discovery 

of  concomitance,  419. 
in  Mineralogy,  528. 
in  Botany,  534. 
in  Zoology,  542. 
in  Diseases,  596. 

Gravity,  an  example  of  Hypothesis. 
460.  * 

contraction  of,  mcredible,  379. 


Hamiltok,  additions  to    syllogism 
178.  ' 

Quantification  of  Predicate,  178. 
syllogism  in  Comprehension  criti- 
cized, 180. 
Health-Disease,  indefinable,  264. 
Heat,  generated  by  collision,  253. 
conservation  of,  264. 
unprofitable  dissipation  of,  265. 
definition  of,  467. 
heads  of  the  science  of^  467. 
propositions  of,  470. 
structural,  should    be  stated    in 
chemical  formulae,  487. 


725 


Herschel,  contributions    to    Induc- 
tion, 693. 
History,  Philosophy  of,  548. 

basis  of  Politics,  561. 

perversions  of,  712. 
HomonymiOy  505. 
Hypothesis,  various  meanings  of,  358. 

of  known  agencies  desirable,  369. 

of  a  new  agent  permissible,  361. 

as  a  representative  fiction,  362. 

differs  from  geometrical  abstrac- 
tions, 364. 

analogical,  377. 

in  Chemistry,  486. 

in  Biology,  502. 

in  Psychology,  516. 

in  Politics,  569. 

in  Medicine,  693. 
Hypothetical  Inference,  116. 


Idea  and  Facts,  696,  699. 
Identification  of  a  Minor,  when  dif. 
ficult,  218. 
not  an  induction,  235,  328. 
Identity,  principle  of,  16. 
Idola^  Bacon's,  609. 
Ignava  RaUo^  717. 
Ignoratio  elenchiy  602,  623,  676. 
Immediate  Inference,  107. 

by  Added  Determinants,  109. 
fallacies  of,  625. 
Import  of  Propositions,  100. 
Hobbes's  view,  100. 
not  the  reference  of  something' 
to  a  class,  101.  ° 

Inconceivability  of  the  opposite,  ex- 
plained,  223. 

rejected  as  ultimate  test  of  truth, 
666. 

Incredibility,     mconsistency     with 

proved  inductions,  379. 
Index,  to  a  classification,  424. 
in  Mineralogy,  530. 
in  Botany,  638. 
in  Zoology,  644. 
in  Diseases,  697. 
Individual,  our  idea  of,  a  conflux 
of  generalities,  7. 
Induction,  first  principles  of,  19. 
explained,  40,  231. 

would  furnish  Formal  processes. 
650.  ^ 


I 


I 


726 


INDEX. 


Induction,  a  branch  of  Logic,  651. 

improperly  so  called,  233,  235. 

cannot  be  brought  under  the  syl- 
logism, 233. 

a  prerequisite  of  deduction,  325. 

in  difference  of  subject,  371. 

postulate  of,  502. 

fallacies  of,  625. 

growth  of,  687. 
Inductive,  Discovery,  326. 

Methods  an  aid  to  Discovery,  702. 

Syllogism,  233. 
Infimae  species,  63. 
Inflammation,  definition  of,  583. 
Intermixture  of  Effects,  310. 
in  Politics,  565. 
in  Medicine,  591. 
International  law,  548. 
Intuition,  an  alleged  source  of  knowl- 
edge, 10. 
Intuitive — symbolical,  716. 
Invention,  how  assisted,  705. 

Joint  Method  of  Agreement  and 
Difference,  291. 
counteractive   to    plurality  of 

causes,  310. 
in  Politics,  566. 
in  Medicine,  691. 
an  aid  to  Discovery,  703. 
Judgment,  formal,  641. 

as   a    synonym    for    proposition, 

80. 
its  significance  with  Aristotle,  80. 
Jurisprudence,  548. 

Knowledge,  the  act  of,  includes  al- 
ways two  things,  8. 

conjoins  Agreement    and    Differ- 
ence, 4. 

of  two  kinds,  called  Object  and 
Subject,  5. 

Individual  or  Concrete,  and  Gen- 
eral OP  Abstract,  5,  22. 

origin  of,  in  Experience,  9. 

limited  by  our  sensibiUties,  13. 

nature  and  classification  of,  21. 

should  be  true,  22. 

conveyed  in  propositions,  44. 

relativity  of,  appears  in  language, 
54. 
Kinds,  63. 


Kinds,  exemplify  co- inhering   attii- 
butes,  24*1. 

liANGUAaE,  truths  expressed  in,  42. 

fallacies  of,  616. 
Law,  confused  meanings  of,  643, 617. 
metaphorical  use  in  ''  Laws  of  Na- 
ture," 239. 
involved  in  Government,  552. 
combined  with  Chance,  319. 
Laws  of  Nature,  by  preeminence, 

239. 
Liberty,  560. 
Life,  definition  of,  488. 
Light,  undulatory  theory  of,  361. 
commutation  of,  not  established, 

258. 
production    of,    an    example    of 

Agreement,  286. 
definition  and  subsidiary  notions 
of,  468. 
Likeness  and  Unlikeness,  common 
to  subject  and  object  expe- 
rience, 666. 
Love,  a  source  of  fallacy,  612. 

Margin,  doubtful,  in  definition,  390. 
Mathematics,  Logic  of,  429. 

the  best  example  of  a  Deductive 
Science,  429,  647. 

notions  of,  430. 

propositions  of,  432. 

definitions  of,  433. 

axioms  of,  437. 

leading  branches  of,  442. 
Materia  Jfedica,  581. 
Method,  expresses  part  of  the  func- 
tion of  Logic,  86. 

an  aid  to  Discovery,  701. 
Mind,  substance  of,  660. 

definition  of,  505. 

difficult  to  estimate  quantity  in, 
517. 
Mind  and  Body,  367,  376,  606. 
Mineralogy,  scope  of,  622. 

relations  to  Chemistry,  622. 

arrangement  of  characters  in,  623. 

maximum  of  affinity  in,  624. 

grades  in,  628. 

agreement  and  difference  in,  629. 

index  for,  630. 
Material  Cause,  248. 


INDEX. 


727 


Material,  names  of,  singular,  48. 
Matter,  as  Resistance,  657. 

defined  by  positive  method,  391. 
by  negative  method,  393. 

constitution  of,  a  hypothesis,  863. 

Force,  Inertia  the  same  fact,  455. 

physical  properties  o^  464. 
Mechanics,  462. 
Medicine,  scope  of,  675. 

based  on  Biology,  577. 

definitions  of  diseases  in,  581. 

general  diseases  in,  679,  581. 

specific  diseases  in,  586. 

propositions  of,  688. 

experimental  methods  in,  590. 

elimination  of  chance  in,  692. 

the  deductive  method  in,  592. 

hypotheses  in,  693. 

classification  in,  596. 
Minor,  identification  of,  not  an  in- 
duction, 235. 
Mnemonics,  147. 
Modals,  99,  717. 

Molar  forces,  conservation  of,  262. 
Molecular  attractions,  464. 
Molecular  forces,  enumerated,  254. 
Motion,  laws    of,  reduced   to  one, 

458. 
Monarchy,  example  of  positive  defini- 
tion, 387. 
Moods,  138. 

usual  enumerations  justified,  163. 
Muscular  Irritability  and  Putrefac- 
tion, an  induction,  303. 
Mystery,  366. 

Names,  why  considered  at  beginning 
of  Logic,  45. 

defined,  46. 

denote  things,  not  ideas  of  things, 
46. 

Tariously  classified,  47. 

De  Morgan's  divisions  of,  61. 

go  in  couples,  64. 

meaning  of,  increases  with  oppo- 
site, 60. 

loosely  extended,  402. 

transitive  apphcation  of,  403. 

class,  409. 

of  generalities  should  be  short, 

410. 
new,  410, 


Names,  precautions  in  appropriating 
old,  412. 
expressive,  414. 
different,  held  to  imply  different 

thmgs,  418. 
improper  use  of,  420. 
Naming,  general,  value  of,  401. 
first  requisite  of,  402. 
second  requisite  of,  407. 
Nature,  explanation  of,  346. 

ambiguity  of  the  word,  616. 
Negation,  variously  expressed,  58. 
Negative  names,  65. 
singular  or  plural,  57. 
of  a  real  property,  also  real,  68. 
Necessary  Truth,  14. 
Necessity,  meanings   of— certainty, 
220. 
implication,  221 
inconceivability  of   the    oppo- 
site, 223. 
Nerve  force,  conservation  of,  268. 
Newton,  contributions  to  Induction, 

693. 
Nomenclature,  412,  414. 

of  Chemistry,  486. 
Non  causa  pro  causa^  676. 
Non  iequitur,  675. 
North-east    wind,   an    example    of 

Agreement,  283. 
Kota  noioe  est  nota  rci  ipsius^  166. 
Notation,  of  Chemistry,  487. 
Notion  and  Proposition,  not  distin- 

guished  by  Whewell,  696. 
Notions,   contrasted  with   Proposi- 
tions, 61.   ' 
disguised  as  Propositions,  66. 
of  singular  or  plural  constitution, 

63. 
indefinable,  ultimate,  398. 

Object,  analysis  of,  486. 

attributes  special  to,  657. 
Object-Subject,  highest  real  couple, 
69. 

greatest  of  all  antitheses,  653. 

attributes  common  to,  655. 
Observation,  why  not  a  department 
of  Logic,  86. 

the  basis  of  Induction,  234. 

compared  with  Experiment,  273. 

in  Biology,  600. 


'Ill 


728 


INDEX 


Observation,  in  Politics,  661. 

erroneous,  causes  of,  562. 

fallacies  of,  600. 

as  an  art  of  Discovery,  698. 
Opposition,  of  propositions,  92. 

error  in  common  square,  94. 

amended  square,  97. 

Aristotle's  square,  98. 
Obversion,  formal,  109. 

material.  111. 
Order,  valuable  aid  to  Discovery,  YOl. 
Order  and  Progress,  666,  670. 
Oxygen,  exemplary  description  of, 
479. 

Parity  of  Reasoning,  235. 
Pathology,  general,  679. 
Per  genm  el  differentiam^  886,  396. 
Persistence  of  Force,  see  Conserva- 
tion. 
Petitio  Principii,  602,  623,  675. 
Physics,  Molar,  divisions  of,  abstract 
and  concrete,  462. 
notions  of,  452. 
propositions  of,  464. 
definitions  of,  466. 
axioms  of  (laws  of  motion),  468. 
concatenation  and  method  of, 
462. 
Physics,  Molecular,  departments  of, 
463. 
notions  of,  464. 
propositions  of,  469. 
predominant  methods  of,  472. 
Plants  and  Animals  contrasted,  495. 
Plato's  dialogues,  how  authenticated, 

710. 
Plurality  of  Causes,  246. 

how  far  subject  to  uniformity,  246. 
^bearing  of,  on  the  Experimental 

Methods,  307. 
in.  Politics,  665. 
in  Medicine,  691. 
Piurium  Interrogaiionum^  676. 
Political  Economy,  648. 
Politics,  two  divisions  of,  647. 
embraces  several  sciences,  649. 
province  of,  649. 
Descriptive,  660. 
Theoretical,  defined,  666. 
propositions  of,  558. 
universal  propositions  of,  669. 


Politics,  Theoretical,  limited  proposi- 
tions of,  660. 
methods  of,  661. 
experiment  in,  663. 
causation  in,  664. 
method  of  agreement  in,  666. 
other  experimental  methods  in. 

566. 
deductive  method  in,  567. 
hypotheses  in,  569. 
simplifying  of,  670. 
fallacious  methods  in,  672. 
Practical,  End  in,  573. 
based  on  Theoretical  Politics, 

674. 
origin  of  political  devices  in. 
675. 
Porphyry's  tree,  716. 
Positive  names,  55. 
Po9t  hoc  ergo  propter  hoc,  675. 
Postulate,  the  universal,  664. 
Potential  energy,  259. 

an  aspect  of  Collocation,  264. 
Practice,  logic  of,  545. 

maxims  of,  in  Politics,  576. 
Predesignate,  717. 
Predicables,  73. 
Predication,  verbal,  76. 
confounded  with  real,  68. 
in  plural  notions,  69. 
in  Natural  Kinds,  69. 
verbal  not  tautological,  70. 
final  analysis  of,  660. 
Predicates,  three  universal,  102. 

Mr.  Mill's  scheme  of,  106. 
Premises,  135. 

Prerogative  Instances  of  Bacon,  688. 
Presentative  and  Representative,  7, 

640. 
Primary  qualities  of  matter,  667. 
Probable  Inference,  explained,  865. 
may  be  estimated,  366. 
how  made  more  precise,  868. 
Probability,  320. 
explained,  821. 
principle  of,  321. 
rules  of,  322. 
applied  to  Causation,  324. 

an    approximate    generalization, 
866. 

comparison  of,  381. 

in  Biology,  601. 


%i> 


INDEX. 


729 


Probability,  in  Psychology,  616. 

ambiguity  of  the  word,  618. 
Progress  and  Order,  555,  670. 
Proof  or  Evidence,  the  scope  of  Logic, 

34,  279. 
Proposition,  a,  contains  two  names, 
and  two  notions,  274,  292. 

verbal,  67. 
Propositions,  78. 
Proprium,  74. 

exemplified  in  Mathematics,  432. 
Psychology,  scope  of,  505. 

subordinate  notions  of,  607. 

propositions  of,  609. 

logical  methods  of,  611. 

empirical  and  derivative  laws  in, 
614. 

hypotheses  in,  616. 

chance  and  probability  in,  616. 

suggesting  arts  of  Discovery,  699. 

a  Concrete  Science  ?  636. 

Quality,  of  Propositions,  Affirma- 
^  five  or  Negative,  83. 
an  ineradicable  distinction,  88. 
designations  of,  84. 
Quantification  of  Predicate,  86. 
makes  two  propositions  in  one, 
88.. 

additions  to  syllogism,  basis  of, 
178. 
Quantity,  of  Propositions,  Total  or 
Partial,  81. 
Universal  and  Particular,  inapt 

names,  82. 
Indefinite,  82. 
one  of  the  three  universal  Predi- 
cates, 333. 
common  to  Object  and  Subject  ex- 
perience, 655. 
subject-matter    of    Mathematics, 

429. 
designations  of,  81. 
sciences  of.  Deductive,  103. 
uniformities  of,  as   a  branch  of 
Logic,  239. 

Ratiocination,  fallacies  of,  601. 
Realism,  6. 

faUacy  of,  619. 
Reasoning,  used  in  defining  Logic, 
30. 


Reasoning,  founded  on  Similarity,  8, 
370. 

from    particulars  to    particulars, 

209. 
chain  of,  reducible  to  a  series  of 

syllogisms,  216. 
causes  of*  complicated,  217. 
formal,  641. 
Heduciio  ad  impossibile^  141. 
Reduction,  147. 
Relativity,  law  of,  2. 
Names  classed  according  to,  54. 
universal,  61. 
aa  affecting  Notions,  66. 
as  classifying  Propositions,  78. 
as  a  basis  of  Definition,  885. 
basis  of  an  enumeration  of  things, 

485. 
fallacies  of,  621. 

of  Proposition  follows  Notion,  79. 
Relative  terms,  for  special  relation- 
ships, 60. 
names,  65. 
Representative  Fictions,  362. 

in  Medicine,  694. 
Residues,  Method  of,  279,  296. 
in  Politics,  669. 
an  aid  to  Discovery,  702. 
Resistance,  657. 

Sanguine    Temperament,  a   source 

offaUacy,  611. 
Science,  the  perfect  form  of  Knowl- 
edge, 23. 
characteristics  of,  23. 
problem    of,    as    conceived    by 
Whewell,  696. 
Sciences,  classified,  26. 
Abstract  and  Concrete,  26. 
Abstract,  25. 
Concrete,  28. 
Practical,  28. 

defined,  646. 
Classification  of,  Bacon,  627. 
D'Alembert,  628. 
Ei«)yclopedia       Metropolitana, 

628. 
Neill  Amott,  629. 
Comte,  629. 
Herbert  Spencer,  630. 
criticism  of  Spencer's  scheme, 
634. 


j 


730 


INDEX. 


'^1. 


Secondary  qualities  of  matter,  66 

Laws,  importance  of,  332. 
Self-interest,  a  source  of  fallacy,  620. 
Series,  Classification  by,  295. 
Serial  order,  in  classification,  417. 
Similarity,  law  of,  3. 

the  foundation  of  Reasonijicr.  8. 
370.  *"     ' 

basis  of  scientific  explanation,  346. 
extension  of  names  through.  402, 
406.  ^  ' 

Singular  Name  explained,  48. 

Propositions,  syllogism  of,  169. 
Smelling,  due  to  oxidation,  indue- 

tively  proved,  297. 
Society,  notion  of,  547. 

structure  of,  550. 
Solid  defined  by  positive  method. 
390.  ' 

by  negative  method,  393. 
Sophhma  Jleterozeteseos^  717. 
Figrum^  715. 
Folyzeteseoa,  716. 
Sorites,  or  heap,  390,  717. 
Space,  an  abstraction,  11. 

characterized,  667. 
Species,  a  predicable,  73. 
Species,  importance  of  in  classifica- 
tion, 420. 
tn/ma,  421. 
in  Mineralogy,  628. 
in  Botany,  636. 
in  Zoology,  642. 
Statistics,  Political,  649,  662. 

Medical,  592. 
Structure  of  Living  Bodies,  490. 
and  Function  viewed  separately. 
463. 
Subject,  explained,  665. 

attributes  special  to,  669. 
Subject-Object,  highest  real  couple, 
59. 
greatest  of  all  antithesis,  663. 
attributes,  common  to,  656. 
Substance,  a  supposed  intuition,  11. 

fundamental  attribute,  660. 
Succession,  one  of  the  three  Uni- 
versal Predicates,  106. 
as  Order  in  Time,  105. 
as  Cause  and  Effect,  the  chief 
part  of  Induction,  106. 
SuflScient  Reason,  600,  717. 


Sumption  and  Suhsumption,  146. 
Syllogism,  defined,  133. 
exaniples  of,  166. 
additions  to,  by  Hamilton,  178. 
by  De  Morgan,  182. 
by  Boole,  190. 
Numerically  Definite,  188. 
functions  and  value  of,  207. 
how  far  a  material  process,  211. 
axiom  of,  reposes  on  experience, 

226. 

an  aid  to  Discovery,  703.  x 
of  the  Will,  meaningless,  876. 
Sympathy,  a  source  of  fallacies,  610. 
Symbolical— Intuitive,  716. 
Symbols,  of  Propositions,  86. 
Synonymous  Propositions,  123. 
Synonyms,  definition  by,  396. 
as  an  aid  to  Discovery,  701. 
Synthesis,  Chemical,  681. 
Logical,  683. 

does  not  apply  to  Simple  Deduc- 
tion, 684. 
Grammatical,  684. 
Mathematical,  686. 
Synthetic  judgment,  76. 

Tabulation,  as  an  Index  Classifica- 
tion,  530,  597. 
as  an  aid  to  Discovery,  704. 
Tabular  arrangement,  Bacon's,  687. 
Terminology,  descriptive,  407. 
Terms,  of  syllogism,  364. 
Therapeutics,  general,  580. 
Things,  enumeration  of,  662. 

Mr.  Mill's  enumeration  of,  661. 
Thought,  Laws  of,  16,  641. 
definition  of  Logic,  30. 
too  limited  to  make  a  Universal 
Postulate,  664. 
Time,  an  abstraction,  240. 
Tradition,  oral,  value  of,  718. 

approaching  to  written  evidence. 
715. 

Truths,  known  tmmecliateti/,  82. 
known  by  the  mediaiion  of  other 
truths,  82. 

Ultimate  Laws  op  Natube,  limited 

in  number,  853. 
Uniformity  of  Nature^  supposed  in 
Deduction,  19. 


INDEX 


731 


Uniformity  of  Nature,   enters  into 
Theoretical  Logic,  645. 
the  ultimate  major  premise  of  all 

Induction,  671. 
a  plurality  not  a  unity,  238. 
axiom  of,  fundamental,  227. 
Uniformities  among  effects  of  same 
cause,  836. 
limited  in  application,  341,  342. 
of  remote  causal  connection,  334. 
Universe,  of  a  term,  66. 

Vanity,  a  source  of  fallacies,  603. 
Variation  of  circumstances,  273. 
Verification,  330. 


Verification,  in  Politics,  667. 
VertB  Cau8(B,  359. 

Whkwell,  contributions  to  Induc- 
tion, 695. 
Wonder,  a  source  of  fallacy,  612. 

Zoology,  difficulties  of,  538. 

arrangement    of    characters    in, 

538. 
laws  of  Concomitance  in,  539. 
maximum  of  affinity  in,  540, 
grades  in,  642. 

agreement  and  difference  in,  648. 
index  in,  544. 


TUB    END. 


D.  APPLE  TON  d  CO/8  PUBLICATIONS. 


ALEXANDER    BAIN'S    WORKS. 
THE    SENSES    AND    THE    INTELLECT.      By  Alkxavder 
^v^'  Cloth,"  $r^*''''^'  ""^  ^^"^  '''  ^^^  University  of  Aberdeen. 

The  object  of  this  treatise  is  to  give  a  full  and  PvstpmAtir  «/./.»»«*  «*■  * 
principal  divisions  of  the  Bcience  of  mind-?he*°n8e7aS^t^^^^ 

rnfIte.PJ?*' j'  puWIoitloii  Is  a  seqnel  to  the  former  one  on  "  The  Senses  and  tl.a 
Intellect,"  and  completes  a  systematic  exposition  of  the  human  mlS  * 

"*2.I-*„?'p??™'S*^*'V  4  Compendium  of  Psychology  and  the  His- 
rXf »  n°Py-  "^'S"^  as  a  Text-book  for  Iligh^hools  and 
ba"k?ri'.80^       Aleiakdeb  Bain,  LL.D.      12mo.     Cloth,  leather 

pressed  and  luc.d  form  thl'itewS'Sh'  ."rSlh^^  S  ex't^ifv^rSLlSa't^"- 
HAW,  LL.  D.     12mo.     Cloth,  leather  back,  $1.60 

^'^mrv^^'^n"??^-     ^^^^""«  ^f  **^^^^  Relations.     By  Alexander 
Bain,  LL.  D.     12mo.     Cloth,  $1.60.  ^»-^i'*» 

therrU'iufiLVrwoXi^bV^^^  liX^?Sf«  ^*T"""  mind  a„d  body,  studying 
gationB."-CArw<ia»^S^rf         ^  """^^  '^®*'*  physiological  inveatl- 


LOGICy   DEDUCTIVE    AND 

Bain,  LL.  D.     Revised  edition. 


INDUCTIVE.    By  Alexandee 
12mo.     Cloth,  leather  back,  |2.00. 

^"Y2*m*"gV,t7t   ""^''^^-     «^  ^"^-^  B-.  "^I>- 

**^dWof  V?J^^T}T^^^  *^^  RHETORIC.  Enlarged 
Ba  N  V  D  i  '".^"«««"»i  E'-'-^"''  of  style.  By  AiexanSer 
A  K^  ;•„  *^™«"'"8  Professor  of  Logic  in  the  Uniyersitv  of 

Aberdeen.     12nio.     Cloth,  leather  back,  $1.50.  ^'"™""y  "^ 

^^  ll^^i^l^^  T.^J'^^^^Yk    ^"^  »«»»»«'  Examples  and  an 

*""  ClotMUO.   *®*^^»-      By  ALEXA«.En  Baik,   LL.  D.     12ma 
KewTork!  D.  APPLETON  &  CO.,  1,  8,  4  6  Bond  Street 


^f*-.. 


|| 


m 


D,  APPLETON  d   00/S  PUBLIOATIONS. 


APPLETONS»  PHYSICAL  GEOGRAPHY.  Illustrated  wiih 
engravings,  diagrams  and  maps  in  color,  and  including  a  separate 
chapter  on  the  geological  history  and  the  physical  featu-.-ea  of  the 
United  States.  By  John  D.  Quackenbos,  A.  M.,  M.  D.,  Adjunct 
Pfofessor  of  the  English  Language  and  Literature,  Columbia  College, 
New  York,  Literary  Editor ;  John  S.  Newbebrt,  M.  D.,  LL.  D., 
Professor  of  Geology  and  Paleontology,  Columbia  College ;  Charles 
H.  Hitchcock,  Ph.  D.,  Professor  of  Geology  and  Mineralogy,  Dart- 
mouth College;  W.  Le  Conte  Stevens,  Ph.  D.,  Professor  of  Physics, 
Packer  Collegiate  Institute ;  Henry  Gannett,  E.  M.,  Chief  Geog- 
rapher of  the  United  States  Geological  Survey ;  William  H.  Ball, 
of  the  United  States  National  Museum ;  C.  Hart  Merriam,  M.  D., 
Ornithologist  of  the  Department  of  Agriculture;  Nathaniel  L.  Brit- 
ton,  E.  M.,  Ph.  D.,  Lecturer  in  Botany,  Columbia  College ;  George 
F.  KuNZ,  Gem  Expert  and  Mineralogist  with  Messrs.  Tiflfany  &  Co., 
New  York;  Lieutenant  George  M.  Stoney,  Naval  Department, 
Washington.     Large  4to.     Cloth,  $1.90. 

APPLETONS*    ATLAS     OF    THE     UNITED     STATES. 

Consisting  of  General  Maps  of  the  United  States  and  Territories, 
and  a  County  Map  of  each  of  the  States,  all  printed  in  Colors, 
together  with  Railway  Maps  and  Descriptive  Text  Outlining  the 
History,  Geography,  and  Political  and  Educational  Organization  of 
the  States,  with  latest  Statistics  of  their  Resources  and  Industries. 
Imperial  8vo,  cloth.     $1.60. 

THE     EARTH     AND    ITS     INHABITANTS.      By  Elisee 
Reclus.      Translated  and  edited  by  E.  G.  Ravenstein.     With  nu- 
merous Illustrations,  Maps,  and  Charts. 
M.  Reclus  the  distinguished  French  Geographer  has  given  in  this  work 

the  most  thorough  and  comprehensive  treatise  on  the  countries  of  the 

world  yet  produced.     Maps,  plans,  and  illustrations  are  lavish.     It  is 

subdivided  as  follows : 

Europe,  in  6  volumes.    Imperial  8vo. 
Asia,  in  4  volumes.    Imperial  8vo. 
Africa,  in  8  volumes.     Imperial  Svo. 
America.     (In  preparation.) 

Price,  $6.00  per  volume  in  library  binding.     Sold  only  by  subscrip- 
tion. 

A  NEW  PHYSICAL  GEOGRAPHY.  By  Elisee  Reclus. 
In  two  volumes.  Vol.  I.  The  Earth.  Vol.  II.  The  Ocean,  Atmos- 
phere, and  Life.  With  Maps  and  Illustrations.  Price,  $6.00  per 
volume,  library  binding.     Sold  only  by  subscription. 


New  York:  D.  APPLETON  &  CO.,  1,  3,  &   5  Bond  Street 


./ 


J  U  IV    «   ;    jy^Q 


I 


)  1 


t.i 


I 


JUL  7    1920 


'i^] 


wrwm 


COLUMBIA   UNIVERSITY   LIBRARIES 

This  book  is  due  on  the  date  indicated  below,  or  at  the 
^A     expiration  of  a  definite  period  after  the  date  of  borrowing,  as 

provided  by  the  library  rules  or  by  special  arrangement  with       j^ 
the  Librarian  in  charge.  ^ 


■'    m: 


¥■■■  'l  :*  •■'! 


^1 1 


cess  003-7 


